LMFDB - Embedded newform 810.4.c.b.649.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,4,Mod(649,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("810.649");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	810.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} + 8 x^{8} + 326 x^{7} + 17389 x^{6} - 26726 x^{5} + 20930 x^{4} + 60664 x^{3} + \cdots + 5604552 $ x^10 - 4x^9 + 8x^8 + 326x^7 + 17389x^6 - 26726x^5 + 20930x^4 + 60664x^3 + 4452100x^2 - 7064280*x + 5604552
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.7
Root			$8.80143 + 8.80143i$ of defining polynomial
Character	$\chi$	$=$	810.649
Dual form			810.4.c.b.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -4.00000 q^{4} +(-4.01358 - 10.4351i) q^{5} +14.0253i q^{7} -8.00000i q^{8} +(20.8702 - 8.02717i) q^{10} -52.5103 q^{11} -21.1274i q^{13} -28.0507 q^{14} +16.0000 q^{16} +82.7470i q^{17} +0.509099 q^{19} +(16.0543 + 41.7404i) q^{20} -105.021i q^{22} -25.9505i q^{23} +(-92.7823 + 83.7642i) q^{25} +42.2548 q^{26} -56.1014i q^{28} -46.6800 q^{29} +189.954 q^{31} +32.0000i q^{32} -165.494 q^{34} +(146.356 - 56.2919i) q^{35} -115.919i q^{37} +1.01820i q^{38} +(-83.4807 + 32.1087i) q^{40} +148.335 q^{41} +239.050i q^{43} +210.041 q^{44} +51.9011 q^{46} -565.182i q^{47} +146.290 q^{49} +(-167.528 - 185.565i) q^{50} +84.5096i q^{52} -391.662i q^{53} +(210.755 + 547.950i) q^{55} +112.203 q^{56} -93.3599i q^{58} -653.898 q^{59} +706.549 q^{61} +379.907i q^{62} -64.0000 q^{64} +(-220.466 + 84.7966i) q^{65} -276.287i q^{67} -330.988i q^{68} +(112.584 + 292.712i) q^{70} +1005.28 q^{71} +488.491i q^{73} +231.837 q^{74} -2.03640 q^{76} -736.476i q^{77} +653.783 q^{79} +(-64.2174 - 166.961i) q^{80} +296.670i q^{82} -394.215i q^{83} +(863.472 - 332.112i) q^{85} -478.099 q^{86} +420.083i q^{88} +1003.84 q^{89} +296.319 q^{91} +103.802i q^{92} +1130.36 q^{94} +(-2.04331 - 5.31250i) q^{95} -680.290i q^{97} +292.579i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 40 q^{4} + 22 q^{5} - 4 q^{10} - 28 q^{11} - 4 q^{14} + 160 q^{16} - 42 q^{19} - 88 q^{20} + 96 q^{25} - 108 q^{26} + 216 q^{29} + 88 q^{31} - 64 q^{34} - 22 q^{35} + 16 q^{40} + 38 q^{41} + 112 q^{44}+ \cdots + 2472 q^{95}+O(q^{100}) $ 10 * q - 40 * q^4 + 22 * q^5 - 4 * q^10 - 28 * q^11 - 4 * q^14 + 160 * q^16 - 42 * q^19 - 88 * q^20 + 96 * q^25 - 108 * q^26 + 216 * q^29 + 88 * q^31 - 64 * q^34 - 22 * q^35 + 16 * q^40 + 38 * q^41 + 112 * q^44 + 172 * q^46 - 1452 * q^49 + 256 * q^50 + 20 * q^55 + 16 * q^56 - 2050 * q^59 + 1064 * q^61 - 640 * q^64 - 2268 * q^65 + 464 * q^70 - 2844 * q^71 + 584 * q^74 + 168 * q^76 - 1608 * q^79 + 352 * q^80 - 526 * q^85 + 184 * q^86 + 1132 * q^89 + 3402 * q^91 - 1268 * q^94 + 2472 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	−4.01358	−	10.4351i	−0.358986	−	0.933343i
$5$	−4.01358	−	10.4351i	−0.358986	−	0.933343i
$6$		0			0
$7$			14.0253i			0.757298i	0.925540	+	0.378649i	$0.123611\pi$
$7$			14.0253i			0.757298i	−0.925540	+	0.378649i	$0.876389\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	20.8702	−	8.02717i	0.659973	−	0.253841i
$11$	−52.5103			−1.43931			−0.719657	−	0.694330i	$-0.755701\pi$
$11$	−52.5103			−1.43931			−0.719657	+	0.694330i	$0.755701\pi$
$12$		0			0
$13$		−	21.1274i		−	0.450745i	−0.974273	−	0.225373i	$-0.927640\pi$
$13$		−	21.1274i		−	0.450745i	0.974273	−	0.225373i	$-0.0723599\pi$
$14$	−28.0507			−0.535490
$15$		0			0
$16$	16.0000			0.250000
$17$			82.7470i			1.18053i	0.807208	+	0.590267i	$0.200978\pi$
$17$			82.7470i			1.18053i	−0.807208	+	0.590267i	$0.799022\pi$
$18$		0			0
$19$	0.509099			0.00614712			0.00307356	−	0.999995i	$-0.499022\pi$
$19$	0.509099			0.00614712			0.00307356	+	0.999995i	$0.499022\pi$
$20$	16.0543	+	41.7404i	0.179493	+	0.466671i
$21$		0			0
$22$		−	105.021i		−	1.01775i
$23$		−	25.9505i		−	0.235263i	−0.993057	−	0.117632i	$-0.962470\pi$
$23$		−	25.9505i		−	0.235263i	0.993057	−	0.117632i	$-0.0375302\pi$
$24$		0			0
$25$	−92.7823	+	83.7642i	−0.742258	+	0.670114i
$26$	42.2548			0.318725
$27$		0			0
$28$		−	56.1014i		−	0.378649i
$29$	−46.6800			−0.298905			−0.149453	−	0.988769i	$-0.547751\pi$
$29$	−46.6800			−0.298905			−0.149453	+	0.988769i	$0.547751\pi$
$30$		0			0
$31$	189.954			1.10054			0.550269	−	0.834987i	$-0.314525\pi$
$31$	189.954			1.10054			0.550269	+	0.834987i	$0.314525\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	−165.494			−0.834764
$35$	146.356	−	56.2919i	0.706818	−	0.271859i
$36$		0			0
$37$		−	115.919i		−	0.515051i	−0.966271	−	0.257526i	$-0.917093\pi$
$37$		−	115.919i		−	0.515051i	0.966271	−	0.257526i	$-0.0829072\pi$
$38$			1.01820i			0.00434667i
$39$		0			0
$40$	−83.4807	+	32.1087i	−0.329987	+	0.126921i
$41$	148.335			0.565025			0.282512	−	0.959264i	$-0.408832\pi$
$41$	148.335			0.565025			0.282512	+	0.959264i	$0.408832\pi$
$42$		0			0
$43$			239.050i			0.847784i	0.905713	+	0.423892i	$0.139336\pi$
$43$			239.050i			0.847784i	−0.905713	+	0.423892i	$0.860664\pi$
$44$	210.041			0.719657
$45$		0			0
$46$	51.9011			0.166356
$47$		−	565.182i		−	1.75405i	−0.480447	−	0.877024i	$-0.659526\pi$
$47$		−	565.182i		−	1.75405i	0.480447	−	0.877024i	$-0.340474\pi$
$48$		0			0
$49$	146.290			0.426500
$50$	−167.528	−	185.565i	−0.473842	−	0.524856i
$51$		0			0
$52$			84.5096i			0.225373i
$53$		−	391.662i		−	1.01507i	−0.861630	−	0.507537i	$-0.830556\pi$
$53$		−	391.662i		−	1.01507i	0.861630	−	0.507537i	$-0.169444\pi$
$54$		0			0
$55$	210.755	+	547.950i	0.516694	+	1.34337i
$56$	112.203			0.267745
$57$		0			0
$58$		−	93.3599i		−	0.211358i
$59$	−653.898			−1.44289			−0.721443	−	0.692474i	$-0.756521\pi$
$59$	−653.898			−1.44289			−0.721443	+	0.692474i	$0.756521\pi$
$60$		0			0
$61$	706.549			1.48302			0.741511	−	0.670941i	$-0.234110\pi$
$61$	706.549			1.48302			0.741511	+	0.670941i	$0.234110\pi$
$62$			379.907i			0.778198i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−220.466	+	84.7966i	−0.420700	+	0.161811i
$66$		0			0
$67$		−	276.287i		−	0.503788i	−0.967755	−	0.251894i	$-0.918947\pi$
