LMFDB - Embedded newform 108.5.g.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(17,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("108.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 $ x^8 - 3x^7 + 6x^6 + 121x^5 + 1104x^4 - 1647x^3 + 6529x^2 + 85254*x + 440076
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$-3.05006 + 3.25531i$ of defining polynomial
Character	$\chi$	$=$	108.89
Dual form			108.5.g.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +O(q^{10})$	$q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +(123.267 + 71.1682i) q^{11} +(96.3079 + 166.810i) q^{13} +325.855i q^{17} +314.164 q^{19} +(443.852 - 256.258i) q^{23} +(188.564 - 326.602i) q^{25} +(136.614 + 78.8739i) q^{29} +(183.725 + 318.221i) q^{31} +2385.82i q^{35} +1737.04 q^{37} +(342.317 - 197.637i) q^{41} +(-360.381 + 624.198i) q^{43} +(-2153.71 - 1243.45i) q^{47} +(-1639.52 - 2839.72i) q^{49} -3986.04i q^{53} -4505.86 q^{55} +(2136.75 - 1233.65i) q^{59} +(-1240.49 + 2148.59i) q^{61} +(-5280.61 - 3048.76i) q^{65} +(3298.19 + 5712.64i) q^{67} +5828.07i q^{71} -8790.44 q^{73} +(9290.13 - 5363.66i) q^{77} +(1934.52 - 3350.69i) q^{79} +(-10422.5 - 6017.43i) q^{83} +(-5157.70 - 8933.39i) q^{85} +7637.03i q^{89} +14516.7 q^{91} +(-8612.88 + 4972.65i) q^{95} +(1455.75 - 2521.44i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) $ 8 * q + 9 * q^5 + 13 * q^7	$ 8 q + 9 q^{5} + 13 q^{7} + 18 q^{11} - 5 q^{13} + 562 q^{19} + 1719 q^{23} + 353 q^{25} - 2115 q^{29} + 187 q^{31} + 16 q^{37} + 7920 q^{41} - 68 q^{43} - 13689 q^{47} - 327 q^{49} - 1818 q^{55} + 20052 q^{59} - 1937 q^{61} - 25965 q^{65} + 154 q^{67} - 7802 q^{73} + 25641 q^{77} - 2195 q^{79} - 37017 q^{83} - 3042 q^{85} + 15830 q^{91} + 37116 q^{95} + 7282 q^{97}+O(q^{100}) $ 8 * q + 9 * q^5 + 13 * q^7 + 18 * q^11 - 5 * q^13 + 562 * q^19 + 1719 * q^23 + 353 * q^25 - 2115 * q^29 + 187 * q^31 + 16 * q^37 + 7920 * q^41 - 68 * q^43 - 13689 * q^47 - 327 * q^49 - 1818 * q^55 + 20052 * q^59 - 1937 * q^61 - 25965 * q^65 + 154 * q^67 - 7802 * q^73 + 25641 * q^77 - 2195 * q^79 - 37017 * q^83 - 3042 * q^85 + 15830 * q^91 + 37116 * q^95 + 7282 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−27.4152	+	15.8282i	−1.09661	+	0.633128i	−0.935329	−	0.353780i	$-0.884896\pi$
$5$	−27.4152	+	15.8282i	−1.09661	+	0.633128i	−0.161281	+	0.986908i	$0.551563\pi$
$6$		0			0
$7$	37.6830	−	65.2688i	0.769041	−	1.33202i	−0.169043	−	0.985609i	$-0.554068\pi$
$7$	37.6830	−	65.2688i	0.769041	−	1.33202i	0.938084	−	0.346409i	$-0.112599\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	123.267	+	71.1682i	1.01873	+	0.588167i	0.913737	−	0.406306i	$-0.133183\pi$
$11$	123.267	+	71.1682i	1.01873	+	0.588167i	0.104997	+	0.994473i	$0.466517\pi$
$12$		0			0
$13$	96.3079	+	166.810i	0.569870	+	0.987043i	0.996578	+	0.0826539i	$0.0263396\pi$
$13$	96.3079	+	166.810i	0.569870	+	0.987043i	−0.426709	+	0.904389i	$0.640327\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			325.855i			1.12753i	0.825937	+	0.563763i	$0.190647\pi$
$17$			325.855i			1.12753i	−0.825937	+	0.563763i	$0.809353\pi$
$18$		0			0
$19$	314.164			0.870260			0.435130	−	0.900368i	$-0.356702\pi$
$19$	314.164			0.870260			0.435130	+	0.900368i	$0.356702\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	443.852	−	256.258i	0.839040	−	0.484420i	−0.0178977	−	0.999840i	$-0.505697\pi$
$23$	443.852	−	256.258i	0.839040	−	0.484420i	0.856938	+	0.515420i	$0.172364\pi$
$24$		0			0
$25$	188.564	−	326.602i	0.301702	−	0.522564i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	136.614	+	78.8739i	0.162442	+	0.0937859i	0.579017	−	0.815315i	$-0.303436\pi$
$29$	136.614	+	78.8739i	0.162442	+	0.0937859i	−0.416575	+	0.909101i	$0.636770\pi$
$30$		0			0
$31$	183.725	+	318.221i	0.191181	+	0.331135i	0.945642	−	0.325210i	$-0.105435\pi$
$31$	183.725	+	318.221i	0.191181	+	0.331135i	−0.754461	+	0.656345i	$0.772102\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			2385.82i			1.94760i
$36$		0			0
$37$	1737.04			1.26884			0.634419	−	0.772989i	$-0.281239\pi$
$37$	1737.04			1.26884			0.634419	+	0.772989i	$0.281239\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	342.317	−	197.637i	0.203639	−	0.117571i	−0.394713	−	0.918805i	$-0.629156\pi$
$41$	342.317	−	197.637i	0.203639	−	0.117571i	0.598352	+	0.801234i	$0.295823\pi$
$42$		0			0
$43$	−360.381	+	624.198i	−0.194906	+	0.337587i	−0.946870	−	0.321618i	$-0.895773\pi$
$43$	−360.381	+	624.198i	−0.194906	+	0.337587i	0.751964	+	0.659204i	$0.229107\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2153.71	−	1243.45i	−0.974971	−	0.562900i	−0.0742227	−	0.997242i	$-0.523648\pi$
$47$	−2153.71	−	1243.45i	−0.974971	−	0.562900i	−0.900748	+	0.434342i	$0.856981\pi$
$48$		0			0
$49$	−1639.52	−	2839.72i	−0.682847	−	1.18273i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	3986.04i		−	1.41902i	−0.704694	−	0.709512i	$-0.748916\pi$
$53$		−	3986.04i		−	1.41902i	0.704694	−	0.709512i	$-0.251084\pi$
$54$		0			0
$55$	−4505.86			−1.48954
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2136.75	−	1233.65i	0.613831	−	0.354396i	−0.160632	−	0.987014i	$-0.551353\pi$
$59$	2136.75	−	1233.65i	0.613831	−	0.354396i	0.774463	+	0.632619i	$0.218020\pi$
$60$		0			0
$61$	−1240.49	+	2148.59i	−0.333375	+	0.577422i	−0.983171	−	0.182686i	$-0.941521\pi$
$61$	−1240.49	+	2148.59i	−0.333375	+	0.577422i	0.649796	+	0.760108i	$0.274854\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5280.61	−	3048.76i	−1.24985	−	0.721601i
$66$		0			0
$67$	3298.19	+	5712.64i	0.734728	+	1.27259i	0.954843	+	0.297112i	$0.0960233\pi$
$67$	3298.19	+	5712.64i	0.734728	+	1.27259i	−0.220115	+	0.975474i	$0.570643\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5828.07i			1.15613i	0.815990	+	0.578066i	$0.196193\pi$
$71$			5828.07i			1.15613i	−0.815990	+	0.578066i	$0.803807\pi$
$72$		0			0
$73$	−8790.44			−1.64955			−0.824774	−	0.565463i	$-0.808697\pi$
