LMFDB - Embedded newform 684.5.y.e.145.3

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} + 2358 x^{12} + 15572 x^{11} + 4050518 x^{10} + 21628620 x^{9} + 2974230644 x^{8} + \cdots + 96\!\cdots\!24 $ x^14 - 2x^13 + 2358x^12 + 15572x^11 + 4050518x^10 + 21628620x^9 + 2974230644x^8 + 5952397856x^7 + 1565987836020x^6 + 2094356466136x^5 + 410050182894688x^4 + 121654699639392x^3 + 75130751452572288x^2 + 84471822440408448*x + 96133502759457024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$-9.25681 + 16.0333i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.e.217.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.25681 - 12.5692i) q^{5} -14.1648 q^{7} +O(q^{10})$	$q+(-7.25681 - 12.5692i) q^{5} -14.1648 q^{7} +23.7451 q^{11} +(-218.739 - 126.289i) q^{13} +(-133.824 - 231.790i) q^{17} +(28.6536 + 359.861i) q^{19} +(-339.319 + 587.718i) q^{23} +(207.177 - 358.842i) q^{25} +(914.743 + 528.127i) q^{29} -335.285i q^{31} +(102.791 + 178.039i) q^{35} -1614.95i q^{37} +(-205.320 + 118.541i) q^{41} +(-174.132 - 301.605i) q^{43} +(-2099.51 + 3636.45i) q^{47} -2200.36 q^{49} +(3361.32 + 1940.66i) q^{53} +(-172.313 - 298.455i) q^{55} +(-1763.59 + 1018.21i) q^{59} +(3196.74 - 5536.92i) q^{61} +3665.82i q^{65} +(1711.48 + 988.125i) q^{67} +(1233.86 - 712.367i) q^{71} +(3051.07 + 5284.60i) q^{73} -336.343 q^{77} +(-89.6151 + 51.7393i) q^{79} +6375.53 q^{83} +(-1942.27 + 3364.11i) q^{85} +(9166.21 + 5292.11i) q^{89} +(3098.39 + 1788.86i) q^{91} +(4315.22 - 2971.60i) q^{95} +(7608.98 - 4393.05i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 30 q^{5} + 106 q^{7}+O(q^{10}) $ 14 * q + 30 * q^5 + 106 * q^7	$ 14 q + 30 q^{5} + 106 q^{7} + 264 q^{11} + 57 q^{13} - 282 q^{17} + 2 q^{19} - 96 q^{23} - 465 q^{25} + 630 q^{29} - 1434 q^{35} + 228 q^{41} - 2093 q^{43} + 4710 q^{47} + 4440 q^{49} - 2364 q^{53} + 6368 q^{55} - 11838 q^{59} - 1661 q^{61} - 20319 q^{67} - 624 q^{71} + 5851 q^{73} + 1080 q^{77} - 13299 q^{79} - 12252 q^{83} - 5740 q^{85} + 20010 q^{89} + 15951 q^{91} - 7770 q^{95} + 44904 q^{97}+O(q^{100}) $ 14 * q + 30 * q^5 + 106 * q^7 + 264 * q^11 + 57 * q^13 - 282 * q^17 + 2 * q^19 - 96 * q^23 - 465 * q^25 + 630 * q^29 - 1434 * q^35 + 228 * q^41 - 2093 * q^43 + 4710 * q^47 + 4440 * q^49 - 2364 * q^53 + 6368 * q^55 - 11838 * q^59 - 1661 * q^61 - 20319 * q^67 - 624 * q^71 + 5851 * q^73 + 1080 * q^77 - 13299 * q^79 - 12252 * q^83 - 5740 * q^85 + 20010 * q^89 + 15951 * q^91 - 7770 * q^95 + 44904 * 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
$5$	−7.25681	−	12.5692i	−0.290272	−	0.502766i	0.683602	−	0.729855i	$-0.260413\pi$
$5$	−7.25681	−	12.5692i	−0.290272	−	0.502766i	−0.973874	+	0.227089i	$0.927079\pi$
$6$		0			0
$7$	−14.1648			−0.289077			−0.144539	−	0.989499i	$-0.546170\pi$
$7$	−14.1648			−0.289077			−0.144539	+	0.989499i	$0.546170\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	23.7451			0.196240			0.0981200	−	0.995175i	$-0.468717\pi$
$11$	23.7451			0.196240			0.0981200	+	0.995175i	$0.468717\pi$
$12$		0			0
$13$	−218.739	−	126.289i	−1.29431	−	0.747273i	−0.314898	−	0.949125i	$-0.601970\pi$
$13$	−218.739	−	126.289i	−1.29431	−	0.747273i	−0.979416	+	0.201853i	$0.935304\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−133.824	−	231.790i	−0.463058	−	0.802040i	0.536053	−	0.844184i	$-0.319915\pi$
$17$	−133.824	−	231.790i	−0.463058	−	0.802040i	−0.999112	+	0.0421439i	$0.986581\pi$
$18$		0			0
$19$	28.6536	+	359.861i	0.0793729	+	0.996845i
$19$	28.6536	+	359.861i	0.0793729	+	0.996845i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−339.319	+	587.718i	−0.641436	+	1.11100i	0.343677	+	0.939088i	$0.388327\pi$
$23$	−339.319	+	587.718i	−0.641436	+	1.11100i	−0.985112	+	0.171911i	$0.945006\pi$
$24$		0			0
$25$	207.177	−	358.842i	0.331484	−	0.574147i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	914.743	+	528.127i	1.08768	+	0.627975i	0.932959	−	0.359983i	$-0.117217\pi$
$29$	914.743	+	528.127i	1.08768	+	0.627975i	0.154726	+	0.987957i	$0.450551\pi$
$30$		0			0
$31$		−	335.285i		−	0.348891i	−0.984667	−	0.174446i	$-0.944187\pi$
$31$		−	335.285i		−	0.348891i	0.984667	−	0.174446i	$-0.0558133\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	102.791	+	178.039i	0.0839111	+	0.145338i
$36$		0			0
$37$		−	1614.95i		−	1.17965i	−0.807530	−	0.589827i	$-0.799196\pi$
$37$		−	1614.95i		−	1.17965i	0.807530	−	0.589827i	$-0.200804\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−205.320	+	118.541i	−0.122141	+	0.0705183i	−0.559826	−	0.828610i	$-0.689132\pi$
$41$	−205.320	+	118.541i	−0.122141	+	0.0705183i	0.437685	+	0.899129i	$0.355799\pi$
$42$		0			0
$43$	−174.132	−	301.605i	−0.0941762	−	0.163118i	0.815088	−	0.579337i	$-0.196688\pi$
$43$	−174.132	−	301.605i	−0.0941762	−	0.163118i	−0.909264	+	0.416219i	$0.863355\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2099.51	+	3636.45i	−0.950434	+	1.64620i	−0.205946	+	0.978563i	$0.566027\pi$
$47$	−2099.51	+	3636.45i	−0.950434	+	1.64620i	−0.744488	+	0.667636i	$0.767306\pi$
$48$		0			0
$49$	−2200.36			−0.916434
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3361.32	+	1940.66i	1.19662	+	0.690871i	0.959801	−	0.280682i	$-0.0905606\pi$
$53$	3361.32	+	1940.66i	1.19662	+	0.690871i	0.236823	+	0.971553i	$0.423894\pi$
$54$		0			0
$55$	−172.313	−	298.455i	−0.0569631	−	0.0986629i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1763.59	+	1018.21i	−0.506632	+	0.292504i	−0.731448	−	0.681897i	$-0.761155\pi$
$59$	−1763.59	+	1018.21i	−0.506632	+	0.292504i	0.224816	+	0.974401i	$0.427822\pi$
$60$		0			0
$61$	3196.74	−	5536.92i	0.859108	−	1.48802i	−0.0136721	−	0.999907i	$-0.504352\pi$
$61$	3196.74	−	5536.92i	0.859108	−	1.48802i	0.872780	−	0.488113i	$-0.162315\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			3665.82i			0.867650i
$66$		0			0
$67$	1711.48	+	988.125i	0.381261	+	0.220121i	0.678367	−	0.734723i	$-0.262688\pi$
