LMFDB - Embedded newform 810.3.b.b.809.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(809,810)]

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([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.809");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.b (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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 230x^{12} - 96x^{10} + 25551x^{8} - 7776x^{6} - 1509030x^{4} + 1062882x^{2} + 43046721 $ x^16 + 2x^14 - 230x^12 - 96x^10 + 25551x^8 - 7776x^6 - 1509030x^4 + 1062882*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			809.1
Root			$-2.97088 + 0.416995i$ of defining polynomial
Character	$\chi$	$=$	810.809
Dual form			810.3.b.b.809.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.00000 q^{4} +(-4.11034 - 2.84695i) q^{5} +9.58750i q^{7} -2.82843 q^{8} +O(q^{10})$	\(q-1.41421 q^{2} +2.00000 q^{4} +(-4.11034 - 2.84695i) q^{5} +9.58750i q^{7} -2.82843 q^{8} +(5.81290 + 4.02619i) q^{10} +10.2064i q^{11} -3.45374i q^{13} -13.5588i q^{14} +4.00000 q^{16} -30.5229 q^{17} +10.0857 q^{19} +(-8.22068 - 5.69390i) q^{20} -14.4340i q^{22} +30.6089 q^{23} +(8.78976 + 23.4038i) q^{25} +4.88433i q^{26} +19.1750i q^{28} -42.0050i q^{29} -10.0394 q^{31} -5.65685 q^{32} +43.1659 q^{34} +(27.2951 - 39.4079i) q^{35} +21.9907i q^{37} -14.2633 q^{38} +(11.6258 + 8.05239i) q^{40} -39.6635i q^{41} -21.6619i q^{43} +20.4128i q^{44} -43.2876 q^{46} -12.5764 q^{47} -42.9202 q^{49} +(-12.4306 - 33.0980i) q^{50} -6.90749i q^{52} -47.0248 q^{53} +(29.0570 - 41.9517i) q^{55} -27.1176i q^{56} +59.4040i q^{58} +32.3891i q^{59} -114.245 q^{61} +14.1979 q^{62} +8.00000 q^{64} +(-9.83263 + 14.1961i) q^{65} -32.2821i q^{67} -61.0458 q^{68} +(-38.6012 + 55.7312i) q^{70} -65.9174i q^{71} -54.1701i q^{73} -31.0995i q^{74} +20.1714 q^{76} -97.8537 q^{77} +88.1260 q^{79} +(-16.4414 - 11.3878i) q^{80} +56.0926i q^{82} -41.1001 q^{83} +(125.459 + 86.8971i) q^{85} +30.6345i q^{86} -28.8680i q^{88} -38.5303i q^{89} +33.1128 q^{91} +61.2179 q^{92} +17.7858 q^{94} +(-41.4556 - 28.7135i) q^{95} -128.257i q^{97} +60.6984 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 16 q^{10} + 64 q^{16} + 144 q^{19} - 12 q^{25} - 56 q^{31} + 272 q^{34} - 32 q^{40} - 56 q^{46} - 24 q^{49} + 20 q^{55} - 136 q^{61} + 128 q^{64} + 224 q^{70} + 288 q^{76} - 840 q^{79} + 272 q^{85} - 168 q^{91} + 328 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 - 16 * q^10 + 64 * q^16 + 144 * q^19 - 12 * q^25 - 56 * q^31 + 272 * q^34 - 32 * q^40 - 56 * q^46 - 24 * q^49 + 20 * q^55 - 136 * q^61 + 128 * q^64 + 224 * q^70 + 288 * q^76 - 840 * q^79 + 272 * q^85 - 168 * q^91 + 328 * q^94

Display 100 coefficients 10 coefficients

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		0			0
$3$		0			0
$4$	2.00000			0.500000
$5$	−4.11034	−	2.84695i	−0.822068	−	0.569390i
$5$	−4.11034	−	2.84695i	−0.822068	−	0.569390i
$6$		0			0