$67$		−	276.287i		−	0.503788i	0.967755	−	0.251894i	$-0.0810534\pi$
$68$		−	330.988i		−	0.590267i
$69$		0			0
$70$	112.584	+	292.712i	0.192233	+	0.499796i
$71$	1005.28			1.68035			0.840177	−	0.542313i	$-0.182451\pi$
$71$	1005.28			1.68035			0.840177	+	0.542313i	$0.182451\pi$
$72$		0			0
$73$			488.491i			0.783199i	0.920136	+	0.391600i	$0.128078\pi$
$73$			488.491i			0.783199i	−0.920136	+	0.391600i	$0.871922\pi$
$74$	231.837			0.364196
$75$		0			0
$76$	−2.03640			−0.00307356
$77$		−	736.476i		−	1.08999i
$78$		0			0
$79$	653.783			0.931092			0.465546	−	0.885024i	$-0.345858\pi$
$79$	653.783			0.931092			0.465546	+	0.885024i	$0.345858\pi$
$80$	−64.2174	−	166.961i	−0.0897465	−	0.233336i
$81$		0			0
$82$			296.670i			0.399533i
$83$		−	394.215i		−	0.521334i	−0.965429	−	0.260667i	$-0.916058\pi$
$83$		−	394.215i		−	0.521334i	0.965429	−	0.260667i	$-0.0839425\pi$
$84$		0			0
$85$	863.472	−	332.112i	1.10184	−	0.423795i
$86$	−478.099			−0.599474
$87$		0			0
$88$			420.083i			0.508874i
$89$	1003.84			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$89$	1003.84			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$90$		0			0
$91$	296.319			0.341348
$92$			103.802i			0.117632i
$93$		0			0
$94$	1130.36			1.24030
$95$	−2.04331	−	5.31250i	−0.00220673	−	0.00573738i
$96$		0			0
$97$		−	680.290i		−	0.712093i	−0.934468	−	0.356046i	$-0.884125\pi$
$97$		−	680.290i		−	0.712093i	0.934468	−	0.356046i	$-0.115875\pi$
$98$			292.579i			0.301581i
$99$		0			0
$100$	371.129	−	335.057i	0.371129	−	0.335057i
$101$	1681.27			1.65636			0.828179	−	0.560463i	$-0.189377\pi$
$101$	1681.27			1.65636			0.828179	+	0.560463i	$0.189377\pi$
$102$		0			0
$103$			776.043i			0.742386i	0.928556	+	0.371193i	$0.121051\pi$
$103$			776.043i			0.742386i	−0.928556	+	0.371193i	$0.878949\pi$
$104$	−169.019			−0.159362
$105$		0			0
$106$	783.324			0.717766
$107$			428.280i			0.386947i	0.981105	+	0.193474i	$0.0619754\pi$
$107$			428.280i			0.386947i	−0.981105	+	0.193474i	$0.938025\pi$
$108$		0			0
$109$	1218.41			1.07067			0.535334	−	0.844641i	$-0.320186\pi$
$109$	1218.41			1.07067			0.535334	+	0.844641i	$0.320186\pi$
$110$	−1095.90	+	421.509i	−0.949909	+	0.365358i
$111$		0			0
$112$			224.406i			0.189324i
$113$		−	1635.43i		−	1.36149i	−0.732522	−	0.680743i	$-0.761657\pi$
$113$		−	1635.43i		−	1.36149i	0.732522	−	0.680743i	$-0.238343\pi$
$114$		0			0
$115$	−270.796	+	104.155i	−0.219581	+	0.0844563i
$116$	186.720			0.149453
$117$		0			0
$118$		−	1307.80i		−	1.02027i
$119$	−1160.56			−0.894016
$120$		0			0
$121$	1426.33			1.07163
$122$			1413.10i			1.04865i
$123$		0			0
$124$	−759.814			−0.550269
$125$	1246.48	+	631.997i	0.891906	+	0.452220i
$126$		0			0
$127$			1122.34i			0.784184i	0.919926	+	0.392092i	$0.128249\pi$
$127$			1122.34i			0.784184i	−0.919926	+	0.392092i	$0.871751\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	−169.593	−	440.933i	−0.114418	−	0.297480i
$131$	−2216.10			−1.47803			−0.739014	−	0.673691i	$-0.764708\pi$
$131$	−2216.10			−1.47803			−0.739014	+	0.673691i	$0.764708\pi$
$132$		0			0
$133$			7.14029i			0.00465520i
$134$	552.573			0.356232
$135$		0			0
$136$	661.976			0.417382
$137$			2456.05i			1.53164i	0.643055	+	0.765820i	$0.277667\pi$
$137$			2456.05i			1.53164i	−0.643055	+	0.765820i	$0.722333\pi$
$138$		0			0
$139$	−1445.09			−0.881805			−0.440903	−	0.897555i	$-0.645342\pi$
$139$	−1445.09			−0.881805			−0.440903	+	0.897555i	$0.645342\pi$
$140$	−585.423	+	225.168i	−0.353409	+	0.135930i
$141$		0			0
$142$			2010.56i			1.18819i
$143$			1109.41i			0.648764i
$144$		0			0
$145$	187.354	+	487.110i	0.107303	+	0.278981i
$146$	−976.982			−0.553806
$147$		0			0
$148$			463.674i			0.257526i
$149$	−2266.69			−1.24627			−0.623135	−	0.782114i	$-0.714141\pi$
$149$	−2266.69			−1.24627			−0.623135	+	0.782114i	$0.714141\pi$
$150$		0			0
$151$	1649.79			0.889124			0.444562	−	0.895748i	$-0.353359\pi$
$151$	1649.79			0.889124			0.444562	+	0.895748i	$0.353359\pi$
$152$		−	4.07279i		−	0.00217334i
$153$		0			0
$154$	1472.95			0.770739
$155$	−762.395	−	1982.18i	−0.395078	−	1.02718i
$156$		0			0
$157$			3307.20i			1.68117i	0.541680	+	0.840585i	$0.317788\pi$
$157$			3307.20i			1.68117i	−0.541680	+	0.840585i	$0.682212\pi$
$158$			1307.57i			0.658382i
$159$		0			0
$160$	333.923	−	128.435i	0.164993	−	0.0634603i
$161$	363.965			0.178164
$162$		0			0
$163$		−	483.406i		−	0.232290i	−0.993232	−	0.116145i	$-0.962946\pi$
$163$		−	483.406i		−	0.232290i	0.993232	−	0.116145i	$-0.0370538\pi$
$164$	−593.339			−0.282512
$165$		0			0
$166$	788.430			0.368639
$167$		−	582.296i		−	0.269817i	−0.990858	−	0.134908i	$-0.956926\pi$
$167$		−	582.296i		−	0.269817i	0.990858	−	0.134908i	$-0.0430740\pi$
$168$		0			0
$169$	1750.63			0.796829
$170$	664.224	+	1726.94i	0.299669	+	0.779121i
$171$		0			0
$172$		−	956.199i		−	0.423892i
$173$		−	2283.85i		−	1.00369i	−0.864958	−	0.501844i	$-0.832655\pi$
$173$		−	2283.85i		−	1.00369i	0.864958	−	0.501844i	$-0.167345\pi$
$174$		0			0
$175$	−1174.82	−	1301.30i	−0.507476	−	0.562110i
$176$	−840.165			−0.359829
$177$		0			0
$178$			2007.68i			0.845405i
$179$	3122.10			1.30367			0.651834	−	0.758361i	$-0.274000\pi$
$179$	3122.10			1.30367			0.651834	+	0.758361i	$0.274000\pi$
$180$		0			0
$181$	579.179			0.237845			0.118923	−	0.992904i	$-0.462056\pi$
$181$	579.179			0.237845			0.118923	+	0.992904i	$0.462056\pi$
$182$			592.638i			0.241370i
$183$		0			0
$184$	−207.604			−0.0831782
$185$	−1209.62	+	465.249i	−0.480720	+	0.184896i
$186$		0			0
$187$		−	4345.07i		−	1.69916i
$188$			2260.73i			0.877024i
$189$		0			0
$190$	10.6250	−	4.08663i	0.00405694	−	0.00156039i
$191$	−658.943			−0.249631			−0.124815	−	0.992180i	$-0.539834\pi$
$191$	−658.943			−0.249631			−0.124815	+	0.992180i	$0.539834\pi$
$192$		0			0
$193$			2039.19i			0.760541i	0.924875	+	0.380270i	$0.124169\pi$
$193$			2039.19i			0.760541i	−0.924875	+	0.380270i	$0.875831\pi$
$194$	1360.58			0.503526
$195$		0			0
$196$	−585.159			−0.213250
$197$			763.154i			0.276002i	0.990432	+	0.138001i	$0.0440678\pi$