$67$	1711.48	+	988.125i	0.381261	+	0.220121i	−0.297106	+	0.954845i	$0.596021\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1233.86	−	712.367i	0.244764	−	0.141315i	−0.372600	−	0.927992i	$-0.621534\pi$
$71$	1233.86	−	712.367i	0.244764	−	0.141315i	0.617364	+	0.786677i	$0.288200\pi$
$72$		0			0
$73$	3051.07	+	5284.60i	0.572540	+	0.991669i	0.996304	+	0.0858959i	$0.0273753\pi$
$73$	3051.07	+	5284.60i	0.572540	+	0.991669i	−0.423764	+	0.905773i	$0.639291\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−336.343			−0.0567285
$78$		0			0
$79$	−89.6151	+	51.7393i	−0.0143591	+	0.00829022i	−0.507162	−	0.861851i	$-0.669306\pi$
$79$	−89.6151	+	51.7393i	−0.0143591	+	0.00829022i	0.492803	+	0.870141i	$0.335972\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6375.53			0.925466			0.462733	−	0.886498i	$-0.346869\pi$
$83$	6375.53			0.925466			0.462733	+	0.886498i	$0.346869\pi$
$84$		0			0
$85$	−1942.27	+	3364.11i	−0.268826	+	0.465620i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9166.21	+	5292.11i	1.15720	+	0.668112i	0.950632	−	0.310320i	$-0.100436\pi$
$89$	9166.21	+	5292.11i	1.15720	+	0.668112i	0.206571	+	0.978432i	$0.433769\pi$
$90$		0			0
$91$	3098.39	+	1788.86i	0.374157	+	0.216019i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4315.22	−	2971.60i	0.478140	−	0.329263i
$96$		0			0
$97$	7608.98	−	4393.05i	0.808692	−	0.466898i	−0.0378096	−	0.999285i	$-0.512038\pi$
$97$	7608.98	−	4393.05i	0.808692	−	0.466898i	0.846501	+	0.532387i	$0.178705\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4417.47	+	7651.28i	−0.433043	+	0.750052i	−0.997134	−	0.0756604i	$-0.975893\pi$
$101$	−4417.47	+	7651.28i	−0.433043	+	0.750052i	0.564091	+	0.825713i	$0.309227\pi$
$102$		0			0
$103$			9554.93i			0.900644i	0.892866	+	0.450322i	$0.148691\pi$
$103$			9554.93i			0.900644i	−0.892866	+	0.450322i	$0.851309\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	3473.41i		−	0.303381i	−0.988428	−	0.151691i	$-0.951528\pi$
$107$		−	3473.41i		−	0.303381i	0.988428	−	0.151691i	$-0.0484717\pi$
$108$		0			0
$109$	−15569.5	+	8989.05i	−1.31045	+	0.756591i	−0.982171	−	0.187989i	$-0.939803\pi$
$109$	−15569.5	+	8989.05i	−1.31045	+	0.756591i	−0.328282	+	0.944580i	$0.606470\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			6008.78i			0.470575i	0.971926	+	0.235288i	$0.0756032\pi$
$113$			6008.78i			0.470575i	−0.971926	+	0.235288i	$0.924397\pi$
$114$		0			0
$115$	9849.50			0.744764
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1895.58	+	3283.25i	0.133860	+	0.231852i
$120$		0			0
$121$	−14077.2			−0.961490
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−15084.8			−0.965427
$126$		0			0
$127$	20666.8	+	11932.0i	1.28135	+	0.739785i	0.977094	−	0.212807i	$-0.0682605\pi$
$127$	20666.8	+	11932.0i	1.28135	+	0.739785i	0.304251	+	0.952592i	$0.401594\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1661.82	+	2878.35i	0.0968368	+	0.167726i	0.910374	−	0.413787i	$-0.135794\pi$
$131$	1661.82	+	2878.35i	0.0968368	+	0.167726i	−0.813537	+	0.581513i	$0.802461\pi$
$132$		0			0
$133$	−405.872	−	5097.35i	−0.0229449	−	0.288165i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13934.4	−	24135.1i	0.742415	−	1.28590i	−0.208978	−	0.977920i	$-0.567014\pi$
$137$	13934.4	−	24135.1i	0.742415	−	1.28590i	0.951393	−	0.307980i	$-0.0996529\pi$
$138$		0			0
$139$	−4610.77	+	7986.09i	−0.238640	+	0.413337i	−0.960324	−	0.278885i	$-0.910035\pi$
$139$	−4610.77	+	7986.09i	−0.238640	+	0.413337i	0.721684	+	0.692223i	$0.243368\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5193.97	−	2998.74i	−0.253996	−	0.146645i
$144$		0			0
$145$		−	15330.1i		−	0.729135i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	19269.5	+	33375.7i	0.867955	+	1.50334i	0.864083	+	0.503349i	$0.167899\pi$
$149$	19269.5	+	33375.7i	0.867955	+	1.50334i	0.00387183	+	0.999993i	$0.498768\pi$
$150$		0			0
$151$			42248.3i			1.85291i	0.376402	+	0.926457i	$0.377161\pi$
$151$			42248.3i			1.85291i	−0.376402	+	0.926457i	$0.622839\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4214.25	+	2433.10i	−0.175411	+	0.101273i
$156$		0			0
$157$	17157.4	+	29717.4i	0.696067	+	1.20562i	0.969820	+	0.243823i	$0.0784017\pi$
$157$	17157.4	+	29717.4i	0.696067	+	1.20562i	−0.273753	+	0.961800i	$0.588265\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4806.39	−	8324.90i	0.185424	−	0.321164i
$162$		0			0
$163$	−1656.97			−0.0623647			−0.0311823	−	0.999514i	$-0.509927\pi$
$163$	−1656.97			−0.0623647			−0.0311823	+	0.999514i	$0.509927\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18982.6	+	10959.6i	0.680649	+	0.392973i	0.800099	−	0.599867i	$-0.204780\pi$
$167$	18982.6	+	10959.6i	0.680649	+	0.392973i	−0.119451	+	0.992840i	$0.538113\pi$
$168$		0			0
$169$	17617.4	+	30514.2i	0.616832	+	1.06839i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13250.2	−	7650.03i	0.442722	−	0.255606i	−0.262029	−	0.965060i	$-0.584392\pi$
$173$	13250.2	−	7650.03i	0.442722	−	0.255606i	0.704752	+	0.709454i	$0.251058\pi$
$174$		0			0
$175$	−2934.62	+	5082.92i	−0.0958244	+	0.165973i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			51643.2i			1.61179i	0.592062	+	0.805893i	$0.298314\pi$
$179$			51643.2i			1.61179i	−0.592062	+	0.805893i	$0.701686\pi$
$180$		0			0
$181$	−46648.6	−	26932.6i	−1.42391	−	0.822093i	−0.427277	−	0.904121i	$-0.640527\pi$
$181$	−46648.6	−	26932.6i	−1.42391	−	0.822093i	−0.996630	+	0.0820277i	$0.973860\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−20298.5	+	11719.4i	−0.593090	+	0.342421i
$186$		0			0
$187$	−3177.65	−	5503.86i	−0.0908706	−	0.157392i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1305.62			0.0357889			0.0178945	−	0.999840i	$-0.494304\pi$
$191$	1305.62			0.0357889			0.0178945	+	0.999840i	$0.494304\pi$
$192$		0			0
$193$	14990.5	−	8654.77i	0.402440	−	0.232349i	−0.285096	−	0.958499i	$-0.592026\pi$
$193$	14990.5	−	8654.77i	0.402440	−	0.232349i	0.687536	+	0.726150i	$0.258692\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	69036.4			1.77888			0.889438	−	0.457056i	$-0.151096\pi$