$73$	−8790.44			−1.64955			−0.824774	+	0.565463i	$0.808697\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9290.13	−	5363.66i	1.56690	−	0.904648i
$78$		0			0
$79$	1934.52	−	3350.69i	0.309970	−	0.536883i	−0.668386	−	0.743815i	$-0.733014\pi$
$79$	1934.52	−	3350.69i	0.309970	−	0.536883i	0.978355	+	0.206932i	$0.0663478\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10422.5	−	6017.43i	−1.51292	−	0.873483i	−0.999886	−	0.0151136i	$-0.995189\pi$
$83$	−10422.5	−	6017.43i	−1.51292	−	0.873483i	−0.513032	−	0.858370i	$-0.671478\pi$
$84$		0			0
$85$	−5157.70	−	8933.39i	−0.713868	−	1.23646i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			7637.03i			0.964150i	0.876130	+	0.482075i	$0.160117\pi$
$89$			7637.03i			0.964150i	−0.876130	+	0.482075i	$0.839883\pi$
$90$		0			0
$91$	14516.7			1.75301
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8612.88	+	4972.65i	−0.954336	+	0.550986i
$96$		0			0
$97$	1455.75	−	2521.44i	0.154719	−	0.267981i	−0.778238	−	0.627970i	$-0.783886\pi$
$97$	1455.75	−	2521.44i	0.154719	−	0.267981i	0.932957	+	0.359989i	$0.117219\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9442.90	+	5451.86i	0.925683	+	0.534444i	0.885444	−	0.464746i	$-0.153855\pi$
$101$	9442.90	+	5451.86i	0.925683	+	0.534444i	0.0402396	+	0.999190i	$0.487188\pi$
$102$		0			0
$103$	3638.56	+	6302.16i	0.342969	+	0.594039i	0.984983	−	0.172654i	$-0.0552341\pi$
$103$	3638.56	+	6302.16i	0.342969	+	0.594039i	−0.642014	+	0.766693i	$0.721901\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5525.48i			0.482617i	0.970449	+	0.241308i	$0.0775765\pi$
$107$			5525.48i			0.482617i	−0.970449	+	0.241308i	$0.922424\pi$
$108$		0			0
$109$	7186.35			0.604861			0.302431	−	0.953171i	$-0.402202\pi$
$109$	7186.35			0.604861			0.302431	+	0.953171i	$0.402202\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10742.0	−	6201.93i	0.841260	−	0.485702i	−0.0164323	−	0.999865i	$-0.505231\pi$
$113$	10742.0	−	6201.93i	0.841260	−	0.485702i	0.857692	+	0.514163i	$0.171897\pi$
$114$		0			0
$115$	−8112.21	+	14050.8i	−0.613400	+	1.06244i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	21268.2	+	12279.2i	1.50188	+	0.867113i
$120$		0			0
$121$	2809.31	+	4865.88i	0.191880	+	0.332346i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	7846.74i		−	0.502191i
$126$		0			0
$127$	9013.28			0.558824			0.279412	−	0.960171i	$-0.409860\pi$
$127$	9013.28			0.558824			0.279412	+	0.960171i	$0.409860\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−309.401	+	178.633i	−0.0180293	+	0.0104092i	−0.508988	−	0.860774i	$-0.669980\pi$
$131$	−309.401	+	178.633i	−0.0180293	+	0.0104092i	0.490958	+	0.871183i	$0.336647\pi$
$132$		0			0
$133$	11838.6	−	20505.1i	0.669265	−	1.15920i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12811.2	−	7396.54i	−0.682571	−	0.394083i	0.118252	−	0.992984i	$-0.462271\pi$
$137$	−12811.2	−	7396.54i	−0.682571	−	0.394083i	−0.800823	+	0.598901i	$0.795604\pi$
$138$		0			0
$139$	−1079.62	−	1869.95i	−0.0558779	−	0.0967834i	0.836733	−	0.547611i	$-0.184462\pi$
$139$	−1079.62	−	1869.95i	−0.0558779	−	0.0967834i	−0.892611	+	0.450827i	$0.851129\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			27416.2i			1.34071i
$144$		0			0
$145$	−4993.73			−0.237514
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−24982.1	+	14423.4i	−1.12527	+	0.649675i	−0.942741	−	0.333526i	$-0.891762\pi$
$149$	−24982.1	+	14423.4i	−1.12527	+	0.649675i	−0.182529	+	0.983201i	$0.558428\pi$
$150$		0			0
$151$	4752.65	−	8231.82i	0.208440	−	0.361029i	−0.742783	−	0.669532i	$-0.766495\pi$
$151$	4752.65	−	8231.82i	0.208440	−	0.361029i	0.951223	+	0.308503i	$0.0998280\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10073.7	−	5816.07i	−0.419302	−	0.242084i
$156$		0			0
$157$	4937.68	+	8552.31i	0.200320	+	0.346964i	0.948631	−	0.316383i	$-0.102469\pi$
$157$	4937.68	+	8552.31i	0.200320	+	0.346964i	−0.748312	+	0.663347i	$0.769135\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	38626.3i		−	1.49015i
$162$		0			0
$163$	−22464.8			−0.845525			−0.422763	−	0.906240i	$-0.638940\pi$
$163$	−22464.8			−0.845525			−0.422763	+	0.906240i	$0.638940\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14694.7	−	8484.01i	0.526901	−	0.304206i	−0.212853	−	0.977084i	$-0.568275\pi$
$167$	14694.7	−	8484.01i	0.526901	−	0.304206i	0.739753	+	0.672878i	$0.234942\pi$
$168$		0			0
$169$	−4269.94	+	7395.76i	−0.149503	+	0.258946i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	32441.8	+	18730.3i	1.08396	+	0.625825i	0.931962	−	0.362556i	$-0.118096\pi$
$173$	32441.8	+	18730.3i	1.08396	+	0.625825i	0.151998	+	0.988381i	$0.451429\pi$
$174$		0			0
$175$	−14211.3	−	24614.7i	−0.464043	−	0.803745i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	44760.9i		−	1.39699i	−0.715615	−	0.698495i	$-0.753853\pi$
$179$		−	44760.9i		−	1.39699i	0.715615	−	0.698495i	$-0.246147\pi$
$180$		0			0
$181$	−29208.0			−0.891548			−0.445774	−	0.895146i	$-0.647071\pi$
$181$	−29208.0			−0.891548			−0.445774	+	0.895146i	$0.647071\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−47621.4	+	27494.2i	−1.39142	+	0.803337i
$186$		0			0
$187$	−23190.5	+	40167.1i	−0.663173	+	1.14865i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−25988.4	−	15004.4i	−0.712383	−	0.411294i	0.0995598	−	0.995032i	$-0.468257\pi$
$191$	−25988.4	−	15004.4i	−0.712383	−	0.411294i	−0.811943	+	0.583737i	$0.801590\pi$
$192$		0			0
$193$	8615.87	+	14923.1i	0.231305	+	0.400632i	0.958192	−	0.286125i	$-0.0923672\pi$
$193$	8615.87	+	14923.1i	0.231305	+	0.400632i	−0.726888	+	0.686756i	$0.759034\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	67892.1i		−	1.74939i	−0.484673	−	0.874695i	$-0.661062\pi$
$197$		−	67892.1i		−	1.74939i	0.484673	−	0.874695i	$-0.338938\pi$
$198$		0			0
$199$	−26996.5			−0.681713			−0.340857	−	0.940115i	$-0.610717\pi$
$199$	−26996.5			−0.681713			−0.340857	+	0.940115i	$0.610717\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10296.0	−	5944.41i	0.249849	−	0.144250i