$197$			763.154i			0.276002i	−0.990432	+	0.138001i	$0.955932\pi$
$198$		0			0
$199$	−2025.78			−0.721627			−0.360814	−	0.932638i	$-0.617501\pi$
$199$	−2025.78			−0.721627			−0.360814	+	0.932638i	$0.617501\pi$
$200$	670.114	+	742.258i	0.236921	+	0.262428i
$201$		0			0
$202$			3362.53i			1.17122i
$203$		−	654.703i		−	0.226360i
$204$		0			0
$205$	−595.355	−	1547.89i	−0.202836	−	0.527362i
$206$	−1552.09			−0.524946
$207$		0			0
$208$		−	338.038i		−	0.112686i
$209$	−26.7330			−0.00884764
$210$		0			0
$211$	1416.50			0.462162			0.231081	−	0.972935i	$-0.425774\pi$
$211$	1416.50			0.462162			0.231081	+	0.972935i	$0.425774\pi$
$212$			1566.65i			0.507537i
$213$		0			0
$214$	−856.559			−0.273613
$215$	2494.51	−	959.446i	0.791274	−	0.304343i
$216$		0			0
$217$			2664.17i			0.833435i
$218$			2436.82i			0.757076i
$219$		0			0
$220$	−843.018	−	2191.80i	−0.258347	−	0.671687i
$221$	1748.23			0.532120
$222$		0			0
$223$		−	5434.74i		−	1.63201i	−0.578047	−	0.816003i	$-0.696185\pi$
$223$		−	5434.74i		−	1.63201i	0.578047	−	0.816003i	$-0.303815\pi$
$224$	−448.811			−0.133873
$225$		0			0
$226$	3270.85			0.962717
$227$			3327.34i			0.972877i	0.873715	+	0.486438i	$0.161704\pi$
$227$			3327.34i			0.972877i	−0.873715	+	0.486438i	$0.838296\pi$
$228$		0			0
$229$	2357.60			0.680325			0.340163	−	0.940367i	$-0.389518\pi$
$229$	2357.60			0.680325			0.340163	+	0.940367i	$0.389518\pi$
$230$	−208.309	−	541.592i	−0.0597196	−	0.155268i
$231$		0			0
$232$			373.440i			0.105679i
$233$		−	6083.13i		−	1.71038i	−0.518312	−	0.855191i	$-0.673439\pi$
$233$		−	6083.13i		−	1.71038i	0.518312	−	0.855191i	$-0.326561\pi$
$234$		0			0
$235$	−5897.72	+	2268.40i	−1.63713	+	0.629678i
$236$	2615.59			0.721443
$237$		0			0
$238$		−	2321.11i		−	0.632165i
$239$	3620.05			0.979754			0.489877	−	0.871791i	$-0.337042\pi$
$239$	3620.05			0.979754			0.489877	+	0.871791i	$0.337042\pi$
$240$		0			0
$241$	2887.00			0.771651			0.385825	−	0.922572i	$-0.373917\pi$
$241$	2887.00			0.771651			0.385825	+	0.922572i	$0.373917\pi$
$242$			2852.67i			0.757754i
$243$		0			0
$244$	−2826.19			−0.741511
$245$	−587.146	−	1526.55i	−0.153108	−	0.398071i
$246$		0			0
$247$		−	10.7559i		−	0.00277079i
$248$		−	1519.63i		−	0.389099i
$249$		0			0
$250$	−1263.99	+	2492.95i	−0.319768	+	0.630673i
$251$	−7003.18			−1.76110			−0.880551	−	0.473951i	$-0.842827\pi$
$251$	−7003.18			−1.76110			−0.880551	+	0.473951i	$0.842827\pi$
$252$		0			0
$253$			1362.67i			0.338618i
$254$	−2244.68			−0.554502
$255$		0			0
$256$	256.000			0.0625000
$257$			1085.48i			0.263464i	0.991285	+	0.131732i	$0.0420538\pi$
$257$			1085.48i			0.263464i	−0.991285	+	0.131732i	$0.957946\pi$
$258$		0			0
$259$	1625.80			0.390047
$260$	881.865	−	339.186i	0.210350	−	0.0809056i
$261$		0			0
$262$		−	4432.20i		−	1.04512i
$263$		−	3824.97i		−	0.896798i	−0.893833	−	0.448399i	$-0.851994\pi$
$263$		−	3824.97i		−	0.896798i	0.893833	−	0.448399i	$-0.148006\pi$
$264$		0			0
$265$	−4087.03	+	1571.97i	−0.947412	+	0.364397i
$266$	−14.2806			−0.00329173
$267$		0			0
$268$			1105.15i			0.251894i
$269$	−1867.03			−0.423178			−0.211589	−	0.977359i	$-0.567864\pi$
$269$	−1867.03			−0.423178			−0.211589	+	0.977359i	$0.567864\pi$
$270$		0			0
$271$	5572.42			1.24908			0.624540	−	0.780993i	$-0.285286\pi$
$271$	5572.42			1.24908			0.624540	+	0.780993i	$0.285286\pi$
$272$			1323.95i			0.295134i
$273$		0			0
$274$	−4912.10			−1.08303
$275$	4872.03	−	4398.49i	1.06834	−	0.964505i
$276$		0			0
$277$		−	6954.86i		−	1.50858i	−0.656540	−	0.754291i	$-0.727981\pi$
$277$		−	6954.86i		−	1.50858i	0.656540	−	0.754291i	$-0.272019\pi$
$278$		−	2890.18i		−	0.623531i
$279$		0			0
$280$	−450.335	−	1170.85i	−0.0961167	−	0.249898i
$281$	7779.54			1.65156			0.825780	−	0.563992i	$-0.190735\pi$
$281$	7779.54			1.65156			0.825780	+	0.563992i	$0.190735\pi$
$282$		0			0
$283$		−	2928.65i		−	0.615160i	−0.951522	−	0.307580i	$-0.900481\pi$
$283$		−	2928.65i		−	0.615160i	0.951522	−	0.307580i	$-0.0995191\pi$
$284$	−4021.13			−0.840177
$285$		0			0
$286$	−2218.81			−0.458745
$287$			2080.45i			0.427892i
$288$		0			0
$289$	−1934.06			−0.393663
$290$	−974.219	+	374.708i	−0.197269	+	0.0758745i
$291$		0			0
$292$		−	1953.96i		−	0.391600i
$293$		−	537.860i		−	0.107243i	−0.998561	−	0.0536214i	$-0.982924\pi$
$293$		−	537.860i		−	0.107243i	0.998561	−	0.0536214i	$-0.0170764\pi$
$294$		0			0
$295$	2624.48	+	6823.49i	0.517976	+	1.34671i
$296$	−927.349			−0.182098
$297$		0			0
$298$		−	4533.37i		−	0.881246i
$299$	−548.267			−0.106044
$300$		0			0
$301$	−3352.75			−0.642025
$302$			3299.57i			0.628705i
$303$		0			0
$304$	8.14559			0.00153678
$305$	−2835.79	−	7372.90i	−0.532384	−	1.38417i
$306$		0			0
$307$		−	656.196i		−	0.121991i	−0.998138	−	0.0609953i	$-0.980573\pi$
$307$		−	656.196i		−	0.121991i	0.998138	−	0.0609953i	$-0.0194275\pi$
$308$			2945.90i			0.544995i
$309$		0			0
$310$	3964.37	−	1524.79i	0.726325	−	0.279362i
$311$	659.872			0.120315			0.0601574	−	0.998189i	$-0.480840\pi$
$311$	659.872			0.120315			0.0601574	+	0.998189i	$0.480840\pi$
$312$		0			0
$313$			8839.73i			1.59633i	0.602439	+	0.798165i	$0.294196\pi$
$313$			8839.73i			1.59633i	−0.602439	+	0.798165i	$0.705804\pi$
$314$	−6614.41			−1.18877
$315$		0			0
$316$	−2615.13			−0.465546
$317$		−	8168.32i		−	1.44725i	−0.690193	−	0.723625i	$-0.742474\pi$
$317$		−	8168.32i		−	1.44725i	0.690193	−	0.723625i	$-0.257526\pi$
$318$		0			0
$319$	2451.18			0.430219
$320$	256.869	+	667.846i	0.0448732	+	0.116668i
$321$		0			0
$322$			727.930i			0.125981i
$323$			42.1264i			0.00725690i
$324$		0			0
$325$	1769.72	+	1960.25i	0.302051	+	0.334569i
$326$	966.813			0.164254
$327$		0			0
$328$		−	1186.68i		−	0.199766i
$329$	7926.87			1.32834
$330$		0			0
$331$	−9601.08			−1.59433			−0.797165	−	0.603762i	$-0.793668\pi$
$331$	−9601.08			−1.59433			−0.797165	+	0.603762i	$0.793668\pi$
$332$			1576.86i			0.260667i
$333$		0			0
$334$	1164.59			0.190789
$335$	−2883.08	+	1108.90i	−0.470207	+	0.180853i
$336$		0			0
$337$			7616.16i			1.23109i	0.788100	+	0.615547i	$0.211065\pi$