$197$	69036.4			1.77888			0.889438	+	0.457056i	$0.151096\pi$
$198$		0			0
$199$	−1.16378	+	2.01572i	−2.93875e−5	+	5.09007e-5i	−0.866040	−	0.499975i	$-0.833343\pi$
$199$	−1.16378	+	2.01572i	−2.93875e−5	+	5.09007e-5i	0.866011	+	0.500025i	$0.166676\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12957.1	−	7480.80i	−0.314425	−	0.181533i
$204$		0			0
$205$	2979.93	+	1720.46i	0.0709085	+	0.0409390i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	680.382	+	8544.92i	0.0155762	+	0.195621i
$210$		0			0
$211$	25532.3	−	14741.1i	0.573489	−	0.331104i	−0.185053	−	0.982729i	$-0.559246\pi$
$211$	25532.3	−	14741.1i	0.573489	−	0.331104i	0.758542	+	0.651625i	$0.225912\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2527.28	+	4377.38i	−0.0546735	+	0.0946972i
$216$		0			0
$217$			4749.23i			0.100857i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			67601.9i			1.38412i
$222$		0			0
$223$	15231.2	−	8793.76i	0.306285	−	0.176834i	−0.338978	−	0.940794i	$-0.610081\pi$
$223$	15231.2	−	8793.76i	0.306285	−	0.176834i	0.645263	+	0.763961i	$0.276748\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	35123.5i		−	0.681625i	−0.940131	−	0.340813i	$-0.889298\pi$
$227$		−	35123.5i		−	0.681625i	0.940131	−	0.340813i	$-0.110702\pi$
$228$		0			0
$229$	16746.8			0.319345			0.159673	−	0.987170i	$-0.448956\pi$
$229$	16746.8			0.319345			0.159673	+	0.987170i	$0.448956\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7611.38	+	13183.3i	0.140201	+	0.242835i	0.927572	−	0.373644i	$-0.121892\pi$
$233$	7611.38	+	13183.3i	0.140201	+	0.242835i	−0.787371	+	0.616479i	$0.788558\pi$
$234$		0			0
$235$	60942.9			1.10354
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−78317.2			−1.37107			−0.685537	−	0.728038i	$-0.740433\pi$
$239$	−78317.2			−1.37107			−0.685537	+	0.728038i	$0.740433\pi$
$240$		0			0
$241$	−74393.7	−	42951.2i	−1.28086	−	0.739505i	−0.303855	−	0.952718i	$-0.598274\pi$
$241$	−74393.7	−	42951.2i	−1.28086	−	0.739505i	−0.977006	+	0.213213i	$0.931607\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	15967.6	+	27656.7i	0.266016	+	0.460753i
$246$		0			0
$247$	39178.8	−	82334.3i	0.642181	−	1.34954i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14290.3	+	24751.5i	−0.226826	+	0.392874i	−0.956866	−	0.290531i	$-0.906168\pi$
$251$	−14290.3	+	24751.5i	−0.226826	+	0.392874i	0.730040	+	0.683405i	$0.239502\pi$
$252$		0			0
$253$	−8057.16	+	13955.4i	−0.125875	+	0.218023i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	31627.6	+	18260.2i	0.478851	+	0.276465i	0.719937	−	0.694039i	$-0.244170\pi$
$257$	31627.6	+	18260.2i	0.478851	+	0.276465i	−0.241087	+	0.970504i	$0.577504\pi$
$258$		0			0
$259$			22875.4i			0.341011i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	43564.0	+	75455.1i	0.629820	+	1.09088i	0.987588	+	0.157069i	$0.0502046\pi$
$263$	43564.0	+	75455.1i	0.629820	+	1.09088i	−0.357768	+	0.933811i	$0.616462\pi$
$264$		0			0
$265$		−	56331.9i		−	0.802163i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−28639.2	+	16534.8i	−0.395782	+	0.228505i	−0.684662	−	0.728860i	$-0.740050\pi$
$269$	−28639.2	+	16534.8i	−0.395782	+	0.228505i	0.288881	+	0.957365i	$0.406717\pi$
$270$		0			0
$271$	−6537.46	−	11323.2i	−0.0890165	−	0.154181i	0.818079	−	0.575106i	$-0.195039\pi$
$271$	−6537.46	−	11323.2i	−0.0890165	−	0.154181i	−0.907096	+	0.420925i	$0.861706\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4919.44	−	8520.72i	0.0650504	−	0.112671i
$276$		0			0
$277$	−25175.4			−0.328107			−0.164054	−	0.986451i	$-0.552457\pi$
$277$	−25175.4			−0.328107			−0.164054	+	0.986451i	$0.552457\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−26003.1	−	15012.9i	−0.329315	−	0.190130i	0.326222	−	0.945293i	$-0.394224\pi$
$281$	−26003.1	−	15012.9i	−0.329315	−	0.190130i	−0.655537	+	0.755163i	$0.727558\pi$
$282$		0			0
$283$	−2231.85	−	3865.68i	−0.0278672	−	0.0482674i	0.851755	−	0.523939i	$-0.175538\pi$
$283$	−2231.85	−	3865.68i	−0.0278672	−	0.0482674i	−0.879623	+	0.475672i	$0.842205\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2908.31	−	1679.11i	0.0353083	−	0.0203852i
$288$		0			0
$289$	5942.89	−	10293.4i	0.0711544	−	0.123243i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			27144.8i			0.316193i	0.987424	+	0.158096i	$0.0505357\pi$
$293$			27144.8i			0.316193i	−0.987424	+	0.158096i	$0.949464\pi$
$294$		0			0
$295$	25596.0	+	14777.9i	0.294123	+	0.169812i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	148445.	−	85704.7i	1.66044	−	0.958654i
$300$		0			0
$301$	2466.54	+	4272.17i	0.0272242	+	0.0471537i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−92792.6			−0.997502
$306$		0			0
$307$	−97912.0	+	56529.5i	−1.03887	+	0.599789i	−0.919512	−	0.393063i	$-0.871416\pi$
$307$	−97912.0	+	56529.5i	−1.03887	+	0.599789i	−0.119354	+	0.992852i	$0.538082\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−63417.7			−0.655677			−0.327838	−	0.944734i	$-0.606320\pi$
$311$	−63417.7			−0.655677			−0.327838	+	0.944734i	$0.606320\pi$
$312$		0			0
$313$	60249.7	−	104356.i	0.614987	−	1.06519i	−0.375399	−	0.926863i	$-0.622494\pi$
$313$	60249.7	−	104356.i	0.614987	−	1.06519i	0.990387	−	0.138326i	$-0.0441722\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−57644.3	−	33280.9i	−0.573638	−	0.331190i	0.184963	−	0.982745i	$-0.440783\pi$
$317$	−57644.3	−	33280.9i	−0.573638	−	0.331190i	−0.758601	+	0.651556i	$0.774117\pi$
$318$		0			0
$319$	21720.6	+	12540.4i	0.213447	+	0.123234i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	79577.5	−	54799.6i	0.762755	−	0.525257i
$324$		0			0
$325$	−90635.6	+	52328.5i	−0.858089	+	0.495418i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	29739.1	−	51509.6i	0.274749	−	0.475879i
$330$		0			0
$331$			39388.7i			0.359514i	0.983711	+	0.179757i	$0.0575311\pi$
$331$			39388.7i			0.359514i	−0.983711	+	0.179757i	$0.942469\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	28682.5i		−	0.255581i
$336$		0			0