$7$			9.58750i			1.36964i	0.728711	+	0.684822i	$0.240120\pi$
$7$			9.58750i			1.36964i	−0.728711	+	0.684822i	$0.759880\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	5.81290	+	4.02619i	0.581290	+	0.402619i
$11$			10.2064i			0.927853i	0.885874	+	0.463926i	$0.153560\pi$
$11$			10.2064i			0.927853i	−0.885874	+	0.463926i	$0.846440\pi$
$12$		0			0
$13$		−	3.45374i		−	0.265673i	−0.991138	−	0.132836i	$-0.957592\pi$
$13$		−	3.45374i		−	0.265673i	0.991138	−	0.132836i	$-0.0424084\pi$
$14$		−	13.5588i		−	0.968484i
$15$		0			0
$16$	4.00000			0.250000
$17$	−30.5229			−1.79546			−0.897732	−	0.440542i	$-0.854786\pi$
$17$	−30.5229			−1.79546			−0.897732	+	0.440542i	$0.854786\pi$
$18$		0			0
$19$	10.0857			0.530826			0.265413	−	0.964135i	$-0.414492\pi$
$19$	10.0857			0.530826			0.265413	+	0.964135i	$0.414492\pi$
$20$	−8.22068	−	5.69390i	−0.411034	−	0.284695i
$21$		0			0
$22$		−	14.4340i		−	0.656091i
$23$	30.6089			1.33082			0.665412	−	0.746476i	$-0.268256\pi$
$23$	30.6089			1.33082			0.665412	+	0.746476i	$0.268256\pi$
$24$		0			0
$25$	8.78976	+	23.4038i	0.351590	+	0.936154i
$26$			4.88433i			0.187859i
$27$		0			0
$28$			19.1750i			0.684822i
$29$		−	42.0050i		−	1.44845i	−0.689565	−	0.724224i	$-0.742198\pi$
$29$		−	42.0050i		−	1.44845i	0.689565	−	0.724224i	$-0.257802\pi$
$30$		0			0
$31$	−10.0394			−0.323853			−0.161926	−	0.986803i	$-0.551771\pi$
$31$	−10.0394			−0.323853			−0.161926	+	0.986803i	$0.551771\pi$
$32$	−5.65685			−0.176777
$33$		0			0
$34$	43.1659			1.26958
$35$	27.2951	−	39.4079i	0.779861	−	1.12594i
$36$		0			0
$37$			21.9907i			0.594343i	0.954824	+	0.297171i	$0.0960433\pi$
$37$			21.9907i			0.594343i	−0.954824	+	0.297171i	$0.903957\pi$
$38$	−14.2633			−0.375351
$39$		0			0
$40$	11.6258	+	8.05239i	0.290645	+	0.201310i
$41$		−	39.6635i		−	0.967402i	−0.875233	−	0.483701i	$-0.839292\pi$
$41$		−	39.6635i		−	0.967402i	0.875233	−	0.483701i	$-0.160708\pi$
$42$		0			0
$43$		−	21.6619i		−	0.503765i	−0.967758	−	0.251883i	$-0.918950\pi$
$43$		−	21.6619i		−	0.503765i	0.967758	−	0.251883i	$-0.0810497\pi$
$44$			20.4128i			0.463926i
$45$		0			0
$46$	−43.2876			−0.941035
$47$	−12.5764			−0.267584			−0.133792	−	0.991009i	$-0.542715\pi$
$47$	−12.5764			−0.267584			−0.133792	+	0.991009i	$0.542715\pi$
$48$		0			0
$49$	−42.9202			−0.875923
$50$	−12.4306	−	33.0980i	−0.248612	−	0.661961i
$51$		0			0
$52$		−	6.90749i		−	0.132836i
$53$	−47.0248			−0.887261			−0.443631	−	0.896210i	$-0.646310\pi$
$53$	−47.0248			−0.887261			−0.443631	+	0.896210i	$0.646310\pi$
$54$		0			0
$55$	29.0570	−	41.9517i	0.528310	−	0.762758i
$56$		−	27.1176i		−	0.484242i
$57$		0			0
$58$			59.4040i			1.02421i
$59$			32.3891i			0.548968i	0.961592	+	0.274484i	$0.0885071\pi$
$59$			32.3891i			0.548968i	−0.961592	+	0.274484i	$0.911493\pi$
$60$		0			0
$61$	−114.245			−1.87287			−0.936436	−	0.350839i	$-0.885896\pi$
$61$	−114.245			−1.87287			−0.936436	+	0.350839i	$0.885896\pi$
$62$	14.1979			0.228998
$63$		0			0
$64$	8.00000			0.125000