$337$			7616.16i			1.23109i	−0.788100	+	0.615547i	$0.788935\pi$
$338$			3501.27i			0.563443i
$339$		0			0
$340$	−3453.89	+	1328.45i	−0.550922	+	0.211898i
$341$	−9974.53			−1.58402
$342$		0			0
$343$			6862.46i			1.08029i
$344$	1912.40			0.299737
$345$		0			0
$346$	4567.70			0.709715
$347$			8132.41i			1.25813i	0.777354	+	0.629064i	$0.216562\pi$
$347$			8132.41i			1.25813i	−0.777354	+	0.629064i	$0.783438\pi$
$348$		0			0
$349$	−10738.2			−1.64699			−0.823497	−	0.567321i	$-0.807980\pi$
$349$	−10738.2			−1.64699			−0.823497	+	0.567321i	$0.807980\pi$
$350$	2602.61	−	2349.65i	0.397472	−	0.358839i
$351$		0			0
$352$		−	1680.33i		−	0.254437i
$353$			2000.45i			0.301624i	0.988562	+	0.150812i	$0.0481888\pi$
$353$			2000.45i			0.301624i	−0.988562	+	0.150812i	$0.951811\pi$
$354$		0			0
$355$	−4034.79	−	10490.2i	−0.603223	−	1.56835i
$356$	−4015.36			−0.597792
$357$		0			0
$358$			6244.20i			0.921833i
$359$	2760.83			0.405880			0.202940	−	0.979191i	$-0.434950\pi$
$359$	2760.83			0.405880			0.202940	+	0.979191i	$0.434950\pi$
$360$		0			0
$361$	−6858.74			−0.999962
$362$			1158.36i			0.168182i
$363$		0			0
$364$	−1185.28			−0.170674
$365$	5097.45	−	1960.60i	0.730994	−	0.281158i
$366$		0			0
$367$		−	8673.55i		−	1.23367i	−0.787094	−	0.616833i	$-0.788415\pi$
$367$		−	8673.55i		−	1.23367i	0.787094	−	0.616833i	$-0.211585\pi$
$368$		−	415.208i		−	0.0588159i
$369$		0			0
$370$	−930.498	−	2419.24i	−0.130741	−	0.339920i
$371$	5493.20			0.768713
$372$		0			0
$373$		−	13507.5i		−	1.87504i	−0.347929	−	0.937521i	$-0.613115\pi$
$373$		−	13507.5i		−	1.87504i	0.347929	−	0.937521i	$-0.386885\pi$
$374$	8690.14			1.20149
$375$		0			0
$376$	−4521.45			−0.620149
$377$			986.226i			0.134730i
$378$		0			0
$379$	−6177.16			−0.837202			−0.418601	−	0.908170i	$-0.637479\pi$
$379$	−6177.16			−0.837202			−0.418601	+	0.908170i	$0.637479\pi$
$380$	8.17325	+	21.2500i	0.00110337	+	0.00286869i
$381$		0			0
$382$		−	1317.89i		−	0.176515i
$383$			212.553i			0.0283576i	0.999899	+	0.0141788i	$0.00451340\pi$
$383$			212.553i			0.0283576i	−0.999899	+	0.0141788i	$0.995487\pi$
$384$		0			0
$385$	−7685.19	+	2955.91i	−1.01733	+	0.391291i
$386$	−4078.39			−0.537783
$387$		0			0
$388$			2721.16i			0.356046i
$389$	1006.08			0.131131			0.0655657	−	0.997848i	$-0.479115\pi$
$389$	1006.08			0.131131			0.0655657	+	0.997848i	$0.479115\pi$
$390$		0			0
$391$	2147.33			0.277737
$392$		−	1170.32i		−	0.150791i
$393$		0			0
$394$	−1526.31			−0.195163
$395$	−2624.01	−	6822.28i	−0.334249	−	0.869028i
$396$		0			0
$397$		−	13571.9i		−	1.71576i	−0.513852	−	0.857879i	$-0.671782\pi$
$397$		−	13571.9i		−	1.71576i	0.513852	−	0.857879i	$-0.328218\pi$
$398$		−	4051.56i		−	0.510268i
$399$		0			0
$400$	−1484.52	+	1340.23i	−0.185565	+	0.167528i
$401$	5809.06			0.723418			0.361709	−	0.932291i	$-0.382193\pi$
$401$	5809.06			0.723418			0.361709	+	0.932291i	$0.382193\pi$
$402$		0			0
$403$		−	4013.23i		−	0.496062i
$404$	−6725.06			−0.828179
$405$		0			0
$406$	1309.41			0.160061
$407$			6086.92i			0.741321i
$408$		0			0
$409$	−10164.8			−1.22889			−0.614445	−	0.788960i	$-0.710620\pi$
$409$	−10164.8			−1.22889			−0.614445	+	0.788960i	$0.710620\pi$
$410$	3095.78	−	1190.71i	0.372901	−	0.143427i
$411$		0			0
$412$		−	3104.17i		−	0.371193i
$413$		−	9171.15i		−	1.09269i
$414$		0			0
$415$	−4113.67	+	1582.22i	−0.486583	+	0.187152i
$416$	676.077			0.0796812
$417$		0			0
$418$		−	53.4659i		−	0.00625623i
$419$	−651.862			−0.0760037			−0.0380018	−	0.999278i	$-0.512099\pi$
$419$	−651.862			−0.0760037			−0.0380018	+	0.999278i	$0.512099\pi$
$420$		0			0
$421$	15288.9			1.76992			0.884962	−	0.465664i	$-0.154185\pi$
$421$	15288.9			1.76992			0.884962	+	0.465664i	$0.154185\pi$
$422$			2833.01i			0.326798i
$423$		0			0
$424$	−3133.30			−0.358883
$425$	−6931.24	−	7677.45i	−0.791093	−	0.876262i
$426$		0			0
$427$			9909.59i			1.12309i
$428$		−	1713.12i		−	0.193474i
$429$		0			0
$430$	1918.89	+	4989.01i	0.215203	+	0.559515i
$431$	−10299.1			−1.15102			−0.575511	−	0.817794i	$-0.695197\pi$
$431$	−10299.1			−1.15102			−0.575511	+	0.817794i	$0.695197\pi$
$432$		0			0
$433$		−	1675.89i		−	0.186001i	−0.995666	−	0.0930003i	$-0.970354\pi$
$433$		−	1675.89i		−	0.186001i	0.995666	−	0.0930003i	$-0.0296458\pi$
$434$	−5328.33			−0.589327
$435$		0			0
$436$	−4873.65			−0.535334
$437$		−	13.2114i		−	0.00144619i
$438$		0			0
$439$	−4079.37			−0.443503			−0.221752	−	0.975103i	$-0.571177\pi$
$439$	−4079.37			−0.443503			−0.221752	+	0.975103i	$0.571177\pi$
$440$	4383.60	−	1686.04i	0.474954	−	0.182679i
$441$		0			0
$442$			3496.46i			0.376266i
$443$			379.021i			0.0406498i	0.999793	+	0.0203249i	$0.00647006\pi$
$443$			379.021i			0.0406498i	−0.999793	+	0.0203249i	$0.993530\pi$
$444$		0			0
$445$	−4029.00	−	10475.2i	−0.429198	−	1.11589i
$446$	10869.5			1.15400
$447$		0			0
$448$		−	897.622i		−	0.0946622i
$449$	7313.50			0.768698			0.384349	−	0.923188i	$-0.374426\pi$
$449$	7313.50			0.768698			0.384349	+	0.923188i	$0.374426\pi$
$450$		0			0
$451$	−7789.11			−0.813248
$452$			6541.71i			0.680743i
$453$		0			0
$454$	−6654.67			−0.687928
$455$	−1189.30	−	3092.12i	−0.122539	−	0.318595i
$456$		0			0
$457$		−	9265.55i		−	0.948411i	−0.880414	−	0.474206i	$-0.842735\pi$
$457$		−	9265.55i		−	0.948411i	0.880414	−	0.474206i	$-0.157265\pi$
$458$			4715.20i			0.481063i
$459$		0			0
$460$	1083.18	−	416.619i	0.109791	−	0.0422281i
$461$	1543.17			0.155906			0.0779530	−	0.996957i	$-0.475162\pi$
$461$	1543.17			0.155906			0.0779530	+	0.996957i	$0.475162\pi$
$462$		0			0
$463$		−	8530.45i		−	0.856249i	−0.903720	−	0.428125i	$-0.859174\pi$
$463$		−	8530.45i		−	0.856249i	0.903720	−	0.428125i	$-0.140826\pi$
$464$	−746.879			−0.0747263
$465$		0			0
$466$	12166.3			1.20942
$467$		−	5681.61i		−	0.562985i	−0.959564	−	0.281492i	$-0.909171\pi$
$467$		−	5681.61i		−	0.562985i	0.959564	−	0.281492i	$-0.0908294\pi$
$468$		0			0
$469$	3875.02			0.381517
$470$	−4536.81	−	11795.4i	−0.445250	−	1.15762i
$471$		0			0
$472$			5231.19i			0.510137i
$473$		−	12552.6i		−	1.22023i
$474$		0			0