$337$	−61596.8	+	35562.9i	−0.542374	+	0.313140i	−0.746040	−	0.665901i	$-0.768047\pi$
$337$	−61596.8	+	35562.9i	−0.542374	+	0.313140i	0.203667	+	0.979040i	$0.434714\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	7961.35i		−	0.0684665i
$342$		0			0
$343$	65177.2			0.553997
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−61262.8	−	106110.i	−0.508789	−	0.881248i	−0.999948	−	0.0101786i	$-0.996760\pi$
$347$	−61262.8	−	106110.i	−0.508789	−	0.881248i	0.491159	−	0.871070i	$-0.336573\pi$
$348$		0			0
$349$	−88315.0			−0.725077			−0.362538	−	0.931969i	$-0.618090\pi$
$349$	−88315.0			−0.725077			−0.362538	+	0.931969i	$0.618090\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−177399.			−1.42364			−0.711821	−	0.702361i	$-0.752129\pi$
$353$	−177399.			−1.42364			−0.711821	+	0.702361i	$0.752129\pi$
$354$		0			0
$355$	−17907.7	−	10339.0i	−0.142097	−	0.0820395i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−98249.8	−	170174.i	−0.762329	−	1.32039i	−0.941647	−	0.336602i	$-0.890722\pi$
$359$	−98249.8	−	170174.i	−0.762329	−	1.32039i	0.179318	−	0.983791i	$-0.442611\pi$
$360$		0			0
$361$	−128679.	+	20622.7i	−0.987400	+	0.158245i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	44282.0	−	76698.7i	0.332385	−	0.575708i
$366$		0			0
$367$	2067.60	−	3581.19i	0.0153509	−	0.0265886i	−0.858248	−	0.513235i	$-0.828447\pi$
$367$	2067.60	−	3581.19i	0.0153509	−	0.0265886i	0.873599	+	0.486647i	$0.161780\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−47612.3	−	27489.0i	−0.345917	−	0.199715i
$372$		0			0
$373$			60234.3i			0.432939i	0.976289	+	0.216469i	$0.0694541\pi$
$373$			60234.3i			0.432939i	−0.976289	+	0.216469i	$0.930546\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−133393.	−	231044.i	−0.938537	−	1.62559i
$378$		0			0
$379$		−	163224.i		−	1.13633i	−0.822913	−	0.568167i	$-0.807653\pi$
$379$		−	163224.i		−	1.13633i	0.822913	−	0.568167i	$-0.192347\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	80248.5	−	46331.5i	0.547066	−	0.315849i	−0.200872	−	0.979618i	$-0.564378\pi$
$383$	80248.5	−	46331.5i	0.547066	−	0.315849i	0.747938	+	0.663769i	$0.231044\pi$
$384$		0			0
$385$	2440.78	+	4227.56i	0.0164667	+	0.0285212i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1426.94	−	2471.54i	0.00942990	−	0.0163331i	−0.861272	−	0.508144i	$-0.830332\pi$
$389$	1426.94	−	2471.54i	0.00942990	−	0.0163331i	0.870702	+	0.491811i	$0.163665\pi$
$390$		0			0
$391$	181636.			1.18809
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1300.64	+	750.924i	0.00833609	+	0.00481284i
$396$		0			0
$397$	105080.	+	182004.i	0.666713	+	1.15478i	0.978818	+	0.204734i	$0.0656328\pi$
$397$	105080.	+	182004.i	0.666713	+	1.15478i	−0.312104	+	0.950048i	$0.601034\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−87496.8	+	50516.3i	−0.544131	+	0.314154i	−0.746752	−	0.665103i	$-0.768388\pi$
$401$	−87496.8	+	50516.3i	−0.544131	+	0.314154i	0.202620	+	0.979257i	$0.435054\pi$
$402$		0			0
$403$	−42342.8	+	73339.8i	−0.260717	+	0.451575i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	38347.0i		−	0.231495i
$408$		0			0
$409$	−107657.	−	62155.8i	−0.643570	−	0.371565i	0.142418	−	0.989807i	$-0.454512\pi$
$409$	−107657.	−	62155.8i	−0.643570	−	0.371565i	−0.785988	+	0.618241i	$0.787845\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24980.8	−	14422.7i	0.146456	−	0.0845563i
$414$		0			0
$415$	−46266.0	−	80135.1i	−0.268637	−	0.465293i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	137777.			0.784781			0.392390	−	0.919799i	$-0.371648\pi$
$419$	137777.			0.784781			0.392390	+	0.919799i	$0.371648\pi$
$420$		0			0
$421$	20280.6	−	11709.0i	0.114424	−	0.0660626i	−0.441696	−	0.897165i	$-0.645623\pi$
$421$	20280.6	−	11709.0i	0.114424	−	0.0660626i	0.556120	+	0.831102i	$0.312290\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−110901.			−0.613985
$426$		0			0
$427$	−45281.2	+	78429.3i	−0.248349	+	0.430152i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	182076.	+	105122.i	0.980163	+	0.565897i	0.902319	−	0.431068i	$-0.141863\pi$
$431$	182076.	+	105122.i	0.980163	+	0.565897i	0.0778435	+	0.996966i	$0.475197\pi$
$432$		0			0
$433$	−17836.4	−	10297.9i	−0.0951332	−	0.0549252i	0.451679	−	0.892181i	$-0.350825\pi$
$433$	−17836.4	−	10297.9i	−0.0951332	−	0.0549252i	−0.546812	+	0.837256i	$0.684159\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−221220.	−	105268.i	−1.15841	−	0.551229i
$438$		0			0
$439$	61027.5	−	35234.2i	0.316662	−	0.182825i	−0.333242	−	0.942841i	$-0.608142\pi$
$439$	61027.5	−	35234.2i	0.316662	−	0.182825i	0.649904	+	0.760016i	$0.274809\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	183637.	−	318069.i	0.935736	−	1.62074i	0.162421	−	0.986722i	$-0.448070\pi$
$443$	183637.	−	318069.i	0.935736	−	1.62074i	0.773316	−	0.634021i	$-0.218597\pi$
$444$		0			0
$445$		−	153615.i		−	0.775738i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			11956.5i			0.0593078i	0.999560	+	0.0296539i	$0.00944051\pi$
$449$			11956.5i			0.0593078i	−0.999560	+	0.0296539i	$0.990559\pi$
$450$		0			0
$451$	−4875.32	+	2814.77i	−0.0239690	+	0.0138385i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	51925.6i		−	0.250818i
$456$		0			0
$457$	349838.			1.67508			0.837538	−	0.546379i	$-0.183994\pi$
$457$	349838.			1.67508			0.837538	+	0.546379i	$0.183994\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−122111.	−	211502.i	−0.574581	−	0.995204i	−0.996087	−	0.0883783i	$-0.971832\pi$
$461$	−122111.	−	211502.i	−0.574581	−	0.995204i	0.421506	−	0.906826i	$-0.361502\pi$
$462$		0			0
$463$	−187407.			−0.874225			−0.437113	−	0.899407i	$-0.643999\pi$
$463$	−187407.			−0.874225			−0.437113	+	0.899407i	$0.643999\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26421.6			0.121150			0.0605752	−	0.998164i	$-0.480707\pi$
$467$	26421.6			0.121150			0.0605752	+	0.998164i	$0.480707\pi$
$468$		0			0
$469$	−24242.8	−	13996.6i	−0.110214	−	0.0636321i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4134.77	−	7161.63i	−0.0184811	−	0.0320103i