$204$		0			0
$205$	−6256.47	+	10836.5i	−0.148875	+	0.257859i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	38726.0	+	22358.5i	0.886564	+	0.511858i
$210$		0			0
$211$	−11819.5	−	20472.1i	−0.265482	−	0.459829i	0.702207	−	0.711972i	$-0.252198\pi$
$211$	−11819.5	−	20472.1i	−0.265482	−	0.459829i	−0.967690	+	0.252143i	$0.918865\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	22816.7i		−	0.493601i
$216$		0			0
$217$	27693.2			0.588103
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−54355.9	+	31382.4i	−1.11292	+	0.642543i
$222$		0			0
$223$	28978.0	−	50191.3i	0.582718	−	1.00930i	−0.412438	−	0.910986i	$-0.635323\pi$
$223$	28978.0	−	50191.3i	0.582718	−	1.00930i	0.995156	−	0.0983112i	$-0.0313441\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8712.47	−	5030.15i	−0.169079	−	0.0976178i	0.413073	−	0.910698i	$-0.364456\pi$
$227$	−8712.47	−	5030.15i	−0.169079	−	0.0976178i	−0.582151	+	0.813080i	$0.697789\pi$
$228$		0			0
$229$	−28899.8	−	50056.0i	−0.551093	−	0.954520i	−0.998196	−	0.0600381i	$-0.980878\pi$
$229$	−28899.8	−	50056.0i	−0.551093	−	0.954520i	0.447104	−	0.894482i	$-0.352456\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			68323.8i			1.25852i	0.777195	+	0.629260i	$0.216642\pi$
$233$			68323.8i			1.25852i	−0.777195	+	0.629260i	$0.783358\pi$
$234$		0			0
$235$	78726.0			1.42555
$236$		0			0
$237$		0			0
$238$		0			0
$239$	30122.2	−	17391.1i	0.527340	−	0.304460i	−0.212592	−	0.977141i	$-0.568191\pi$
$239$	30122.2	−	17391.1i	0.527340	−	0.304460i	0.739933	+	0.672681i	$0.234857\pi$
$240$		0			0
$241$	−45982.8	+	79644.5i	−0.791701	+	1.37127i	0.133213	+	0.991087i	$0.457471\pi$
$241$	−45982.8	+	79644.5i	−0.791701	+	1.37127i	−0.924913	+	0.380178i	$0.875863\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	89895.4	+	51901.2i	1.49763	+	0.864659i
$246$		0			0
$247$	30256.5	+	52405.7i	0.495935	+	0.858984i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			69806.6i			1.10802i	0.832509	+	0.554012i	$0.186904\pi$
$251$			69806.6i			1.10802i	−0.832509	+	0.554012i	$0.813096\pi$
$252$		0			0
$253$	72949.7			1.13968
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15210.4	+	8781.70i	−0.230289	+	0.132957i	−0.610705	−	0.791858i	$-0.709114\pi$
$257$	−15210.4	+	8781.70i	−0.230289	+	0.132957i	0.380416	+	0.924815i	$0.375781\pi$
$258$		0			0
$259$	65456.8	−	113375.i	0.975788	−	1.69011i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26492.4	−	15295.4i	−0.383009	−	0.221131i	0.296117	−	0.955152i	$-0.404308\pi$
$263$	−26492.4	−	15295.4i	−0.383009	−	0.221131i	−0.679127	+	0.734021i	$0.737641\pi$
$264$		0			0
$265$	63091.8	+	109278.i	0.898423	+	1.55611i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			59574.8i			0.823299i	0.911342	+	0.411650i	$0.135047\pi$
$269$			59574.8i			0.823299i	−0.911342	+	0.411650i	$0.864953\pi$
$270$		0			0
$271$	−94290.1			−1.28389			−0.641945	−	0.766751i	$-0.721872\pi$
$271$	−94290.1			−1.28389			−0.641945	+	0.766751i	$0.721872\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	46487.4	−	26839.5i	0.614709	−	0.354902i
$276$		0			0
$277$	49687.7	−	86061.7i	0.647574	−	1.12163i	−0.336126	−	0.941817i	$-0.609117\pi$
$277$	49687.7	−	86061.7i	0.647574	−	1.12163i	0.983700	−	0.179815i	$-0.0575499\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−68740.8	−	39687.5i	−0.870567	−	0.502622i	−0.00303013	−	0.999995i	$-0.500965\pi$
$281$	−68740.8	−	39687.5i	−0.870567	−	0.502622i	−0.867536	+	0.497374i	$0.834298\pi$
$282$		0			0
$283$	−33460.0	−	57954.4i	−0.417785	−	0.723625i	0.577931	−	0.816085i	$-0.303860\pi$
$283$	−33460.0	−	57954.4i	−0.417785	−	0.723625i	−0.995716	+	0.0924607i	$0.970527\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	29790.2i		−	0.361667i
$288$		0			0
$289$	−22660.4			−0.271314
$290$		0			0
$291$		0			0
$292$		0			0
$293$	48467.1	−	27982.5i	0.564562	−	0.325950i	−0.190413	−	0.981704i	$-0.560983\pi$
$293$	48467.1	−	27982.5i	0.564562	−	0.325950i	0.754974	+	0.655754i	$0.227649\pi$
$294$		0			0
$295$	−39053.0	+	67641.7i	−0.448756	+	0.777268i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	85493.0	+	49359.4i	0.956287	+	0.552112i
$300$		0			0
$301$	27160.4	+	47043.3i	0.299781	+	0.519236i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	78538.8i		−	0.844276i
$306$		0			0
$307$	8707.80			0.0923914			0.0461957	−	0.998932i	$-0.485290\pi$
$307$	8707.80			0.0923914			0.0461957	+	0.998932i	$0.485290\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	48339.3	−	27908.7i	0.499781	−	0.288549i	−0.228842	−	0.973464i	$-0.573494\pi$
$311$	48339.3	−	27908.7i	0.499781	−	0.288549i	0.728623	+	0.684915i	$0.240161\pi$
$312$		0			0
$313$	−29519.7	+	51129.6i	−0.301316	+	0.521895i	−0.976434	−	0.215815i	$-0.930759\pi$
$313$	−29519.7	+	51129.6i	−0.301316	+	0.521895i	0.675118	+	0.737710i	$0.264093\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	26277.2	+	15171.2i	0.261494	+	0.150973i	0.625016	−	0.780612i	$-0.285093\pi$
$317$	26277.2	+	15171.2i	0.261494	+	0.150973i	−0.363522	+	0.931586i	$0.618426\pi$
$318$		0			0
$319$	11226.6	+	19445.1i	0.110323	+	0.191086i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			102372.i			0.981240i
$324$		0			0
$325$	72640.8			0.687724
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−162316.	+	93713.5i	−1.49958	+	0.865785i
$330$		0			0
$331$	−63460.5	+	109917.i	−0.579225	+	1.00325i	0.416343	+	0.909207i	$0.363311\pi$
$331$	−63460.5	+	109917.i	−0.579225	+	1.00325i	−0.995568	+	0.0940397i	$0.970022\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−180842.	−	104409.i	−1.61142	−	0.930353i
$336$		0			0
$337$	−89198.2	−	154496.i	−0.785410	−	1.36037i	−0.928754	−	0.370697i	$-0.879119\pi$
$337$	−89198.2	−	154496.i	−0.785410	−	1.36037i	0.143344	−	0.989673i	$-0.454214\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			52301.4i			0.449785i
$342$		0			0