$475$	−47.2354	+	42.6443i	−0.00456275	+	0.00411927i
$476$	4642.22			0.447008
$477$		0			0
$478$			7240.09i			0.692791i
$479$	5261.48			0.501885			0.250943	−	0.968002i	$-0.419259\pi$
$479$	5261.48			0.501885			0.250943	+	0.968002i	$0.419259\pi$
$480$		0			0
$481$	−2449.06			−0.232157
$482$			5773.99i			0.545639i
$483$		0			0
$484$	−5705.34			−0.535813
$485$	−7098.89	+	2730.40i	−0.664627	+	0.255631i
$486$		0			0
$487$			9628.87i			0.895946i	0.894047	+	0.447973i	$0.147854\pi$
$487$			9628.87i			0.895946i	−0.894047	+	0.447973i	$0.852146\pi$
$488$		−	5652.39i		−	0.524327i
$489$		0			0
$490$	3053.09	−	1174.29i	0.281479	−	0.108263i
$491$	6806.82			0.625636			0.312818	−	0.949813i	$-0.398727\pi$
$491$	6806.82			0.625636			0.312818	+	0.949813i	$0.398727\pi$
$492$		0			0
$493$		−	3862.63i		−	0.352868i
$494$	21.5119			0.00195924
$495$		0			0
$496$	3039.26			0.275134
$497$			14099.4i			1.27253i
$498$		0			0
$499$	8434.75			0.756696			0.378348	−	0.925663i	$-0.376492\pi$
$499$	8434.75			0.756696			0.378348	+	0.925663i	$0.376492\pi$
$500$	−4985.91	−	2527.99i	−0.445953	−	0.226110i
$501$		0			0
$502$		−	14006.4i		−	1.24529i
$503$			12595.8i			1.11654i	0.829660	+	0.558269i	$0.188534\pi$
$503$			12595.8i			1.11654i	−0.829660	+	0.558269i	$0.811466\pi$
$504$		0			0
$505$	−6747.90	−	17544.2i	−0.594609	−	1.54595i
$506$	−2725.34			−0.239439
$507$		0			0
$508$		−	4489.35i		−	0.392092i
$509$	−15456.3			−1.34595			−0.672976	−	0.739664i	$-0.734984\pi$
$509$	−15456.3			−1.34595			−0.672976	+	0.739664i	$0.734984\pi$
$510$		0			0
$511$	−6851.26			−0.593115
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−2170.95			−0.186297
$515$	8098.08	−	3114.71i	0.692901	−	0.266506i
$516$		0			0
$517$			29677.9i			2.52463i
$518$			3251.60i			0.275805i
$519$		0			0
$520$	678.373	+	1763.73i	0.0572089	+	0.148740i
$521$	15300.5			1.28662			0.643309	−	0.765607i	$-0.277561\pi$
$521$	15300.5			1.28662			0.643309	+	0.765607i	$0.277561\pi$
$522$		0			0
$523$			7037.51i			0.588392i	0.955745	+	0.294196i	$0.0950518\pi$
$523$			7037.51i			0.588392i	−0.955745	+	0.294196i	$0.904948\pi$
$524$	8864.40			0.739014
$525$		0			0
$526$	7649.95			0.634132
$527$			15718.1i			1.29922i
$528$		0			0
$529$	11493.6			0.944651
$530$	−3143.94	−	8174.06i	−0.257668	−	0.669922i
$531$		0			0
$532$		−	28.5612i		−	0.00232760i
$533$		−	3133.93i		−	0.254682i
$534$		0			0
$535$	4469.14	−	1718.94i	0.361154	−	0.138909i
$536$	−2210.29			−0.178116
$537$		0			0
$538$		−	3734.06i		−	0.299232i
$539$	−7681.72			−0.613868
$540$		0			0
$541$	5929.44			0.471214			0.235607	−	0.971848i	$-0.424292\pi$
$541$	5929.44			0.471214			0.235607	+	0.971848i	$0.424292\pi$
$542$			11144.8i			0.883233i
$543$		0			0
$544$	−2647.90			−0.208691
$545$	−4890.20	−	12714.2i	−0.384354	−	0.999300i
$546$		0			0
$547$			1212.28i			0.0947597i	0.998877	+	0.0473799i	$0.0150871\pi$
$547$			1212.28i			0.0947597i	−0.998877	+	0.0473799i	$0.984913\pi$
$548$		−	9824.21i		−	0.765820i
$549$		0			0
$550$	8796.97	+	9744.06i	0.682008	+	0.755433i
$551$	−23.7647			−0.00183741
$552$		0			0
$553$			9169.53i			0.705114i
$554$	13909.7			1.06673
$555$		0			0
$556$	5780.36			0.440903
$557$			20048.2i			1.52508i	0.646943	+	0.762539i	$0.276047\pi$
$557$			20048.2i			1.52508i	−0.646943	+	0.762539i	$0.723953\pi$
$558$		0			0
$559$	5050.50			0.382135
$560$	2341.69	−	900.671i	0.176705	−	0.0679648i
$561$		0			0
$562$			15559.1i			1.16783i
$563$			21986.7i			1.64587i	0.568132	+	0.822937i	$0.307666\pi$
$563$			21986.7i			1.64587i	−0.568132	+	0.822937i	$0.692334\pi$
$564$		0			0
$565$	−17065.8	+	6563.92i	−1.27073	+	0.488755i
$566$	5857.30			0.434984
$567$		0			0
$568$		−	8042.26i		−	0.594095i
$569$	−13733.6			−1.01185			−0.505926	−	0.862577i	$-0.668849\pi$
$569$	−13733.6			−1.01185			−0.505926	+	0.862577i	$0.668849\pi$
$570$		0			0
$571$	−1117.81			−0.0819248			−0.0409624	−	0.999161i	$-0.513042\pi$
$571$	−1117.81			−0.0819248			−0.0409624	+	0.999161i	$0.513042\pi$
$572$		−	4437.63i		−	0.324382i
$573$		0			0
$574$	−4160.90			−0.302565
$575$	2173.73	+	2407.75i	0.157653	+	0.174626i
$576$		0			0
$577$		−	10950.0i		−	0.790045i	−0.918671	−	0.395022i	$-0.870737\pi$
$577$		−	10950.0i		−	0.790045i	0.918671	−	0.395022i	$-0.129263\pi$
$578$		−	3868.13i		−	0.278362i
$579$		0			0
$580$	−749.416	−	1948.44i	−0.0536514	−	0.139491i
$581$	5529.00			0.394805
$582$		0			0
$583$			20566.3i			1.46101i
$584$	3907.93			0.276903
$585$		0			0
$586$	1075.72			0.0758320
$587$			22487.0i			1.58116i	0.612362	+	0.790578i	$0.290220\pi$
$587$			22487.0i			1.58116i	−0.612362	+	0.790578i	$0.709780\pi$
$588$		0			0
$589$	96.7052			0.00676514
$590$	−13647.0	+	5248.95i	−0.952266	+	0.366264i
$591$		0			0
$592$		−	1854.70i		−	0.128763i
$593$		−	220.992i		−	0.0153036i	−0.999971	−	0.00765182i	$-0.997564\pi$
$593$		−	220.992i		−	0.0153036i	0.999971	−	0.00765182i	$-0.00243567\pi$
$594$		0			0
$595$	4657.99	+	12110.5i	0.320939	+	0.834424i
$596$	9066.74			0.623135
$597$		0			0
$598$		−	1096.53i		−	0.0749843i
$599$	−25281.8			−1.72452			−0.862258	−	0.506470i	$-0.830950\pi$
$599$	−25281.8			−1.72452			−0.862258	+	0.506470i	$0.830950\pi$
$600$		0			0
$601$	4498.03			0.305289			0.152644	−	0.988281i	$-0.451221\pi$
$601$	4498.03			0.305289			0.152644	+	0.988281i	$0.451221\pi$
$602$		−	6705.51i		−	0.453980i
$603$		0			0
$604$	−6599.14			−0.444562
$605$	−5724.71	−	14883.9i	−0.384699	−	1.00019i
$606$		0			0
$607$			26455.9i			1.76905i	0.466495	+	0.884524i	$0.345517\pi$
$607$			26455.9i			1.76905i	−0.466495	+	0.884524i	$0.654483\pi$
$608$			16.2912i			0.00108667i
$609$		0			0
$610$	14745.8	−	5671.59i	0.978754	−	0.376452i
$611$	−11940.8			−0.790628
$612$		0			0
$613$		−	13618.2i		−	0.897280i	−0.893713	−	0.448640i	$-0.851909\pi$
$613$		−	13618.2i		−	0.897280i	0.893713	−	0.448640i	$-0.148091\pi$
$614$	1312.39			0.0862603
$615$		0			0
$616$	−5891.80			−0.385369
$617$			19616.1i			1.27993i	0.768406	+	0.639963i	$0.221050\pi$
$617$			19616.1i			1.27993i	−0.768406	+	0.639963i	$0.778950\pi$
$618$		0			0