$474$		0			0
$475$	135070.	+	64273.0i	0.598646	+	0.284866i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−112903.	+	195554.i	−0.492079	+	0.852306i	−0.999958	−	0.00912253i	$-0.997096\pi$
$479$	−112903.	+	195554.i	−0.492079	+	0.852306i	0.507880	+	0.861428i	$0.330430\pi$
$480$		0			0
$481$	−203950.	+	353252.i	−0.881523	+	1.52684i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−110434.	−	63759.0i	−0.469482	−	0.271055i
$486$		0			0
$487$		−	294086.i		−	1.23999i	−0.784607	−	0.619993i	$-0.787135\pi$
$487$		−	294086.i		−	1.23999i	0.784607	−	0.619993i	$-0.212865\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	183375.	+	317614.i	0.760634	+	1.31746i	0.942524	+	0.334139i	$0.108445\pi$
$491$	183375.	+	317614.i	0.760634	+	1.31746i	−0.181889	+	0.983319i	$0.558221\pi$
$492$		0			0
$493$		−	282704.i		−	1.16316i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17477.3	+	10090.5i	−0.0707557	+	0.0408508i
$498$		0			0
$499$	−93836.0	−	162529.i	−0.376850	−	0.652723i	0.613752	−	0.789499i	$-0.289659\pi$
$499$	−93836.0	−	162529.i	−0.376850	−	0.652723i	−0.990602	+	0.136776i	$0.956326\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24396.2	−	42255.4i	0.0964242	−	0.167012i	−0.813778	−	0.581176i	$-0.802593\pi$
$503$	24396.2	−	42255.4i	0.0964242	−	0.167012i	0.910202	+	0.414164i	$0.135926\pi$
$504$		0			0
$505$	128227.			0.502802
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−403454.	−	232934.i	−1.55725	−	0.899079i	−0.997518	−	0.0704060i	$-0.977571\pi$
$509$	−403454.	−	232934.i	−1.55725	−	0.899079i	−0.559733	−	0.828673i	$-0.689096\pi$
$510$		0			0
$511$	−43217.7	−	74855.2i	−0.165508	−	0.286669i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	120097.	−	69338.3i	0.452813	−	0.261432i
$516$		0			0
$517$	−49852.9	+	86347.8i	−0.186513	+	0.323050i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	159622.i		−	0.588053i	−0.955797	−	0.294027i	$-0.905005\pi$
$521$		−	159622.i		−	0.588053i	0.955797	−	0.294027i	$-0.0949954\pi$
$522$		0			0
$523$	−265246.	−	153140.i	−0.969716	−	0.559866i	−0.0705666	−	0.997507i	$-0.522481\pi$
$523$	−265246.	−	153140.i	−0.969716	−	0.559866i	−0.899150	+	0.437641i	$0.855814\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−77715.5	+	44869.0i	−0.279825	+	0.161557i
$528$		0			0
$529$	−90354.8	−	156499.i	−0.322879	−	0.559243i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	59881.9			0.210786
$534$		0			0
$535$	−43657.8	+	25205.9i	−0.152530	+	0.0880631i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−52247.6			−0.179841
$540$		0			0
$541$	25053.6	−	43394.0i	0.0856002	−	0.148264i	−0.820047	−	0.572297i	$-0.806053\pi$
$541$	25053.6	−	43394.0i	0.0856002	−	0.148264i	0.905647	+	0.424033i	$0.139386\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	225970.	+	130464.i	0.760777	+	0.439235i
$546$		0			0
$547$	350515.	+	202370.i	1.17147	+	0.676351i	0.954027	−	0.299722i	$-0.0968938\pi$
$547$	350515.	+	202370.i	1.17147	+	0.676351i	0.217447	+	0.976072i	$0.430227\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−163842.	+	344313.i	−0.539661	+	1.13410i
$552$		0			0
$553$	1269.38	−	732.876i	0.00415088	−	0.00239651i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−120982.	+	209546.i	−0.389950	+	0.675413i	−0.992442	−	0.122712i	$-0.960841\pi$
$557$	−120982.	+	209546.i	−0.389950	+	0.675413i	0.602493	+	0.798125i	$0.294174\pi$
$558$		0			0
$559$			87963.7i			0.281501i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			209485.i			0.660901i	0.943823	+	0.330450i	$0.107201\pi$
$563$			209485.i			0.660901i	−0.943823	+	0.330450i	$0.892799\pi$
$564$		0			0
$565$	75525.3	−	43604.6i	0.236590	−	0.136595i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			33843.1i			0.104531i	0.998633	+	0.0522655i	$0.0166442\pi$
$569$			33843.1i			0.104531i	−0.998633	+	0.0522655i	$0.983356\pi$
$570$		0			0
$571$	−414909.			−1.27257			−0.636284	−	0.771455i	$-0.719529\pi$
$571$	−414909.			−1.27257			−0.636284	+	0.771455i	$0.719529\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	140599.	+	243524.i	0.425251	+	0.736557i
$576$		0			0
$577$	−153388.			−0.460723			−0.230361	−	0.973105i	$-0.573991\pi$
$577$	−153388.			−0.460723			−0.230361	+	0.973105i	$0.573991\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−90308.0			−0.267531
$582$		0			0
$583$	79814.6	+	46081.0i	0.234826	+	0.135577i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	148051.	+	256432.i	0.429671	+	0.744212i	0.996844	−	0.0793866i	$-0.0252962\pi$
$587$	148051.	+	256432.i	0.429671	+	0.744212i	−0.567173	+	0.823599i	$0.691963\pi$
$588$		0			0
$589$	120656.	−	9607.12i	0.347791	−	0.0276925i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−214705.	+	371880.i	−0.610566	+	1.05753i	0.380580	+	0.924748i	$0.375725\pi$
$593$	−214705.	+	371880.i	−0.610566	+	1.05753i	−0.991145	+	0.132783i	$0.957609\pi$
$594$		0			0
$595$	27511.8	−	47651.8i	0.0777115	−	0.134600i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	598846.	+	345744.i	1.66902	+	0.963610i	0.968167	+	0.250305i	$0.0805309\pi$
$599$	598846.	+	345744.i	1.66902	+	0.963610i	0.700854	+	0.713305i	$0.252802\pi$
$600$		0			0
$601$		−	510299.i		−	1.41278i	−0.707821	−	0.706392i	$-0.750321\pi$
$601$		−	510299.i		−	1.41278i	0.707821	−	0.706392i	$-0.249679\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	102155.	+	176938.i	0.279094	+	0.483405i
$606$		0			0
$607$		−	497634.i		−	1.35062i	−0.737535	−	0.675309i	$-0.764010\pi$
$607$		−	497634.i		−	1.35062i	0.737535	−	0.675309i	$-0.235990\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	918489.	−	530290.i	2.46032	−	1.42047i
$612$		0			0
$613$	120296.	+	208358.i	0.320132	+	0.554484i	0.980515	−	0.196444i	$-0.0629395\pi$
$613$	120296.	+	208358.i	0.320132	+	0.554484i	−0.660383	+	0.750929i	$0.729606\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9342.69	−	16182.0i	0.0245415	−	0.0425072i	−0.853494	−	0.521103i	$-0.825521\pi$