$65$	−9.83263	+	14.1961i	−0.151271	+	0.218401i
$66$		0			0
$67$		−	32.2821i		−	0.481822i	−0.970547	−	0.240911i	$-0.922554\pi$
$67$		−	32.2821i		−	0.481822i	0.970547	−	0.240911i	$-0.0774463\pi$
$68$	−61.0458			−0.897732
$69$		0			0
$70$	−38.6012	+	55.7312i	−0.551445	+	0.796159i
$71$		−	65.9174i		−	0.928414i	−0.885727	−	0.464207i	$-0.846339\pi$
$71$		−	65.9174i		−	0.928414i	0.885727	−	0.464207i	$-0.153661\pi$
$72$		0			0
$73$		−	54.1701i		−	0.742056i	−0.928622	−	0.371028i	$-0.879005\pi$
$73$		−	54.1701i		−	0.742056i	0.928622	−	0.371028i	$-0.120995\pi$
$74$		−	31.0995i		−	0.420264i
$75$		0			0
$76$	20.1714			0.265413
$77$	−97.8537			−1.27083
$78$		0			0
$79$	88.1260			1.11552			0.557759	−	0.830003i	$-0.311661\pi$
$79$	88.1260			1.11552			0.557759	+	0.830003i	$0.311661\pi$
$80$	−16.4414	−	11.3878i	−0.205517	−	0.142347i
$81$		0			0
$82$			56.0926i			0.684056i
$83$	−41.1001			−0.495182			−0.247591	−	0.968865i	$-0.579639\pi$
$83$	−41.1001			−0.495182			−0.247591	+	0.968865i	$0.579639\pi$
$84$		0			0
$85$	125.459	+	86.8971i	1.47599	+	1.02232i
$86$			30.6345i			0.356216i
$87$		0			0
$88$		−	28.8680i		−	0.328046i
$89$		−	38.5303i		−	0.432925i	−0.976291	−	0.216462i	$-0.930548\pi$
$89$		−	38.5303i		−	0.432925i	0.976291	−	0.216462i	$-0.0694519\pi$
$90$		0			0
$91$	33.1128			0.363877
$92$	61.2179			0.665412
$93$		0			0
$94$	17.7858			0.189210
$95$	−41.4556	−	28.7135i	−0.436375	−	0.302247i
$96$		0			0
$97$		−	128.257i		−	1.32224i	−0.750281	−	0.661119i	$-0.770082\pi$
$97$		−	128.257i		−	1.32224i	0.750281	−	0.661119i	$-0.229918\pi$
$98$	60.6984			0.619371
$99$		0			0
$100$	17.5795	+	46.8077i	0.175795	+	0.468077i
$101$			61.1219i			0.605168i	0.953123	+	0.302584i	$0.0978492\pi$
$101$			61.1219i			0.605168i	−0.953123	+	0.302584i	$0.902151\pi$
$102$		0			0
$103$		−	82.4492i		−	0.800477i	−0.916411	−	0.400239i	$-0.868927\pi$
$103$		−	82.4492i		−	0.800477i	0.916411	−	0.400239i	$-0.131073\pi$
$104$			9.76866i			0.0939294i
$105$		0			0
$106$	66.5032			0.627388
$107$	−60.4035			−0.564518			−0.282259	−	0.959338i	$-0.591084\pi$
$107$	−60.4035			−0.564518			−0.282259	+	0.959338i	$0.591084\pi$
$108$		0			0
$109$	−145.496			−1.33482			−0.667411	−	0.744690i	$-0.732597\pi$
$109$	−145.496			−1.33482			−0.667411	+	0.744690i	$0.732597\pi$
$110$	−41.0929	+	59.3286i	−0.373572	+	0.539351i
$111$		0			0
$112$			38.3500i			0.342411i
$113$	−79.0429			−0.699494			−0.349747	−	0.936844i	$-0.613733\pi$
$113$	−79.0429			−0.699494			−0.349747	+	0.936844i	$0.613733\pi$
$114$		0			0
$115$	−125.813	−	87.1421i	−1.09403	−	0.757758i
$116$		−	84.0100i		−	0.724224i
$117$		0			0
$118$		−	45.8052i		−	0.388179i
$119$		−	292.638i		−	2.45915i
$120$		0			0
$121$	16.8298			0.139089
$122$	161.567			1.32432
$123$		0			0
$124$	−20.0789			−0.161926
$125$	30.5007	−	121.222i	0.244005	−	0.969774i
$126$		0			0
$127$		−	233.011i		−	1.83473i	−0.398047	−	0.917365i	$-0.630312\pi$
$127$		−	233.011i		−	1.83473i	0.398047	−	0.917365i	$-0.369688\pi$