$343$	−66173.6			−0.562466
$344$		0			0
$345$		0			0
$346$		0			0
$347$	97741.3	−	56431.0i	0.811744	−	0.468661i	−0.0358168	−	0.999358i	$-0.511403\pi$
$347$	97741.3	−	56431.0i	0.811744	−	0.468661i	0.847561	+	0.530697i	$0.178070\pi$
$348$		0			0
$349$	36754.1	−	63660.0i	0.301756	−	0.522656i	−0.674778	−	0.738021i	$-0.735761\pi$
$349$	36754.1	−	63660.0i	0.301756	−	0.522656i	0.976534	+	0.215365i	$0.0690940\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−183043.	−	105680.i	−1.46894	−	0.848091i	−0.469544	−	0.882909i	$-0.655582\pi$
$353$	−183043.	−	105680.i	−1.46894	−	0.848091i	−0.999394	+	0.0348180i	$0.988915\pi$
$354$		0			0
$355$	−92247.8	−	159778.i	−0.731980	−	1.26783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	36755.1i		−	0.285186i	−0.989781	−	0.142593i	$-0.954456\pi$
$359$		−	36755.1i		−	0.285186i	0.989781	−	0.142593i	$-0.0455440\pi$
$360$		0			0
$361$	−31622.1			−0.242648
$362$		0			0
$363$		0			0
$364$		0			0
$365$	240992.	−	139137.i	1.80891	−	1.04437i
$366$		0			0
$367$	73577.0	−	127439.i	0.546273	−	0.946173i	−0.452252	−	0.891890i	$-0.649379\pi$
$367$	73577.0	−	127439.i	0.546273	−	0.946173i	0.998526	−	0.0542832i	$-0.0172874\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−260164.	−	150206.i	−1.89016	−	1.09129i
$372$		0			0
$373$	21799.0	+	37757.1i	0.156682	+	0.271382i	0.933670	−	0.358134i	$-0.116587\pi$
$373$	21799.0	+	37757.1i	0.156682	+	0.271382i	−0.776988	+	0.629515i	$0.783253\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			30384.7i			0.213783i
$378$		0			0
$379$	−169833.			−1.18234			−0.591170	−	0.806547i	$-0.701334\pi$
$379$	−169833.			−1.18234			−0.591170	+	0.806547i	$0.701334\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	106228.	−	61330.5i	0.724169	−	0.418099i	−0.0921163	−	0.995748i	$-0.529363\pi$
$383$	106228.	−	61330.5i	0.724169	−	0.418099i	0.816285	+	0.577649i	$0.196030\pi$
$384$		0			0
$385$	−169794.	+	294092.i	−1.14552	+	1.98409i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	50495.3	+	29153.5i	0.333696	+	0.192660i	0.657481	−	0.753471i	$-0.271622\pi$
$389$	50495.3	+	29153.5i	0.333696	+	0.192660i	−0.323785	+	0.946131i	$0.604955\pi$
$390$		0			0
$391$	83503.0	+	144631.i	0.546196	+	0.946039i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			122480.i			0.785002i
$396$		0			0
$397$	−134572.			−0.853834			−0.426917	−	0.904291i	$-0.640400\pi$
$397$	−134572.			−0.853834			−0.426917	+	0.904291i	$0.640400\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−185654.	+	107187.i	−1.15456	+	0.666584i	−0.949994	−	0.312269i	$-0.898911\pi$
$401$	−185654.	+	107187.i	−1.15456	+	0.666584i	−0.204563	+	0.978853i	$0.565577\pi$
$402$		0			0
$403$	−35388.3	+	61294.4i	−0.217896	+	0.377408i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	214119.	+	123622.i	1.29261	+	0.746288i
$408$		0			0
$409$	24369.5	+	42209.2i	0.145680	+	0.252325i	0.929626	−	0.368503i	$-0.120130\pi$
$409$	24369.5	+	42209.2i	0.145680	+	0.252325i	−0.783946	+	0.620828i	$0.786796\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	185951.i		−	1.09018i
$414$		0			0
$415$	380980.			2.21211
$416$		0			0
$417$		0			0
$418$		0			0
$419$	59650.3	−	34439.1i	0.339770	−	0.196166i	−0.320400	−	0.947282i	$-0.603817\pi$
$419$	59650.3	−	34439.1i	0.339770	−	0.196166i	0.660170	+	0.751116i	$0.270484\pi$
$420$		0			0
$421$	157677.	−	273105.i	0.889620	−	1.54087i	0.0492953	−	0.998784i	$-0.484302\pi$
$421$	157677.	−	273105.i	0.889620	−	1.54087i	0.840325	−	0.542083i	$-0.182364\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	106425.	+	61444.5i	0.589204	+	0.340177i
$426$		0			0
$427$	93490.6	+	161930.i	0.512758	+	0.888122i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			151597.i			0.816088i	0.912962	+	0.408044i	$0.133789\pi$
$431$			151597.i			0.816088i	−0.912962	+	0.408044i	$0.866211\pi$
$432$		0			0
$433$	−237835.			−1.26853			−0.634265	−	0.773116i	$-0.718697\pi$
$433$	−237835.			−1.26853			−0.634265	+	0.773116i	$0.718697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	139442.	−	80507.1i	0.730183	−	0.421571i
$438$		0			0
$439$	−32350.4	+	56032.6i	−0.167861	+	0.290745i	−0.937668	−	0.347533i	$-0.887019\pi$
$439$	−32350.4	+	56032.6i	−0.167861	+	0.290745i	0.769806	+	0.638278i	$0.220353\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4469.49	+	2580.46i	0.0227746	+	0.0131489i	0.511344	−	0.859376i	$-0.329148\pi$
$443$	4469.49	+	2580.46i	0.0227746	+	0.0131489i	−0.488569	+	0.872525i	$0.662481\pi$
$444$		0			0
$445$	−120880.	−	209371.i	−0.610430	−	1.05730i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	165679.i		−	0.821816i	−0.911677	−	0.410908i	$-0.865212\pi$
$449$		−	165679.i		−	0.821816i	0.911677	−	0.410908i	$-0.134788\pi$
$450$		0			0
$451$	56261.8			0.276605
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−397979.	+	229773.i	−1.92237	+	1.10988i
$456$		0			0
$457$	204489.	−	354185.i	0.979121	−	1.69589i	0.313519	−	0.949582i	$-0.398492\pi$
$457$	204489.	−	354185.i	0.979121	−	1.69589i	0.665603	−	0.746306i	$-0.268174\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	75485.9	+	43581.8i	0.355193	+	0.205071i	0.666970	−	0.745085i	$-0.267591\pi$
$461$	75485.9	+	43581.8i	0.355193	+	0.205071i	−0.311777	+	0.950155i	$0.600924\pi$
$462$		0			0
$463$	−8403.24	−	14554.8i	−0.0391999	−	0.0678962i	0.845760	−	0.533564i	$-0.179148\pi$
$463$	−8403.24	−	14554.8i	−0.0391999	−	0.0678962i	−0.884960	+	0.465668i	$0.845814\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			394500.i			1.80889i	0.426585	+	0.904447i	$0.359716\pi$
$467$			394500.i			1.80889i	−0.426585	+	0.904447i	$0.640284\pi$
$468$		0			0
$469$	497143.			2.26014
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−88846.0	+	51295.3i	−0.397114	+	0.229274i
$474$		0			0
$475$	59240.0	−	102607.i	0.262559	−	0.454766i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	90406.6	+	52196.3i	0.394030	+	0.227493i	0.683905	−	0.729571i	$-0.260280\pi$