$617$	9342.69	−	16182.0i	0.0245415	−	0.0425072i	0.878035	+	0.478596i	$0.158854\pi$
$618$		0			0
$619$	230388.			0.601282			0.300641	−	0.953737i	$-0.402799\pi$
$619$	230388.			0.601282			0.300641	+	0.953737i	$0.402799\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−129837.	−	74961.6i	−0.334521	−	0.193136i
$624$		0			0
$625$	−20018.4	−	34672.8i	−0.0512470	−	0.0887625i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−374328.	+	216118.i	−0.946130	+	0.546248i
$630$		0			0
$631$	52980.3	−	91764.6i	0.133062	−	0.230471i	−0.791793	−	0.610789i	$-0.790852\pi$
$631$	52980.3	−	91764.6i	0.133062	−	0.230471i	0.924856	+	0.380318i	$0.124186\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	346353.i		−	0.858957i
$636$		0			0
$637$	481304.	+	277881.i	1.18615	+	0.684826i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−109804.	+	63395.1i	−0.267239	+	0.154291i	−0.627632	−	0.778510i	$-0.715976\pi$
$641$	−109804.	+	63395.1i	−0.267239	+	0.154291i	0.360393	+	0.932801i	$0.382643\pi$
$642$		0			0
$643$	65121.8	+	112794.i	0.157509	+	0.272813i	0.933970	−	0.357352i	$-0.116320\pi$
$643$	65121.8	+	112794.i	0.157509	+	0.272813i	−0.776461	+	0.630165i	$0.782987\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−521278.			−1.24526			−0.622631	−	0.782516i	$-0.713936\pi$
$647$	−521278.			−1.24526			−0.622631	+	0.782516i	$0.713936\pi$
$648$		0			0
$649$	−41876.5	+	24177.4i	−0.0994216	+	0.0574011i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−458291.			−1.07477			−0.537385	−	0.843337i	$-0.680588\pi$
$653$	−458291.			−1.07477			−0.537385	+	0.843337i	$0.680588\pi$
$654$		0			0
$655$	24119.0	−	41775.3i	0.0562181	−	0.0973726i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	248511.	+	143478.i	0.572235	+	0.330380i	0.758042	−	0.652206i	$-0.226156\pi$
$659$	248511.	+	143478.i	0.572235	+	0.330380i	−0.185806	+	0.982586i	$0.559490\pi$
$660$		0			0
$661$	39674.5	+	22906.1i	0.0908047	+	0.0524261i	0.544715	−	0.838621i	$-0.316638\pi$
$661$	39674.5	+	22906.1i	0.0908047	+	0.0524261i	−0.453910	+	0.891047i	$0.649971\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−61124.1	+	42092.0i	−0.138220	+	0.0951823i
$666$		0			0
$667$	−620780.	+	358407.i	−1.39536	+	0.805611i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	75906.8	−	131474.i	0.168592	−	0.292009i
$672$		0			0
$673$			598607.i			1.32163i	0.750547	+	0.660817i	$0.229790\pi$
$673$			598607.i			1.32163i	−0.750547	+	0.660817i	$0.770210\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			10293.6i			0.0224590i	0.999937	+	0.0112295i	$0.00357454\pi$
$677$			10293.6i			0.0224590i	−0.999937	+	0.0112295i	$0.996425\pi$
$678$		0			0
$679$	−107780.	+	62226.6i	−0.233774	+	0.134970i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			519155.i			1.11290i	0.830881	+	0.556450i	$0.187837\pi$
$683$			519155.i			1.11290i	−0.830881	+	0.556450i	$0.812163\pi$
$684$		0			0
$685$	−404477.			−0.862010
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−490167.	−	848995.i	−1.03254	−	1.78841i
$690$		0			0
$691$	−504101.			−1.05575			−0.527876	−	0.849322i	$-0.677011\pi$
$691$	−504101.			−1.05575			−0.527876	+	0.849322i	$0.677011\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	133838.			0.277083
$696$		0			0
$697$	54953.3	+	31727.3i	0.113117	+	0.0653082i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	178216.	+	308678.i	0.362668	+	0.628160i	0.988399	−	0.151879i	$-0.0485325\pi$
$701$	178216.	+	308678.i	0.362668	+	0.628160i	−0.625731	+	0.780039i	$0.715199\pi$
$702$		0			0
$703$	581156.	−	46274.1i	1.17593	−	0.0936326i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	62572.5	−	108379.i	0.125183	−	0.216823i
$708$		0			0
$709$	−282984.	+	490143.i	−0.562949	+	0.975057i	0.434288	+	0.900774i	$0.357000\pi$
$709$	−282984.	+	490143.i	−0.562949	+	0.975057i	−0.997237	+	0.0742828i	$0.976333\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	197053.	+	113769.i	0.387618	+	0.223791i
$714$		0			0
$715$			87045.1i			0.170268i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	272553.	+	472076.i	0.527222	+	0.913175i	0.999497	+	0.0317237i	$0.0100997\pi$
$719$	272553.	+	472076.i	0.527222	+	0.913175i	−0.472275	+	0.881451i	$0.656567\pi$
$720$		0			0
$721$		−	135343.i		−	0.260356i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	379028.	−	218832.i	0.721100	−	0.416327i
$726$		0			0
$727$	482539.	+	835782.i	0.912985	+	1.58134i	0.809824	+	0.586672i	$0.199562\pi$
$727$	482539.	+	835782.i	0.912985	+	1.58134i	0.103161	+	0.994665i	$0.467104\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−46605.9	+	80723.9i	−0.0872181	+	0.151066i
$732$		0			0
$733$	308704.			0.574558			0.287279	−	0.957847i	$-0.407249\pi$
$733$	308704.			0.574558			0.287279	+	0.957847i	$0.407249\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	40639.2	+	23463.1i	0.0748188	+	0.0431966i
$738$		0			0
$739$	411918.	+	713463.i	0.754262	+	1.30642i	0.945741	+	0.324923i	$0.105338\pi$
$739$	411918.	+	713463.i	0.754262	+	1.30642i	−0.191479	+	0.981497i	$0.561328\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	518987.	−	299637.i	0.940110	−	0.542773i	0.0501149	−	0.998743i	$-0.484041\pi$
$743$	518987.	−	299637.i	0.940110	−	0.542773i	0.889995	+	0.455971i	$0.150708\pi$
$744$		0			0
$745$	279670.	−	484402.i	0.503887	−	0.872757i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			49200.1i			0.0877005i
$750$		0			0
$751$	880467.	+	508338.i	1.56111	+	0.901307i	0.997145	+	0.0755067i	$0.0240574\pi$
$751$	880467.	+	508338.i	1.56111	+	0.901307i	0.563963	+	0.825800i	$0.309276\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	531025.	−	306588.i	0.931583	−	0.537850i
$756$		0			0
$757$	−32294.5	−	55935.8i	−0.0563556	−	0.0976108i	0.836471	−	0.548011i	$-0.184615\pi$
$757$	−32294.5	−	55935.8i	−0.0563556	−	0.0976108i	−0.892827	+	0.450400i	$0.851281\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	551019.			0.951476			0.475738	−	0.879587i	$-0.342181\pi$