$619$	17780.3			1.15452			0.577262	−	0.816559i	$-0.304121\pi$
$619$	17780.3			1.15452			0.577262	+	0.816559i	$0.304121\pi$
$620$	3049.58	+	7928.73i	0.197539	+	0.513590i
$621$		0			0
$622$			1319.74i			0.0850754i
$623$			14079.2i			0.905413i
$624$		0			0
$625$	1592.10	−	15543.7i	0.101895	−	0.994795i
$626$	−17679.5			−1.12878
$627$		0			0
$628$		−	13228.8i		−	0.840585i
$629$	9591.92			0.608036
$630$		0			0
$631$	11555.7			0.729042			0.364521	−	0.931195i	$-0.381233\pi$
$631$	11555.7			0.729042			0.364521	+	0.931195i	$0.381233\pi$
$632$		−	5230.26i		−	0.329191i
$633$		0			0
$634$	16336.6			1.02336
$635$	11711.7	−	4504.60i	0.731913	−	0.281511i
$636$		0			0
$637$		−	3090.72i		−	0.192243i
$638$			4902.36i			0.304211i
$639$		0			0
$640$	−1335.69	+	513.739i	−0.0824966	+	0.0317302i
$641$	−3245.63			−0.199992			−0.0999958	−	0.994988i	$-0.531883\pi$
$641$	−3245.63			−0.199992			−0.0999958	+	0.994988i	$0.531883\pi$
$642$		0			0
$643$		−	27598.8i		−	1.69267i	−0.532648	−	0.846337i	$-0.678803\pi$
$643$		−	27598.8i		−	1.69267i	0.532648	−	0.846337i	$-0.321197\pi$
$644$	−1455.86			−0.0890822
$645$		0			0
$646$	−84.2529			−0.00513140
$647$			29412.9i			1.78724i	0.448827	+	0.893619i	$0.351842\pi$
$647$			29412.9i			1.78724i	−0.448827	+	0.893619i	$0.648158\pi$
$648$		0			0
$649$	34336.4			2.07677
$650$	−3920.50	+	3539.44i	−0.236576	+	0.213582i
$651$		0			0
$652$			1933.63i			0.116145i
$653$		−	9847.46i		−	0.590139i	−0.955476	−	0.295070i	$-0.904657\pi$
$653$		−	9847.46i		−	0.590139i	0.955476	−	0.295070i	$-0.0953429\pi$
$654$		0			0
$655$	8894.50	+	23125.2i	0.530591	+	1.37951i
$656$	2373.36			0.141256
$657$		0			0
$658$			15853.7i			0.939275i
$659$	−12575.0			−0.743324			−0.371662	−	0.928368i	$-0.621212\pi$
$659$	−12575.0			−0.743324			−0.371662	+	0.928368i	$0.621212\pi$
$660$		0			0
$661$	1744.88			0.102674			0.0513372	−	0.998681i	$-0.483652\pi$
$661$	1744.88			0.102674			0.0513372	+	0.998681i	$0.483652\pi$
$662$		−	19202.2i		−	1.12736i
$663$		0			0
$664$	−3153.72			−0.184319
$665$	74.5096	−	28.6582i	0.00434490	−	0.00167115i
$666$		0			0
$667$			1211.37i			0.0703215i
$668$			2329.18i			0.134908i
$669$		0			0
$670$	−2217.80	−	5766.15i	−0.127882	−	0.332487i
$671$	−37101.1			−2.13453
$672$		0			0
$673$			13646.3i			0.781616i	0.920472	+	0.390808i	$0.127804\pi$
$673$			13646.3i			0.781616i	−0.920472	+	0.390808i	$0.872196\pi$
$674$	−15232.3			−0.870515
$675$		0			0
$676$	−7002.53			−0.398414
$677$		−	3649.90i		−	0.207204i	−0.994619	−	0.103602i	$-0.966963\pi$
$677$		−	3649.90i		−	0.207204i	0.994619	−	0.103602i	$-0.0330368\pi$
$678$		0			0
$679$	9541.31			0.539266
$680$	−2656.90	−	6907.78i	−0.149834	−	0.389561i
$681$		0			0
$682$		−	19949.1i		−	1.12007i
$683$			3066.68i			0.171806i	0.996304	+	0.0859029i	$0.0273775\pi$
$683$			3066.68i			0.171806i	−0.996304	+	0.0859029i	$0.972623\pi$
$684$		0			0
$685$	25629.1	−	9857.57i	1.42955	−	0.549837i
$686$	−13724.9			−0.763877
$687$		0			0
$688$			3824.79i			0.211946i
$689$	−8274.80			−0.457540
$690$		0			0
$691$	2855.12			0.157184			0.0785919	−	0.996907i	$-0.474958\pi$
$691$	2855.12			0.157184			0.0785919	+	0.996907i	$0.474958\pi$
$692$			9135.41i			0.501844i
$693$		0			0
$694$	−16264.8			−0.889631
$695$	5799.99	+	15079.6i	0.316556	+	0.823027i
$696$		0			0
$697$			12274.3i			0.667031i
$698$		−	21476.3i		−	1.16460i
$699$		0			0
$700$	4699.29	+	5205.21i	0.253738	+	0.281055i
$701$	33677.5			1.81453			0.907263	−	0.420564i	$-0.138168\pi$
$701$	33677.5			1.81453			0.907263	+	0.420564i	$0.138168\pi$
$702$		0			0
$703$		−	59.0141i		−	0.00316608i
$704$	3360.66			0.179914
$705$		0			0
$706$	−4000.90			−0.213280
$707$			23580.3i			1.25436i
$708$		0			0
$709$	5793.96			0.306906			0.153453	−	0.988156i	$-0.450961\pi$
$709$	5793.96			0.306906			0.153453	+	0.988156i	$0.450961\pi$
$710$	20980.4	−	8069.57i	1.10899	−	0.426543i
$711$		0			0
$712$		−	8030.73i		−	0.422703i
$713$		−	4929.40i		−	0.258916i
$714$		0			0
$715$	11576.8	−	4452.70i	0.605519	−	0.232897i
$716$	−12488.4			−0.651834
$717$		0			0
$718$			5521.65i			0.287000i
$719$	33612.1			1.74342			0.871712	−	0.490019i	$-0.163010\pi$
$719$	33612.1			1.74342			0.871712	+	0.490019i	$0.163010\pi$
$720$		0			0
$721$	−10884.3			−0.562207
$722$		−	13717.5i		−	0.707080i
$723$		0			0
$724$	−2316.72			−0.118923
$725$	4331.07	−	3910.11i	0.221865	−	0.200301i
$726$		0			0
$727$		−	29752.0i		−	1.51780i	−0.651207	−	0.758900i	$-0.725737\pi$
$727$		−	29752.0i		−	1.51780i	0.651207	−	0.758900i	$-0.274263\pi$
$728$		−	2370.55i		−	0.120685i
$729$		0			0
$730$	3921.20	+	10194.9i	0.198808	+	0.516891i
$731$	−19780.6			−1.00084
$732$		0			0
$733$			30803.9i			1.55221i	0.630605	+	0.776104i	$0.282807\pi$
$733$			30803.9i			1.55221i	−0.630605	+	0.776104i	$0.717193\pi$
$734$	17347.1			0.872334
$735$		0			0
$736$	830.417			0.0415891
$737$			14507.9i			0.725109i
$738$		0			0
$739$	19199.9			0.955725			0.477863	−	0.878435i	$-0.341412\pi$
$739$	19199.9			0.955725			0.477863	+	0.878435i	$0.341412\pi$
$740$	4838.48	−	1861.00i	0.240360	−	0.0924481i
$741$		0			0
$742$			10986.4i			0.543562i
$743$		−	25489.7i		−	1.25858i	−0.777171	−	0.629290i	$-0.783346\pi$
$743$		−	25489.7i		−	1.25858i	0.777171	−	0.629290i	$-0.216654\pi$
$744$		0			0
$745$	9097.54	+	23653.1i	0.447393	+	1.16320i
$746$	27015.0			1.32585
$747$		0			0
$748$			17380.3i			0.849580i
$749$	−6006.77			−0.293034
$750$		0			0
$751$	14864.4			0.722248			0.361124	−	0.932518i	$-0.382393\pi$
$751$	14864.4			0.722248			0.361124	+	0.932518i	$0.382393\pi$
$752$		−	9042.91i		−	0.438512i
$753$		0			0
$754$	−1972.45			−0.0952685
$755$	−6621.56	−	17215.7i	−0.319183	−	0.829857i
$756$		0			0
$757$		−	14713.0i		−	0.706412i	−0.935546	−	0.353206i	$-0.885091\pi$
$757$		−	14713.0i		−	0.706412i	0.935546	−	0.353206i	$-0.114909\pi$
$758$		−	12354.3i		−	0.591991i
$759$		0			0
$760$	−42.5000	+	16.3465i	−0.00202847	+	0.000780197i
$761$	10378.9			0.494396			0.247198	−	0.968965i	$-0.420490\pi$
$761$	10378.9			0.494396			0.247198	+	0.968965i	$0.420490\pi$
$762$		0			0
$763$			17088.7i			0.810814i