$479$	90406.6	+	52196.3i	0.394030	+	0.227493i	−0.289875	+	0.957065i	$0.593614\pi$
$480$		0			0
$481$	167291.	+	289756.i	0.723072	+	1.25240i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			92167.7i			0.391828i
$486$		0			0
$487$	106236.			0.447936			0.223968	−	0.974597i	$-0.428099\pi$
$487$	106236.			0.447936			0.223968	+	0.974597i	$0.428099\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−78832.6	+	45514.0i	−0.326997	+	0.188792i	−0.654507	−	0.756056i	$-0.727124\pi$
$491$	−78832.6	+	45514.0i	−0.326997	+	0.188792i	0.327510	+	0.944848i	$0.393790\pi$
$492$		0			0
$493$	−25701.5	+	44516.2i	−0.105746	+	0.183157i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	380391.	+	219619.i	1.53999	+	0.889113i
$498$		0			0
$499$	69176.0	+	119816.i	0.277814	+	0.481188i	0.970841	−	0.239723i	$-0.0770567\pi$
$499$	69176.0	+	119816.i	0.277814	+	0.481188i	−0.693027	+	0.720912i	$0.743723\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	63792.4i		−	0.252135i	−0.992022	−	0.126067i	$-0.959764\pi$
$503$		−	63792.4i		−	0.252135i	0.992022	−	0.126067i	$-0.0402356\pi$
$504$		0			0
$505$	−345172.			−1.35348
$506$		0			0
$507$		0			0
$508$		0			0
$509$	423634.	−	244585.i	1.63514	−	0.944049i	0.652668	−	0.757644i	$-0.273650\pi$
$509$	423634.	−	244585.i	1.63514	−	0.944049i	0.982473	−	0.186405i	$-0.0596838\pi$
$510$		0			0
$511$	−331250.	+	573742.i	−1.26857	+	2.19723i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−199504.	−	115184.i	−0.752206	−	0.434286i
$516$		0			0
$517$	−176987.	−	306551.i	−0.662158	−	1.14689i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	339386.i		−	1.25031i	−0.780500	−	0.625156i	$-0.785035\pi$
$521$		−	339386.i		−	1.25031i	0.780500	−	0.625156i	$-0.214965\pi$
$522$		0			0
$523$	379243.			1.38648			0.693242	−	0.720705i	$-0.256182\pi$
$523$	379243.			1.38648			0.693242	+	0.720705i	$0.256182\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−103694.	+	59867.6i	−0.373363	+	0.215561i
$528$		0			0
$529$	−8583.94	+	14867.8i	−0.0306744	+	0.0531295i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	65935.7	+	38068.0i	0.232095	+	0.134000i
$534$		0			0
$535$	−87458.4	−	151482.i	−0.305558	−	0.529242i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	466725.i		−	1.60651i
$540$		0			0
$541$	−494913.			−1.69096			−0.845481	−	0.534005i	$-0.820686\pi$
$541$	−494913.			−1.69096			−0.845481	+	0.534005i	$0.820686\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−197016.	+	113747.i	−0.663297	+	0.382955i
$546$		0			0
$547$	93045.4	−	161159.i	0.310971	−	0.538618i	−0.667602	−	0.744519i	$-0.732679\pi$
$547$	93045.4	−	161159.i	0.310971	−	0.538618i	0.978573	+	0.205901i	$0.0660124\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	42919.1	+	24779.3i	0.141367	+	0.0816181i
$552$		0			0
$553$	−145797.	−	252528.i	−0.476759	−	0.825770i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	119662.i		−	0.385698i	−0.981228	−	0.192849i	$-0.938227\pi$
$557$		−	119662.i		−	0.385698i	0.981228	−	0.192849i	$-0.0617728\pi$
$558$		0			0
$559$	−138830.			−0.444283
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22885.5	+	13213.0i	−0.0722012	+	0.0416854i	−0.535666	−	0.844430i	$-0.679939\pi$
$563$	−22885.5	+	13213.0i	−0.0722012	+	0.0416854i	0.463465	+	0.886115i	$0.346606\pi$
$564$		0			0
$565$	−196331.	+	340055.i	−0.615023	+	1.06525i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−453562.	−	261864.i	−1.40092	−	0.808820i	−0.406430	−	0.913682i	$-0.633226\pi$
$569$	−453562.	−	261864.i	−1.40092	−	0.808820i	−0.994487	+	0.104862i	$0.966560\pi$
$570$		0			0
$571$	161586.	+	279875.i	0.495600	+	0.858405i	0.999987	−	0.00507280i	$-0.00161473\pi$
$571$	161586.	+	279875.i	0.495600	+	0.858405i	−0.504387	+	0.863478i	$0.668281\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	193284.i		−	0.584603i
$576$		0			0
$577$	350692.			1.05335			0.526676	−	0.850066i	$-0.323438\pi$
$577$	350692.			1.05335			0.526676	+	0.850066i	$0.323438\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−785501.	+	453509.i	−2.32699	+	1.34349i
$582$		0			0
$583$	283679.	−	491346.i	0.834622	−	1.44561i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	415397.	+	239829.i	1.20555	+	0.696027i	0.961785	−	0.273806i	$-0.0882827\pi$
$587$	415397.	+	239829.i	1.20555	+	0.696027i	0.243769	+	0.969833i	$0.421616\pi$
$588$		0			0
$589$	57719.7	+	99973.4i	0.166377	+	0.288173i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	177843.i		−	0.505740i	−0.967500	−	0.252870i	$-0.918625\pi$
$593$		−	177843.i		−	0.505740i	0.967500	−	0.252870i	$-0.0813745\pi$
$594$		0			0
$595$	−777430.			−2.19597
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16977.8	+	9802.11i	−0.0473180	+	0.0273191i	−0.523472	−	0.852043i	$-0.675364\pi$
$599$	−16977.8	+	9802.11i	−0.0473180	+	0.0273191i	0.476154	+	0.879362i	$0.342030\pi$
$600$		0			0
$601$	−197404.	+	341913.i	−0.546520	+	0.946600i	0.451990	+	0.892023i	$0.350714\pi$
$601$	−197404.	+	341913.i	−0.546520	+	0.946600i	−0.998510	+	0.0545772i	$0.982619\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−154036.	−	88932.8i	−0.420835	−	0.242969i
$606$		0			0
$607$	−351729.	−	609212.i	−0.954620	−	1.65345i	−0.735235	−	0.677813i	$-0.762928\pi$
$607$	−351729.	−	609212.i	−0.954620	−	1.65345i	−0.219386	−	0.975638i	$-0.570405\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	479015.i		−	1.28312i
$612$		0			0
$613$	96392.2			0.256520			0.128260	−	0.991741i	$-0.459061\pi$
$613$	96392.2			0.256520			0.128260	+	0.991741i	$0.459061\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	439772.	−	253903.i	1.15520	−	0.666956i	0.205052	−	0.978751i	$-0.434264\pi$
$617$	439772.	−	253903.i	1.15520	−	0.666956i	0.950149	+	0.311796i	$0.100930\pi$
$618$		0			0
$619$	43453.6	−	75263.9i	0.113408	−	0.196429i	−0.803734	−	0.594989i	$-0.797157\pi$
$619$	43453.6	−	75263.9i	0.113408	−	0.196429i	0.917142	+	0.398560i	$0.130490\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	498460.	+	287786.i	1.28426	+	0.741470i