$761$	551019.			0.951476			0.475738	+	0.879587i	$0.342181\pi$
$762$		0			0
$763$	220539.	−	127328.i	0.378822	−	0.218713i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	514354.			0.874322
$768$		0			0
$769$	134363.	−	232724.i	0.227210	−	0.393540i	−0.729770	−	0.683693i	$-0.760373\pi$
$769$	134363.	−	232724.i	0.227210	−	0.393540i	0.956980	+	0.290153i	$0.0937062\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	560401.	+	323548.i	0.937864	+	0.541476i	0.889290	−	0.457344i	$-0.151199\pi$
$773$	560401.	+	323548.i	0.937864	+	0.541476i	0.0485738	+	0.998820i	$0.484532\pi$
$774$		0			0
$775$	−120314.	−	69463.4i	−0.200315	−	0.115652i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−48541.5	−	70489.9i	−0.0799905	−	0.116159i
$780$		0			0
$781$	29298.0	−	16915.2i	0.0480325	−	0.0277316i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	249015.	−	431307.i	0.404098	−	0.699918i
$786$		0			0
$787$			797943.i			1.28832i	0.764892	+	0.644158i	$0.222792\pi$
$787$			797943.i			1.28832i	−0.764892	+	0.644158i	$0.777208\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	85113.0i		−	0.136033i
$792$		0			0
$793$	−1.39850e6	+	807427.i	−2.22391	+	1.28398i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.05538e6i			1.66146i	0.556674	+	0.830731i	$0.312077\pi$
$797$			1.05538e6i			1.66146i	−0.556674	+	0.830731i	$0.687923\pi$
$798$		0			0
$799$	1.12386e6			1.76042
$800$		0			0
$801$		0			0
$802$		0			0
$803$	72447.7	+	125483.i	0.112355	+	0.194605i
$804$		0			0
$805$	−139516.			−0.215294
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.02438e6			−1.56518			−0.782590	−	0.622538i	$-0.786102\pi$
$809$	−1.02438e6			−1.56518			−0.782590	+	0.622538i	$0.786102\pi$
$810$		0			0
$811$	−925675.	−	534439.i	−1.40740	−	0.812562i	−0.412261	−	0.911066i	$-0.635261\pi$
$811$	−925675.	−	534439.i	−1.40740	−	0.812562i	−0.995137	+	0.0985039i	$0.968594\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12024.3	+	20826.7i	0.0181027	+	0.0313549i
$816$		0			0
$817$	103546.	−	71305.3i	0.155128	−	0.106826i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−410534.	+	711065.i	−0.609063	+	1.05493i	0.382332	+	0.924025i	$0.375121\pi$
$821$	−410534.	+	711065.i	−0.609063	+	1.05493i	−0.991395	+	0.130904i	$0.958212\pi$
$822$		0			0
$823$	341729.	−	591892.i	0.504524	−	0.873861i	−0.495462	−	0.868630i	$-0.665001\pi$
$823$	341729.	−	591892.i	0.504524	−	0.873861i	0.999986	−	0.00523191i	$-0.00166538\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.02004e6	−	588923.i	−1.49145	−	0.861088i	−0.491496	−	0.870880i	$-0.663550\pi$
$827$	−1.02004e6	−	588923.i	−1.49145	−	0.861088i	−0.999952	+	0.00979243i	$0.996883\pi$
$828$		0			0
$829$			353281.i			0.514056i	0.966404	+	0.257028i	$0.0827433\pi$
$829$			353281.i			0.514056i	−0.966404	+	0.257028i	$0.917257\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	294460.	+	510020.i	0.424362	+	0.735017i
$834$		0			0
$835$		−	318127.i		−	0.456277i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−766709.	+	442659.i	−1.08920	+	0.628848i	−0.933363	−	0.358935i	$-0.883140\pi$
$839$	−766709.	+	442659.i	−1.08920	+	0.628848i	−0.155834	+	0.987783i	$0.549807\pi$
$840$		0			0
$841$	204196.	+	353677.i	0.288705	+	0.500052i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	255692.	−	442871.i	0.358099	−	0.620245i
$846$		0			0
$847$	199400.			0.277945
$848$		0			0
$849$		0			0
$850$		0			0
$851$	949134.	+	547983.i	1.31059	+	0.756672i
$852$		0			0
$853$	387390.	+	670980.i	0.532415	+	0.922171i	0.999284	+	0.0378437i	$0.0120489\pi$
$853$	387390.	+	670980.i	0.532415	+	0.922171i	−0.466868	+	0.884327i	$0.654618\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−122350.	+	70638.6i	−0.166587	+	0.0961791i	−0.580976	−	0.813921i	$-0.697329\pi$
$857$	−122350.	+	70638.6i	−0.166587	+	0.0961791i	0.414388	+	0.910100i	$0.363995\pi$
$858$		0			0
$859$	−87213.3	+	151058.i	−0.118194	+	0.204718i	−0.919052	−	0.394136i	$-0.871044\pi$
$859$	−87213.3	+	151058.i	−0.118194	+	0.204718i	0.800858	+	0.598854i	$0.204377\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	119410.i		−	0.160332i	−0.996782	−	0.0801659i	$-0.974455\pi$
$863$		−	119410.i		−	0.160332i	0.996782	−	0.0801659i	$-0.0255450\pi$
$864$		0			0
$865$	−192309.	−	111030.i	−0.257020	−	0.148391i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2127.91	+	1228.55i	−0.00281783	+	0.00162687i
$870$		0			0
$871$	−249579.	−	432283.i	−0.328981	−	0.569812i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	213673.			0.279083
$876$		0			0
$877$	−1.01464e6	+	585802.i	−1.31920	+	0.761643i	−0.983601	−	0.180360i	$-0.942274\pi$
$877$	−1.01464e6	+	585802.i	−1.31920	+	0.761643i	−0.335604	+	0.942003i	$0.608940\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	800717.			1.03164			0.515819	−	0.856698i	$-0.327488\pi$
$881$	800717.			1.03164			0.515819	+	0.856698i	$0.327488\pi$
$882$		0			0
$883$	−307803.	+	533130.i	−0.394777	+	0.683773i	−0.993073	−	0.117502i	$-0.962511\pi$
$883$	−307803.	+	533130.i	−0.394777	+	0.683773i	0.598296	+	0.801275i	$0.295845\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.13476e6	−	655156.i	−1.44231	−	0.832717i	−0.444304	−	0.895876i	$-0.646549\pi$
$887$	−1.13476e6	−	655156.i	−1.44231	−	0.832717i	−0.998003	+	0.0631593i	$0.979882\pi$
$888$		0			0
$889$	−292741.	−	169014.i	−0.370408	−	0.213855i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.36878e6	−	651333.i	−1.71644	−	0.816771i
$894$		0			0
$895$	649112.	−	374765.i	0.810352	−	0.467857i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	177073.	−	306699.i	0.219095	−	0.379484i
$900$		0			0
$901$		−	1.03882e6i		−	1.27965i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			781779.i			0.954524i
$906$		0			0
$907$	818967.	−	472831.i	0.995525	−	0.574767i	0.0886037	−	0.996067i	$-0.471760\pi$
$907$	818967.	−	472831.i	0.995525	−	0.574767i	0.906921	+	0.421300i	$0.138426\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			385153.i			0.464084i	0.972706	+	0.232042i	$0.0745407\pi$