$764$	2635.77			0.124815
$765$		0			0
$766$	−425.106			−0.0200518
$767$			13815.2i			0.650374i
$768$		0			0
$769$	28877.6			1.35417			0.677083	−	0.735907i	$-0.263244\pi$
$769$	28877.6			1.35417			0.677083	+	0.735907i	$0.263244\pi$
$770$	−5911.81	−	15370.4i	−0.276684	−	0.719364i
$771$		0			0
$772$		−	8156.77i		−	0.380270i
$773$		−	17861.5i		−	0.831092i	−0.909572	−	0.415546i	$-0.863591\pi$
$773$		−	17861.5i		−	0.831092i	0.909572	−	0.415546i	$-0.136409\pi$
$774$		0			0
$775$	−17624.3	+	15911.3i	−0.816883	+	0.737486i
$776$	−5442.32			−0.251763
$777$		0			0
$778$			2012.15i			0.0927239i
$779$	75.5172			0.00347328
$780$		0			0
$781$	−52787.7			−2.41856
$782$			4294.66i			0.196390i
$783$		0			0
$784$	2340.63			0.106625
$785$	34511.0	−	13273.7i	1.56911	−	0.603516i
$786$		0			0
$787$		−	27737.0i		−	1.25631i	−0.778088	−	0.628155i	$-0.783810\pi$
$787$		−	27737.0i		−	1.25631i	0.778088	−	0.628155i	$-0.216190\pi$
$788$		−	3052.62i		−	0.138001i
$789$		0			0
$790$	13644.6	−	5248.02i	0.614496	−	0.236350i
$791$	22937.4			1.03105
$792$		0			0
$793$		−	14927.5i		−	0.668464i
$794$	27143.9			1.21322
$795$		0			0
$796$	8103.13			0.360814
$797$		−	5397.76i		−	0.239898i	−0.992780	−	0.119949i	$-0.961727\pi$
$797$		−	5397.76i		−	0.239898i	0.992780	−	0.119949i	$-0.0382730\pi$
$798$		0			0
$799$	46767.1			2.07071
$800$	−2680.46	−	2969.03i	−0.118461	−	0.131214i
$801$		0			0
$802$			11618.1i			0.511534i
$803$		−	25650.8i		−	1.12727i
$804$		0			0
$805$	−1460.80	−	3798.01i	−0.0639585	−	0.166289i
$806$	8026.45			0.350769
$807$		0			0
$808$		−	13450.1i		−	0.585611i
$809$	31266.7			1.35881			0.679405	−	0.733764i	$-0.262238\pi$
$809$	31266.7			1.35881			0.679405	+	0.733764i	$0.262238\pi$
$810$		0			0
$811$	−1701.66			−0.0736788			−0.0368394	−	0.999321i	$-0.511729\pi$
$811$	−1701.66			−0.0736788			−0.0368394	+	0.999321i	$0.511729\pi$
$812$			2618.81i			0.113180i
$813$		0			0
$814$	−12173.8			−0.524193
$815$	−5044.39	+	1940.19i	−0.216806	+	0.0833889i
$816$		0			0
$817$			121.700i			0.00521144i
$818$		−	20329.6i		−	0.868956i
$819$		0			0
$820$	2381.42	+	6191.55i	0.101418	+	0.263681i
$821$	−19686.1			−0.836846			−0.418423	−	0.908252i	$-0.637417\pi$
$821$	−19686.1			−0.836846			−0.418423	+	0.908252i	$0.637417\pi$
$822$		0			0
$823$		−	30326.8i		−	1.28448i	−0.766505	−	0.642239i	$-0.778006\pi$
$823$		−	30326.8i		−	1.28448i	0.766505	−	0.642239i	$-0.221994\pi$
$824$	6208.34			0.262473
$825$		0			0
$826$	18342.3			0.772652
$827$			40104.4i			1.68630i	0.537682	+	0.843148i	$0.319300\pi$
$827$			40104.4i			1.68630i	−0.537682	+	0.843148i	$0.680700\pi$
$828$		0			0
$829$	−21809.6			−0.913727			−0.456864	−	0.889537i	$-0.651027\pi$
$829$	−21809.6			−0.913727			−0.456864	+	0.889537i	$0.651027\pi$
$830$	−3164.43	−	8227.34i	−0.132336	−	0.344066i
$831$		0			0
$832$			1352.15i			0.0563431i
$833$			12105.0i			0.503499i
$834$		0			0
$835$	−6076.31	+	2337.09i	−0.251831	+	0.0968604i
$836$	106.932			0.00442382
$837$		0			0
$838$		−	1303.72i		−	0.0537427i
$839$	−9528.13			−0.392071			−0.196035	−	0.980597i	$-0.562807\pi$
$839$	−9528.13			−0.392071			−0.196035	+	0.980597i	$0.562807\pi$
$840$		0			0
$841$	−22210.0			−0.910656
$842$			30577.9i			1.25152i
$843$		0			0
$844$	−5666.01			−0.231081
$845$	−7026.31	−	18268.0i	−0.286050	−	0.743715i
$846$		0			0
$847$			20004.8i			0.811540i
$848$		−	6266.59i		−	0.253768i
$849$		0			0
$850$	15354.9	−	13862.5i	0.619611	−	0.559387i
$851$	−3008.15			−0.121173
$852$		0			0
$853$			40782.8i			1.63702i	0.574494	+	0.818509i	$0.305199\pi$
$853$			40782.8i			1.63702i	−0.574494	+	0.818509i	$0.694801\pi$
$854$	−19819.2			−0.794143
$855$		0			0
$856$	3426.24			0.136806
$857$		−	30598.2i		−	1.21962i	−0.792548	−	0.609810i	$-0.791246\pi$
$857$		−	30598.2i		−	1.21962i	0.792548	−	0.609810i	$-0.208754\pi$
$858$		0			0
$859$	−1102.88			−0.0438066			−0.0219033	−	0.999760i	$-0.506973\pi$
$859$	−1102.88			−0.0438066			−0.0219033	+	0.999760i	$0.506973\pi$
$860$	−9978.02	+	3837.78i	−0.395637	+	0.152171i
$861$		0			0
$862$		−	20598.2i		−	0.813896i
$863$			17309.3i			0.682751i	0.939927	+	0.341376i	$0.110893\pi$
$863$			17309.3i			0.682751i	−0.939927	+	0.341376i	$0.889107\pi$
$864$		0			0
$865$	−23832.2	+	9166.43i	−0.936785	+	0.360310i
$866$	3351.79			0.131522
$867$		0			0
$868$		−	10656.7i		−	0.416717i
$869$	−34330.3			−1.34013
$870$		0			0
$871$	−5837.22			−0.227080
$872$		−	9747.30i		−	0.378538i
$873$		0			0
$874$	26.4228			0.00102261
$875$	−8863.97	+	17482.3i	−0.342465	+	0.675439i
$876$		0			0
$877$			11596.3i			0.446500i	0.974761	+	0.223250i	$0.0716667\pi$
$877$			11596.3i			0.446500i	−0.974761	+	0.223250i	$0.928333\pi$
$878$		−	8158.75i		−	0.313604i
$879$		0			0
$880$	3372.07	+	8767.20i	0.129173	+	0.335843i
$881$	−32848.2			−1.25617			−0.628085	−	0.778145i	$-0.716161\pi$
$881$	−32848.2			−1.25617			−0.628085	+	0.778145i	$0.716161\pi$
$882$		0			0
$883$			4249.50i			0.161956i	0.996716	+	0.0809779i	$0.0258043\pi$
$883$			4249.50i			0.161956i	−0.996716	+	0.0809779i	$0.974196\pi$
$884$	−6992.91			−0.266060
$885$		0			0
$886$	−758.043			−0.0287437
$887$		−	11404.9i		−	0.431722i	−0.976424	−	0.215861i	$-0.930744\pi$
$887$		−	11404.9i		−	0.431722i	0.976424	−	0.215861i	$-0.0692559\pi$
$888$		0			0
$889$	−15741.2			−0.593861
$890$	20950.3	−	8058.00i	0.789053	−	0.303489i
$891$		0			0
$892$			21739.0i			0.816003i
$893$		−	287.734i		−	0.0107823i
$894$		0			0
$895$	−12530.8	−	32579.4i	−0.467999	−	1.21677i
$896$	1795.24			0.0669363
$897$		0			0
$898$			14627.0i			0.543552i
$899$	−8867.03			−0.328957
$900$		0			0
$901$	32408.9			1.19833
$902$		−	15578.2i		−	0.575053i
$903$		0			0
$904$	−13083.4			−0.481358
$905$	−2324.58	−	6043.78i	−0.0853832	−	0.221991i
$906$		0			0
$907$			22836.1i			0.836008i	0.908445	+	0.418004i	$0.137270\pi$
$907$			22836.1i			0.836008i	−0.908445	+	0.418004i	$0.862730\pi$
$908$		−	13309.3i		−	0.486438i
$909$		0			0
$910$	6184.23	−	2378.60i	0.225281	−	0.0866483i
$911$	−23102.2			−0.840188			−0.420094	−	0.907481i	$-0.638003\pi$