$624$		0			0
$625$	242052.	+	419247.i	0.619654	+	1.07327i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			566023.i			1.43065i
$630$		0			0
$631$	−571591.			−1.43558			−0.717788	−	0.696261i	$-0.754846\pi$
$631$	−571591.			−1.43558			−0.717788	+	0.696261i	$0.754846\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−247101.	+	142664.i	−0.612812	+	0.353807i
$636$		0			0
$637$	315797.	−	546976.i	0.778267	−	1.34800i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−332304.	−	191856.i	−0.808759	−	0.466937i	0.0377659	−	0.999287i	$-0.487976\pi$
$641$	−332304.	−	191856.i	−0.808759	−	0.466937i	−0.846525	+	0.532350i	$0.821309\pi$
$642$		0			0
$643$	405119.	+	701687.i	0.979853	+	1.69716i	0.662888	+	0.748718i	$0.269330\pi$
$643$	405119.	+	701687.i	0.979853	+	1.69716i	0.316965	+	0.948437i	$0.397336\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	687173.i		−	1.64156i	−0.571243	−	0.820781i	$-0.693539\pi$
$647$		−	687173.i		−	1.64156i	0.571243	−	0.820781i	$-0.306461\pi$
$648$		0			0
$649$	351187.			0.833775
$650$		0			0
$651$		0			0
$652$		0			0
$653$	189470.	−	109391.i	0.444339	−	0.256539i	−0.261097	−	0.965312i	$-0.584084\pi$
$653$	189470.	−	109391.i	0.444339	−	0.256539i	0.705437	+	0.708773i	$0.250751\pi$
$654$		0			0
$655$	5654.87	−	9794.52i	0.0131807	−	0.0228297i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−71298.2	−	41164.1i	−0.164175	−	0.0947867i	0.415661	−	0.909520i	$-0.363550\pi$
$659$	−71298.2	−	41164.1i	−0.164175	−	0.0947867i	−0.579836	+	0.814733i	$0.696884\pi$
$660$		0			0
$661$	−205017.	−	355100.i	−0.469231	−	0.812732i	0.530150	−	0.847904i	$-0.322136\pi$
$661$	−205017.	−	355100.i	−0.469231	−	0.812732i	−0.999381	+	0.0351716i	$0.988802\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			749537.i			1.69492i
$666$		0			0
$667$	80848.4			0.181727
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−305822.	+	176566.i	−0.679241	+	0.392160i
$672$		0			0
$673$	−265864.	+	460490.i	−0.586989	+	1.01669i	0.407636	+	0.913145i	$0.366353\pi$
$673$	−265864.	+	460490.i	−0.586989	+	1.01669i	−0.994624	+	0.103549i	$0.966980\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−149580.	−	86360.3i	−0.326361	−	0.188424i	0.327864	−	0.944725i	$-0.393671\pi$
$677$	−149580.	−	86360.3i	−0.326361	−	0.188424i	−0.654224	+	0.756301i	$0.727005\pi$
$678$		0			0
$679$	−109714.	−	190030.i	−0.237970	−	0.412177i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			452646.i			0.970324i	0.874424	+	0.485162i	$0.161239\pi$
$683$			452646.i			0.970324i	−0.874424	+	0.485162i	$0.838761\pi$
$684$		0			0
$685$	468296.			0.998019
$686$		0			0
$687$		0			0
$688$		0			0
$689$	664912.	−	383887.i	1.40064	−	0.808658i
$690$		0			0
$691$	−117795.	+	204027.i	−0.246701	+	0.427298i	−0.962608	−	0.270897i	$-0.912680\pi$
$691$	−117795.	+	204027.i	−0.246701	+	0.427298i	0.715908	+	0.698195i	$0.246013\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	59196.0	+	34176.8i	0.122553	+	0.0707558i
$696$		0			0
$697$	64400.9	+	111546.i	0.132564	+	0.229608i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	41298.8i		−	0.0840430i	−0.999117	−	0.0420215i	$-0.986620\pi$
$701$		−	41298.8i		−	0.0840430i	0.999117	−	0.0420215i	$-0.0133798\pi$
$702$		0			0
$703$	545715.			1.10422
$704$		0			0
$705$		0			0
$706$		0			0
$707$	711673.	−	410885.i	1.42378	−	0.822018i
$708$		0			0
$709$	−32914.9	+	57010.2i	−0.0654786	+	0.113412i	−0.896906	−	0.442221i	$-0.854191\pi$
$709$	−32914.9	+	57010.2i	−0.0654786	+	0.113412i	0.831428	+	0.555633i	$0.187524\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	163093.	+	94162.0i	0.320817	+	0.185224i
$714$		0			0
$715$	−433950.	−	751623.i	−0.848843	−	1.47024i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			551850.i			1.06749i	0.845646	+	0.533745i	$0.179216\pi$
$719$			551850.i			1.06749i	−0.845646	+	0.533745i	$0.820784\pi$
$720$		0			0
$721$	548447.			1.05503
$722$		0			0
$723$		0			0
$724$		0			0
$725$	51520.8	−	29745.6i	0.0980182	−	0.0565908i
$726$		0			0
$727$	−69946.0	+	121150.i	−0.132341	+	0.229221i	−0.924579	−	0.380992i	$-0.875583\pi$
$727$	−69946.0	+	121150.i	−0.132341	+	0.229221i	0.792238	+	0.610213i	$0.208916\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−203398.	−	117432.i	−0.380638	−	0.219761i
$732$		0			0
$733$	348037.	+	602817.i	0.647764	+	1.12196i	0.983656	+	0.180060i	$0.0576291\pi$
$733$	348037.	+	602817.i	0.647764	+	1.12196i	−0.335891	+	0.941901i	$0.609038\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			938905.i			1.72857i
$738$		0			0
$739$	360220.			0.659598			0.329799	−	0.944051i	$-0.393019\pi$
$739$	360220.			0.659598			0.329799	+	0.944051i	$0.393019\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−55134.1	+	31831.7i	−0.0998718	+	0.0576610i	−0.549104	−	0.835754i	$-0.685031\pi$
$743$	−55134.1	+	31831.7i	−0.0998718	+	0.0576610i	0.449232	+	0.893415i	$0.351698\pi$
$744$		0			0
$745$	456594.	−	790844.i	0.822655	−	1.42488i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	360641.	+	208216.i	0.642854	+	0.371152i
$750$		0			0
$751$	369552.	+	640082.i	0.655232	+	1.13490i	0.981836	+	0.189734i	$0.0607626\pi$
$751$	369552.	+	640082.i	0.655232	+	1.13490i	−0.326603	+	0.945162i	$0.605904\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			300903.i			0.527877i
$756$		0			0
$757$	−315416.			−0.550416			−0.275208	−	0.961385i	$-0.588747\pi$
$757$	−315416.			−0.550416			−0.275208	+	0.961385i	$0.588747\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−814012.	+	469970.i	−1.40560	+	0.811523i	−0.994960	−	0.100274i	$-0.968028\pi$
$761$	−814012.	+	469970.i	−1.40560	+	0.811523i	−0.410640	+	0.911798i	$0.634695\pi$
$762$		0			0
$763$	270803.	−	469045.i	0.465163	−	0.805685i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	411571.	+	237621.i	0.699607	+	0.403919i
$768$		0			0