$128$	−11.3137			−0.0883883
$129$		0			0
$130$	13.9054	−	20.0762i	0.106965	−	0.154433i
$131$			74.5978i			0.569449i	0.958609	+	0.284724i	$0.0919021\pi$
$131$			74.5978i			0.569449i	−0.958609	+	0.284724i	$0.908098\pi$
$132$		0			0
$133$			96.6967i			0.727043i
$134$			45.6538i			0.340700i
$135$		0			0
$136$	86.3318			0.634792
$137$	−23.4980			−0.171518			−0.0857592	−	0.996316i	$-0.527332\pi$
$137$	−23.4980			−0.171518			−0.0857592	+	0.996316i	$0.527332\pi$
$138$		0			0
$139$	−216.225			−1.55558			−0.777789	−	0.628526i	$-0.783659\pi$
$139$	−216.225			−1.55558			−0.777789	+	0.628526i	$0.783659\pi$
$140$	54.5903	−	78.8158i	0.389931	−	0.562970i
$141$		0			0
$142$			93.2212i			0.656488i
$143$	35.2502			0.246505
$144$		0			0
$145$	−119.586	+	172.655i	−0.824731	+	1.19072i
$146$			76.6081i			0.524713i
$147$		0			0
$148$			43.9814i			0.297171i
$149$		−	224.199i		−	1.50469i	−0.658767	−	0.752347i	$-0.728922\pi$
$149$		−	224.199i		−	1.50469i	0.658767	−	0.752347i	$-0.271078\pi$
$150$		0			0
$151$	2.76731			0.0183266			0.00916329	−	0.999958i	$-0.497083\pi$
$151$	2.76731			0.0183266			0.00916329	+	0.999958i	$0.497083\pi$
$152$	−28.5267			−0.187675
$153$		0			0
$154$	138.386			0.898611
$155$	41.2654	+	28.5817i	0.266229	+	0.184398i
$156$		0			0
$157$		−	179.546i		−	1.14360i	−0.820392	−	0.571802i	$-0.806245\pi$
$157$		−	179.546i		−	1.14360i	0.820392	−	0.571802i	$-0.193755\pi$
$158$	−124.629			−0.788791
$159$		0			0
$160$	23.2516	+	16.1048i	0.145322	+	0.100655i
$161$			293.463i			1.82275i
$162$		0			0
$163$			63.2552i			0.388069i	0.980995	+	0.194034i	$0.0621573\pi$
$163$			63.2552i			0.388069i	−0.980995	+	0.194034i	$0.937843\pi$
$164$		−	79.3269i		−	0.483701i
$165$		0			0
$166$	58.1244			0.350147
$167$	73.9408			0.442759			0.221380	−	0.975188i	$-0.428944\pi$
$167$	73.9408			0.442759			0.221380	+	0.975188i	$0.428944\pi$
$168$		0			0
$169$	157.072			0.929418
$170$	−177.426	−	122.891i	−1.04368	−	0.722889i
$171$		0			0
$172$		−	43.3238i		−	0.251883i
$173$	−12.5767			−0.0726978			−0.0363489	−	0.999339i	$-0.511573\pi$
$173$	−12.5767			−0.0726978			−0.0363489	+	0.999339i	$0.511573\pi$
$174$		0			0
$175$	−224.384	+	84.2719i	−1.28220	+	0.481553i
$176$			40.8255i			0.231963i
$177$		0			0
$178$			54.4901i			0.306124i
$179$			224.517i			1.25428i	0.778905	+	0.627142i	$0.215775\pi$
$179$			224.517i			1.25428i	−0.778905	+	0.627142i	$0.784225\pi$
$180$		0			0
$181$	−44.8248			−0.247651			−0.123825	−	0.992304i	$-0.539516\pi$
$181$	−44.8248			−0.247651			−0.123825	+	0.992304i	$0.539516\pi$
$182$	−46.8285			−0.257300
$183$		0			0
$184$	−86.5752			−0.470517
$185$	62.6064	−	90.3891i	0.338413	−	0.488590i
$186$		0			0
$187$		−	311.528i		−	1.66593i
$188$	−25.1529			−0.133792
$189$		0			0
$190$	58.6271	+	40.6070i	0.308564	+	0.213721i
$191$			278.640i			1.45885i	0.684061	+	0.729425i	$0.260212\pi$
$191$			278.640i			1.45885i	−0.684061	+	0.729425i	$0.739788\pi$