$911$	−23102.2			−0.840188			−0.420094	+	0.907481i	$0.638003\pi$
$912$		0			0
$913$			20700.4i			0.750364i
$914$	18531.1			0.670628
$915$		0			0
$916$	−9430.39			−0.340163
$917$		−	31081.6i		−	1.11931i
$918$		0			0
$919$	15564.1			0.558664			0.279332	−	0.960195i	$-0.409887\pi$
$919$	15564.1			0.558664			0.279332	+	0.960195i	$0.409887\pi$
$920$	833.237	+	2166.37i	0.0298598	+	0.0776338i
$921$		0			0
$922$			3086.34i			0.110242i
$923$		−	21239.0i		−	0.757411i
$924$		0			0
$925$	9709.83	+	10755.2i	0.345143	+	0.382301i
$926$	17060.9			0.605460
$927$		0			0
$928$		−	1493.76i		−	0.0528395i
$929$	52002.7			1.83655			0.918273	−	0.395947i	$-0.129584\pi$
$929$	52002.7			1.83655			0.918273	+	0.395947i	$0.129584\pi$
$930$		0			0
$931$	74.4759			0.00262175
$932$			24332.5i			0.855191i
$933$		0			0
$934$	11363.2			0.398090
$935$	−45341.2	+	17439.3i	−1.58590	+	0.609975i
$936$		0			0
$937$		−	54231.8i		−	1.89080i	−0.325918	−	0.945398i	$-0.605673\pi$
$937$		−	54231.8i		−	1.89080i	0.325918	−	0.945398i	$-0.394327\pi$
$938$			7750.03i			0.269774i
$939$		0			0
$940$	23590.9	−	9073.62i	0.818564	−	0.314839i
$941$	20521.3			0.710918			0.355459	−	0.934692i	$-0.384325\pi$
$941$	20521.3			0.710918			0.355459	+	0.934692i	$0.384325\pi$
$942$		0			0
$943$		−	3849.37i		−	0.132930i
$944$	−10462.4			−0.360722
$945$		0			0
$946$	25105.1			0.862832
$947$			54047.1i			1.85459i	0.374333	+	0.927294i	$0.377872\pi$
$947$			54047.1i			1.85459i	−0.374333	+	0.927294i	$0.622128\pi$
$948$		0			0
$949$	10320.5			0.353023
$950$	−85.2886	−	94.4708i	−0.00291277	−	0.00322635i
$951$		0			0
$952$			9284.44i			0.316082i
$953$			6404.29i			0.217687i	0.994059	+	0.108843i	$0.0347147\pi$
$953$			6404.29i			0.217687i	−0.994059	+	0.108843i	$0.965285\pi$
$954$		0			0
$955$	2644.72	+	6876.13i	0.0896139	+	0.232991i
$956$	−14480.2			−0.489877
$957$		0			0
$958$			10523.0i			0.354886i
$959$	−34447.0			−1.15991
$960$		0			0
$961$	6291.38			0.211184
$962$		−	4898.12i		−	0.164160i
$963$		0			0
$964$	−11548.0			−0.385825
$965$	21279.2	−	8184.47i	0.709845	−	0.273023i
$966$		0			0
$967$			23519.6i			0.782152i	0.920358	+	0.391076i	$0.127897\pi$
$967$			23519.6i			0.782152i	−0.920358	+	0.391076i	$0.872103\pi$
$968$		−	11410.7i		−	0.378877i
$969$		0			0
$970$	−5460.80	−	14197.8i	−0.180759	−	0.469962i
$971$	3036.25			0.100348			0.0501739	−	0.998740i	$-0.484022\pi$
$971$	3036.25			0.100348			0.0501739	+	0.998740i	$0.484022\pi$
$972$		0			0
$973$		−	20267.9i		−	0.667789i
$974$	−19257.7			−0.633530
$975$		0			0
$976$	11304.8			0.370755
$977$		−	15308.8i		−	0.501302i	−0.968077	−	0.250651i	$-0.919355\pi$
$977$		−	15308.8i		−	0.501302i	0.968077	−	0.250651i	$-0.0806447\pi$
$978$		0			0
$979$	−52712.0			−1.72082
$980$	2348.58	+	6106.18i	0.0765538	+	0.199036i
$981$		0			0
$982$			13613.6i			0.442392i
$983$			1973.16i			0.0640225i	0.999488	+	0.0320112i	$0.0101912\pi$
$983$			1973.16i			0.0640225i	−0.999488	+	0.0320112i	$0.989809\pi$
$984$		0			0
$985$	7963.58	−	3062.98i	0.257605	−	0.0990810i
$986$	7725.25			0.249515
$987$		0			0
$988$			43.0238i			0.00138539i
$989$	6203.47			0.199453
$990$		0			0
$991$	−60485.8			−1.93884			−0.969422	−	0.245400i	$-0.921081\pi$
$991$	−60485.8			−1.93884			−0.969422	+	0.245400i	$0.921081\pi$
$992$			6078.52i			0.194549i
$993$		0			0
$994$	−28198.9			−0.899813
$995$	8130.65	+	21139.2i	0.259054	+	0.673526i
$996$		0			0
$997$		−	2557.84i		−	0.0812512i	−0.999174	−	0.0406256i	$-0.987065\pi$
$997$		−	2557.84i		−	0.0812512i	0.999174	−	0.0406256i	$-0.0129351\pi$
$998$			16869.5i			0.535065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.c.b.649.7	yes	10
3.2	odd	2		810.4.c.a.649.4	✓	10
5.4	even	2	inner	810.4.c.b.649.2	yes	10
15.14	odd	2		810.4.c.a.649.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.4.c.a.649.4	✓	10	3.2	odd	2
810.4.c.a.649.9	yes	10	15.14	odd	2
810.4.c.b.649.2	yes	10	5.4	even	2	inner
810.4.c.b.649.7	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(-4.01358 - 10.4351i) q^{5} +14.0253i q^{7} -8.00000i q^{8} +(20.8702 - 8.02717i) q^{10} -52.5103 q^{11} -21.1274i q^{13} -28.0507 q^{14} +16.0000 q^{16} +82.7470i q^{17} +0.509099 q^{19} +(16.0543 + 41.7404i) q^{20} -105.021i q^{22} -25.9505i q^{23} +(-92.7823 + 83.7642i) q^{25} +42.2548 q^{26} -56.1014i q^{28} -46.6800 q^{29} +189.954 q^{31} +32.0000i q^{32} -165.494 q^{34} +(146.356 - 56.2919i) q^{35} -115.919i q^{37} +1.01820i q^{38} +(-83.4807 + 32.1087i) q^{40} +148.335 q^{41} +239.050i q^{43} +210.041 q^{44} +51.9011 q^{46} -565.182i q^{47} +146.290 q^{49} +(-167.528 - 185.565i) q^{50} +84.5096i q^{52} -391.662i q^{53} +(210.755 + 547.950i) q^{55} +112.203 q^{56} -93.3599i q^{58} -653.898 q^{59} +706.549 q^{61} +379.907i q^{62} -64.0000 q^{64} +(-220.466 + 84.7966i) q^{65} -276.287i q^{67} -330.988i q^{68} +(112.584 + 292.712i) q^{70} +1005.28 q^{71} +488.491i q^{73} +231.837 q^{74} -2.03640 q^{76} -736.476i q^{77} +653.783 q^{79} +(-64.2174 - 166.961i) q^{80} +296.670i q^{82} -394.215i q^{83} +(863.472 - 332.112i) q^{85} -478.099 q^{86} +420.083i q^{88} +1003.84 q^{89} +296.319 q^{91} +103.802i q^{92} +1130.36 q^{94} +(-2.04331 - 5.31250i) q^{95} -680.290i q^{97} +292.579i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 40 q^{4} + 22 q^{5} - 4 q^{10} - 28 q^{11} - 4 q^{14} + 160 q^{16} - 42 q^{19} - 88 q^{20} + 96 q^{25} - 108 q^{26} + 216 q^{29} + 88 q^{31} - 64 q^{34} - 22 q^{35} + 16 q^{40} + 38 q^{41} + 112 q^{44}+ \cdots + 2472 q^{95}+O(q^{100}) \) 10 * q - 40 * q^4 + 22 * q^5 - 4 * q^10 - 28 * q^11 - 4 * q^14 + 160 * q^16 - 42 * q^19 - 88 * q^20 + 96 * q^25 - 108 * q^26 + 216 * q^29 + 88 * q^31 - 64 * q^34 - 22 * q^35 + 16 * q^40 + 38 * q^41 + 112 * q^44 + 172 * q^46 - 1452 * q^49 + 256 * q^50 + 20 * q^55 + 16 * q^56 - 2050 * q^59 + 1064 * q^61 - 640 * q^64 - 2268 * q^65 + 464 * q^70 - 2844 * q^71 + 584 * q^74 + 168 * q^76 - 1608 * q^79 + 352 * q^80 - 526 * q^85 + 184 * q^86 + 1132 * q^89 + 3402 * q^91 - 1268 * q^94 + 2472 * q^95

Introduction

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