$769$	−173503.	−	300517.i	−0.293397	−	0.508178i	0.681214	−	0.732085i	$-0.261452\pi$
$769$	−173503.	−	300517.i	−0.293397	−	0.508178i	−0.974611	+	0.223906i	$0.928119\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			4630.27i			0.00774903i	0.999992	+	0.00387451i	$0.00123330\pi$
$773$			4630.27i			0.00774903i	−0.999992	+	0.00387451i	$0.998767\pi$
$774$		0			0
$775$	138576.			0.230719
$776$		0			0
$777$		0			0
$778$		0			0
$779$	107544.	−	62090.3i	0.177219	−	0.102317i
$780$		0			0
$781$	−414773.	+	718407.i	−0.679999	+	1.17779i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−270735.	−	156309.i	−0.439345	−	0.253656i
$786$		0			0
$787$	−251477.	−	435571.i	−0.406021	−	0.703250i	0.588418	−	0.808557i	$-0.299751\pi$
$787$	−251477.	−	435571.i	−0.406021	−	0.703250i	−0.994440	+	0.105307i	$0.966417\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	934828.i		−	1.49410i
$792$		0			0
$793$	−477875.			−0.759921
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−210541.	+	121556.i	−0.331451	+	0.191363i	−0.656485	−	0.754339i	$-0.727958\pi$
$797$	−210541.	+	121556.i	−0.331451	+	0.191363i	0.325034	+	0.945702i	$0.394624\pi$
$798$		0			0
$799$	405183.	−	701797.i	0.634684	−	1.09930i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.08357e6	−	625599.i	−1.68045	−	0.970209i
$804$		0			0
$805$	611385.	+	1.05895e6i	0.943459	+	1.63412i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			600348.i			0.917289i	0.888620	+	0.458644i	$0.151665\pi$
$809$			600348.i			0.917289i	−0.888620	+	0.458644i	$0.848335\pi$
$810$		0			0
$811$	−168852.			−0.256722			−0.128361	−	0.991727i	$-0.540972\pi$
$811$	−168852.			−0.256722			−0.128361	+	0.991727i	$0.540972\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	615877.	−	355577.i	0.927211	−	0.535326i
$816$		0			0
$817$	−113219.	+	196100.i	−0.169619	+	0.293788i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−445541.	−	257233.i	−0.660999	−	0.381628i	0.131658	−	0.991295i	$-0.457970\pi$
$821$	−445541.	−	257233.i	−0.660999	−	0.381628i	−0.792658	+	0.609667i	$0.791303\pi$
$822$		0			0
$823$	−602121.	−	1.04290e6i	−0.888963	−	1.53973i	−0.841103	−	0.540875i	$-0.818093\pi$
$823$	−602121.	−	1.04290e6i	−0.888963	−	1.53973i	−0.0478604	−	0.998854i	$-0.515240\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	682316.i		−	0.997641i	−0.866705	−	0.498821i	$-0.833767\pi$
$827$		−	682316.i		−	0.997641i	0.866705	−	0.498821i	$-0.166233\pi$
$828$		0			0
$829$	−1.14603e6			−1.66758			−0.833791	−	0.552081i	$-0.813834\pi$
$829$	−1.14603e6			−1.66758			−0.833791	+	0.552081i	$0.813834\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	925338.	−	534244.i	1.33355	−	0.769927i
$834$		0			0
$835$	−268573.	+	465182.i	−0.385203	+	0.667191i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−284696.	−	164370.i	−0.404444	−	0.233506i	0.283956	−	0.958837i	$-0.408353\pi$
$839$	−284696.	−	164370.i	−0.404444	−	0.233506i	−0.688400	+	0.725332i	$0.741686\pi$
$840$		0			0
$841$	−341198.	−	590973.i	−0.482408	−	0.835556i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	270342.i		−	0.378617i
$846$		0			0
$847$	423453.			0.590254
$848$		0			0
$849$		0			0
$850$		0			0
$851$	770989.	−	445131.i	1.06461	−	0.614651i
$852$		0			0
$853$	−188763.	+	326948.i	−0.259430	+	0.449346i	−0.966089	−	0.258208i	$-0.916868\pi$
$853$	−188763.	+	326948.i	−0.259430	+	0.449346i	0.706660	+	0.707554i	$0.250201\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−372750.	−	215207.i	−0.507524	−	0.293019i	0.224291	−	0.974522i	$-0.427993\pi$
$857$	−372750.	−	215207.i	−0.507524	−	0.293019i	−0.731815	+	0.681503i	$0.761327\pi$
$858$		0			0
$859$	84365.9	+	146126.i	0.114335	+	0.198035i	0.917514	−	0.397704i	$-0.130193\pi$
$859$	84365.9	+	146126.i	0.114335	+	0.198035i	−0.803178	+	0.595738i	$0.796859\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			641651.i			0.861543i	0.902461	+	0.430772i	$0.141759\pi$
$863$			641651.i			0.861543i	−0.902461	+	0.430772i	$0.858241\pi$
$864$		0			0
$865$	−1.18587e6			−1.58491
$866$		0			0
$867$		0			0
$868$		0			0
$869$	476925.	−	275353.i	0.631554	−	0.364628i
$870$		0			0
$871$	−635284.	+	1.10034e6i	−0.837398	+	1.45042i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−512148.	−	295689.i	−0.668928	−	0.386206i
$876$		0			0
$877$	559865.	+	969715.i	0.727921	+	1.26080i	0.957760	+	0.287568i	$0.0928468\pi$
$877$	559865.	+	969715.i	0.727921	+	1.26080i	−0.229839	+	0.973229i	$0.573820\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			293548.i			0.378205i	0.981957	+	0.189103i	$0.0605579\pi$
$881$			293548.i			0.378205i	−0.981957	+	0.189103i	$0.939442\pi$
$882$		0			0
$883$	−1.07664e6			−1.38085			−0.690426	−	0.723403i	$-0.742577\pi$
$883$	−1.07664e6			−1.38085			−0.690426	+	0.723403i	$0.742577\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.09244e6	+	630719.i	−1.38851	+	0.801657i	−0.993148	−	0.116867i	$-0.962715\pi$
$887$	−1.09244e6	+	630719.i	−1.38851	+	0.801657i	−0.395364	+	0.918525i	$0.629381\pi$
$888$		0			0
$889$	339647.	−	588286.i	0.429759	−	0.744364i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−676618.	−	390645.i	−0.848478	−	0.489869i
$894$		0			0
$895$	708485.	+	1.22713e6i	0.884473	+	1.53195i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			57964.4i			0.0717203i
$900$		0			0
$901$	1.29887e6			1.59999
$902$		0			0
$903$		0			0
$904$		0			0
$905$	800745.	−	462310.i	0.977680	−	0.564464i
$906$		0			0
$907$	106701.	−	184812.i	0.129705	−	0.224655i	−0.793857	−	0.608104i	$-0.791930\pi$
$907$	106701.	−	184812.i	0.129705	−	0.224655i	0.923562	+	0.383449i	$0.125264\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	735102.	+	424411.i	0.885749	+	0.511388i	0.872550	−	0.488525i	$-0.162465\pi$
$911$	735102.	+	424411.i	0.885749	+	0.511388i	0.0131995	+	0.999913i	$0.495798\pi$
$912$		0			0
$913$	−856498.	−	1.48350e6i	−1.02751	−	1.77970i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			26925.7i			0.0320205i