$911$			385153.i			0.464084i	−0.972706	+	0.232042i	$0.925459\pi$
$912$		0			0
$913$	151387.			0.181613
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23539.3	−	40771.2i	−0.0279933	−	0.0484858i
$918$		0			0
$919$	−673709.			−0.797703			−0.398852	−	0.917015i	$-0.630591\pi$
$919$	−673709.			−0.797703			−0.398852	+	0.917015i	$0.630591\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−359857.			−0.422402
$924$		0			0
$925$	−579510.	−	334580.i	−0.677295	−	0.391036i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	112707.	+	195214.i	0.130593	+	0.226193i	0.923905	−	0.382621i	$-0.124979\pi$
$929$	112707.	+	195214.i	0.130593	+	0.226193i	−0.793312	+	0.608815i	$0.791645\pi$
$930$		0			0
$931$	−63048.3	−	791823.i	−0.0727401	−	0.913543i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−46119.2	+	79880.9i	−0.0527544	+	0.0913733i
$936$		0			0
$937$	−3763.85	+	6519.17i	−0.00428699	+	0.00742529i	−0.868161	−	0.496283i	$-0.834698\pi$
$937$	−3763.85	+	6519.17i	−0.00428699	+	0.00742529i	0.863874	+	0.503708i	$0.168031\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	828882.	+	478555.i	0.936081	+	0.540447i	0.888730	−	0.458432i	$-0.151589\pi$
$941$	828882.	+	478555.i	0.936081	+	0.540447i	0.0473515	+	0.998878i	$0.484922\pi$
$942$		0			0
$943$		−	160893.i		−	0.180932i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	577837.	+	1.00084e6i	0.644326	+	1.11601i	0.984457	+	0.175627i	$0.0561953\pi$
$947$	577837.	+	1.00084e6i	0.644326	+	1.11601i	−0.340131	+	0.940378i	$0.610471\pi$
$948$		0			0
$949$		−	1.54127e6i		−	1.71137i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	614636.	−	354861.i	0.676757	−	0.390726i	−0.121875	−	0.992545i	$-0.538891\pi$
$953$	614636.	−	354861.i	0.676757	−	0.390726i	0.798632	+	0.601820i	$0.205557\pi$
$954$		0			0
$955$	−9474.60	−	16410.5i	−0.0103885	−	0.0179935i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−197377.	+	341868.i	−0.214615	+	0.371724i
$960$		0			0
$961$	811105.			0.878275
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−217566.	−	125612.i	−0.233635	−	0.134889i
$966$		0			0
$967$	125121.	+	216717.i	0.133807	+	0.231761i	0.925141	−	0.379623i	$-0.123946\pi$
$967$	125121.	+	216717.i	0.133807	+	0.231761i	−0.791334	+	0.611384i	$0.790613\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	675942.	−	390255.i	0.716921	−	0.413914i	−0.0966977	−	0.995314i	$-0.530828\pi$
$971$	675942.	−	390255.i	0.716921	−	0.413914i	0.813618	+	0.581400i	$0.197495\pi$
$972$		0			0
$973$	65310.5	−	113121.i	0.0689855	−	0.119486i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	966420.i		−	1.01246i	−0.862399	−	0.506229i	$-0.831039\pi$
$977$		−	966420.i		−	1.01246i	0.862399	−	0.506229i	$-0.168961\pi$
$978$		0			0
$979$	217652.	+	125662.i	0.227090	+	0.131110i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	683044.	−	394356.i	0.706874	−	0.408114i	−0.103029	−	0.994678i	$-0.532853\pi$
$983$	683044.	−	394356.i	0.706874	−	0.408114i	0.809902	+	0.586565i	$0.199520\pi$
$984$		0			0
$985$	−500984.	−	867730.i	−0.516359	−	0.894359i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	236345.			0.241632
$990$		0			0
$991$	−1.18412e6	+	683654.i	−1.20573	+	0.696128i	−0.961823	−	0.273672i	$-0.911762\pi$
$991$	−1.18412e6	+	683654.i	−1.20573	+	0.696128i	−0.243905	+	0.969799i	$0.578429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	33.7812			3.41216e−5
$996$		0			0
$997$	103797.	−	179781.i	0.104422	−	0.180865i	−0.809080	−	0.587699i	$-0.800034\pi$
$997$	103797.	−	179781.i	0.104422	−	0.180865i	0.913502	+	0.406834i	$0.133367\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.e.145.3		14
3.2	odd	2		228.5.l.a.145.5	✓	14
19.8	odd	6	inner	684.5.y.e.217.3		14
57.8	even	6		228.5.l.a.217.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.a.145.5	✓	14	3.2	odd	2
228.5.l.a.217.5	yes	14	57.8	even	6
684.5.y.e.145.3		14	1.1	even	1	trivial
684.5.y.e.217.3		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)

\(f(q)\)	\(=\)	\(q+(-7.25681 - 12.5692i) q^{5} -14.1648 q^{7} +O(q^{10})\)	\(q+(-7.25681 - 12.5692i) q^{5} -14.1648 q^{7} +23.7451 q^{11} +(-218.739 - 126.289i) q^{13} +(-133.824 - 231.790i) q^{17} +(28.6536 + 359.861i) q^{19} +(-339.319 + 587.718i) q^{23} +(207.177 - 358.842i) q^{25} +(914.743 + 528.127i) q^{29} -335.285i q^{31} +(102.791 + 178.039i) q^{35} -1614.95i q^{37} +(-205.320 + 118.541i) q^{41} +(-174.132 - 301.605i) q^{43} +(-2099.51 + 3636.45i) q^{47} -2200.36 q^{49} +(3361.32 + 1940.66i) q^{53} +(-172.313 - 298.455i) q^{55} +(-1763.59 + 1018.21i) q^{59} +(3196.74 - 5536.92i) q^{61} +3665.82i q^{65} +(1711.48 + 988.125i) q^{67} +(1233.86 - 712.367i) q^{71} +(3051.07 + 5284.60i) q^{73} -336.343 q^{77} +(-89.6151 + 51.7393i) q^{79} +6375.53 q^{83} +(-1942.27 + 3364.11i) q^{85} +(9166.21 + 5292.11i) q^{89} +(3098.39 + 1788.86i) q^{91} +(4315.22 - 2971.60i) q^{95} +(7608.98 - 4393.05i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 30 q^{5} + 106 q^{7}+O(q^{10}) \) 14 * q + 30 * q^5 + 106 * q^7	\( 14 q + 30 q^{5} + 106 q^{7} + 264 q^{11} + 57 q^{13} - 282 q^{17} + 2 q^{19} - 96 q^{23} - 465 q^{25} + 630 q^{29} - 1434 q^{35} + 228 q^{41} - 2093 q^{43} + 4710 q^{47} + 4440 q^{49} - 2364 q^{53} + 6368 q^{55} - 11838 q^{59} - 1661 q^{61} - 20319 q^{67} - 624 q^{71} + 5851 q^{73} + 1080 q^{77} - 13299 q^{79} - 12252 q^{83} - 5740 q^{85} + 20010 q^{89} + 15951 q^{91} - 7770 q^{95} + 44904 q^{97}+O(q^{100}) \) 14 * q + 30 * q^5 + 106 * q^7 + 264 * q^11 + 57 * q^13 - 282 * q^17 + 2 * q^19 - 96 * q^23 - 465 * q^25 + 630 * q^29 - 1434 * q^35 + 228 * q^41 - 2093 * q^43 + 4710 * q^47 + 4440 * q^49 - 2364 * q^53 + 6368 * q^55 - 11838 * q^59 - 1661 * q^61 - 20319 * q^67 - 624 * q^71 + 5851 * q^73 + 1080 * q^77 - 13299 * q^79 - 12252 * q^83 - 5740 * q^85 + 20010 * q^89 + 15951 * q^91 - 7770 * q^95 + 44904 * q^97

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