$918$		0			0
$919$	−650728.			−0.770493			−0.385246	−	0.922814i	$-0.625884\pi$
$919$	−650728.			−0.770493			−0.385246	+	0.922814i	$0.625884\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−972181.	+	561289.i	−1.14115	+	0.658845i
$924$		0			0
$925$	327543.	−	567321.i	0.382811	−	0.663049i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−236742.	−	136683.i	−0.274312	−	0.158374i	0.356534	−	0.934282i	$-0.383959\pi$
$929$	−236742.	−	136683.i	−0.274312	−	0.158374i	−0.630846	+	0.775908i	$0.717292\pi$
$930$		0			0
$931$	−515076.	−	892138.i	−0.594254	−	1.02928i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1.46826e6i		−	1.67949i
$936$		0			0
$937$	1.19093e6			1.35646			0.678232	−	0.734848i	$-0.262746\pi$
$937$	1.19093e6			1.35646			0.678232	+	0.734848i	$0.262746\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.21799e6	+	703208.i	−1.37551	+	0.794153i	−0.991616	−	0.129222i	$-0.958752\pi$
$941$	−1.21799e6	+	703208.i	−1.37551	+	0.794153i	−0.383898	+	0.923375i	$0.625419\pi$
$942$		0			0
$943$	101292.	−	175443.i	0.113907	−	0.197293i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.13971e6	+	658009.i	1.27085	+	0.733723i	0.975147	−	0.221558i	$-0.0711144\pi$
$947$	1.13971e6	+	658009.i	1.27085	+	0.733723i	0.295698	+	0.955281i	$0.404448\pi$
$948$		0			0
$949$	−846589.	−	1.46634e6i	−0.940027	−	1.62817i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.09774e6i		−	1.20868i	−0.796725	−	0.604342i	$-0.793436\pi$
$953$		−	1.09774e6i		−	1.20868i	0.796725	−	0.604342i	$-0.206564\pi$
$954$		0			0
$955$	949973.			1.04161
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−965527.	+	557447.i	−1.04985	+	0.606131i
$960$		0			0
$961$	394251.	−	682863.i	0.426900	−	0.739412i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−472412.	−	272747.i	−0.507302	−	0.292891i
$966$		0			0
$967$	24500.4	+	42436.0i	0.0262012	+	0.0453817i	0.878829	−	0.477137i	$-0.158326\pi$
$967$	24500.4	+	42436.0i	0.0262012	+	0.0453817i	−0.852628	+	0.522519i	$0.824992\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1.83854e6i			1.95000i	0.222198	+	0.975001i	$0.428677\pi$
$971$			1.83854e6i			1.95000i	−0.222198	+	0.975001i	$0.571323\pi$
$972$		0			0
$973$	−162733.			−0.171890
$974$		0			0
$975$		0			0
$976$		0			0
$977$	549300.	−	317138.i	0.575467	−	0.332246i	−0.183863	−	0.982952i	$-0.558860\pi$
$977$	549300.	−	317138.i	0.575467	−	0.332246i	0.759330	+	0.650706i	$0.225527\pi$
$978$		0			0
$979$	−543513.	+	941393.i	−0.567081	+	0.982213i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	791690.	+	457082.i	0.819310	+	0.473029i	0.850178	−	0.526495i	$-0.176494\pi$
$983$	791690.	+	457082.i	0.819310	+	0.473029i	−0.0308686	+	0.999523i	$0.509827\pi$
$984$		0			0
$985$	1.07461e6	+	1.86128e6i	1.10759	+	1.91840i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			369402.i			0.377665i
$990$		0			0
$991$	−119.608			−0.000121790			−6.08950e−5	−	1.00000i	$-0.500019\pi$
$991$	−119.608			−0.000121790			−6.08950e−5		1.00000i	$0.500019\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	740117.	−	427306.i	0.747574	−	0.431612i
$996$		0			0
$997$	−569592.	+	986562.i	−0.573025	+	0.992508i	0.423228	+	0.906023i	$0.360897\pi$
$997$	−569592.	+	986562.i	−0.573025	+	0.992508i	−0.996253	+	0.0864852i	$0.972436\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.g.a.89.1		8
3.2	odd	2		36.5.g.a.29.1	yes	8
4.3	odd	2		432.5.q.c.305.1		8
9.2	odd	6		324.5.c.a.161.7		8
9.4	even	3		36.5.g.a.5.1	✓	8
9.5	odd	6	inner	108.5.g.a.17.1		8
9.7	even	3		324.5.c.a.161.2		8
12.11	even	2		144.5.q.c.65.4		8
36.7	odd	6		1296.5.e.g.161.2		8
36.11	even	6		1296.5.e.g.161.7		8
36.23	even	6		432.5.q.c.17.1		8
36.31	odd	6		144.5.q.c.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.1	✓	8	9.4	even	3
36.5.g.a.29.1	yes	8	3.2	odd	2
108.5.g.a.17.1		8	9.5	odd	6	inner
108.5.g.a.89.1		8	1.1	even	1	trivial
144.5.q.c.65.4		8	12.11	even	2
144.5.q.c.113.4		8	36.31	odd	6
324.5.c.a.161.2		8	9.7	even	3
324.5.c.a.161.7		8	9.2	odd	6
432.5.q.c.17.1		8	36.23	even	6
432.5.q.c.305.1		8	4.3	odd	2
1296.5.e.g.161.2		8	36.7	odd	6
1296.5.e.g.161.7		8	36.11	even	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +O(q^{10})\)	\(q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +(123.267 + 71.1682i) q^{11} +(96.3079 + 166.810i) q^{13} +325.855i q^{17} +314.164 q^{19} +(443.852 - 256.258i) q^{23} +(188.564 - 326.602i) q^{25} +(136.614 + 78.8739i) q^{29} +(183.725 + 318.221i) q^{31} +2385.82i q^{35} +1737.04 q^{37} +(342.317 - 197.637i) q^{41} +(-360.381 + 624.198i) q^{43} +(-2153.71 - 1243.45i) q^{47} +(-1639.52 - 2839.72i) q^{49} -3986.04i q^{53} -4505.86 q^{55} +(2136.75 - 1233.65i) q^{59} +(-1240.49 + 2148.59i) q^{61} +(-5280.61 - 3048.76i) q^{65} +(3298.19 + 5712.64i) q^{67} +5828.07i q^{71} -8790.44 q^{73} +(9290.13 - 5363.66i) q^{77} +(1934.52 - 3350.69i) q^{79} +(-10422.5 - 6017.43i) q^{83} +(-5157.70 - 8933.39i) q^{85} +7637.03i q^{89} +14516.7 q^{91} +(-8612.88 + 4972.65i) q^{95} +(1455.75 - 2521.44i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) \) 8 * q + 9 * q^5 + 13 * q^7	\( 8 q + 9 q^{5} + 13 q^{7} + 18 q^{11} - 5 q^{13} + 562 q^{19} + 1719 q^{23} + 353 q^{25} - 2115 q^{29} + 187 q^{31} + 16 q^{37} + 7920 q^{41} - 68 q^{43} - 13689 q^{47} - 327 q^{49} - 1818 q^{55} + 20052 q^{59} - 1937 q^{61} - 25965 q^{65} + 154 q^{67} - 7802 q^{73} + 25641 q^{77} - 2195 q^{79} - 37017 q^{83} - 3042 q^{85} + 15830 q^{91} + 37116 q^{95} + 7282 q^{97}+O(q^{100}) \) 8 * q + 9 * q^5 + 13 * q^7 + 18 * q^11 - 5 * q^13 + 562 * q^19 + 1719 * q^23 + 353 * q^25 - 2115 * q^29 + 187 * q^31 + 16 * q^37 + 7920 * q^41 - 68 * q^43 - 13689 * q^47 - 327 * q^49 - 1818 * q^55 + 20052 * q^59 - 1937 * q^61 - 25965 * q^65 + 154 * q^67 - 7802 * q^73 + 25641 * q^77 - 2195 * q^79 - 37017 * q^83 - 3042 * q^85 + 15830 * q^91 + 37116 * q^95 + 7282 * q^97

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