$192$		0			0
$193$		−	327.088i		−	1.69475i	−0.530991	−	0.847377i	$-0.678180\pi$
$193$		−	327.088i		−	1.69475i	0.530991	−	0.847377i	$-0.321820\pi$
$194$			181.383i			0.934964i
$195$		0			0
$196$	−85.8405			−0.437961
$197$	195.249			0.991112			0.495556	−	0.868576i	$-0.334964\pi$
$197$	195.249			0.991112			0.495556	+	0.868576i	$0.334964\pi$
$198$		0			0
$199$	−117.737			−0.591643			−0.295821	−	0.955243i	$-0.595593\pi$
$199$	−117.737			−0.591643			−0.295821	+	0.955243i	$0.595593\pi$
$200$	−24.8612	−	66.1961i	−0.124306	−	0.330980i
$201$		0			0
$202$		−	86.4395i		−	0.427918i
$203$	402.723			1.98386
$204$		0			0
$205$	−112.920	+	163.030i	−0.550829	+	0.795270i
$206$			116.601i			0.566023i
$207$		0			0
$208$		−	13.8150i		−	0.0664181i
$209$			102.938i			0.492529i
$210$		0			0
$211$	70.1191			0.332318			0.166159	−	0.986099i	$-0.446863\pi$
$211$	70.1191			0.332318			0.166159	+	0.986099i	$0.446863\pi$
$212$	−94.0497			−0.443631
$213$		0			0
$214$	85.4234			0.399175
$215$	−61.6703	+	89.0377i	−0.286839	+	0.414129i
$216$		0			0
$217$		−	96.2531i		−	0.443562i
$218$	205.762			0.943861
$219$		0			0
$220$	58.1141	−	83.9034i	0.264155	−	0.381379i
$221$			105.418i			0.477005i
$222$		0			0
$223$			146.188i			0.655551i	0.944756	+	0.327775i	$0.106299\pi$
$223$			146.188i			0.655551i	−0.944756	+	0.327775i	$0.893701\pi$
$224$		−	54.2351i		−	0.242121i
$225$		0			0
$226$	111.784			0.494617
$227$	−161.475			−0.711344			−0.355672	−	0.934611i	$-0.615748\pi$
$227$	−161.475			−0.711344			−0.355672	+	0.934611i	$0.615748\pi$
$228$		0			0
$229$	25.6646			0.112072			0.0560361	−	0.998429i	$-0.482154\pi$
$229$	25.6646			0.112072			0.0560361	+	0.998429i	$0.482154\pi$
$230$	177.927	+	123.238i	0.773594	+	0.535816i
$231$		0			0
$232$			118.808i			0.512104i
$233$	−103.288			−0.443295			−0.221648	−	0.975127i	$-0.571143\pi$
$233$	−103.288			−0.443295			−0.221648	+	0.975127i	$0.571143\pi$
$234$		0			0
$235$	51.6934	+	35.8044i	0.219972	+	0.152359i
$236$			64.7783i			0.274484i
$237$		0			0
$238$			413.853i			1.73888i
$239$			285.875i			1.19613i	0.801447	+	0.598066i	$0.204064\pi$
$239$			285.875i			1.19613i	−0.801447	+	0.598066i	$0.795936\pi$
$240$		0			0
$241$	246.688			1.02360			0.511801	−	0.859104i	$-0.328978\pi$
$241$	246.688			1.02360			0.511801	+	0.859104i	$0.328978\pi$
$242$	−23.8009			−0.0983508
$243$		0			0
$244$	−228.490			−0.936436
$245$	176.417	+	122.192i	0.720068	+	0.498742i
$246$		0			0
$247$		−	34.8334i		−	0.141026i
$248$	28.3958			0.114499
$249$		0			0
$250$	−43.1345	+	171.433i	−0.172538	+	0.685734i
$251$			27.8147i			0.110815i	0.998464	+	0.0554077i	$0.0176459\pi$
$251$			27.8147i			0.110815i	−0.998464	+	0.0554077i	$0.982354\pi$
$252$		0			0
$253$			312.407i			1.23481i
$254$			329.527i			1.29735i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−151.862			−0.590902			−0.295451	−	0.955358i	$-0.595470\pi$
$257$	−151.862			−0.590902			−0.295451	+	0.955358i	$0.595470\pi$
$258$		0			0
$259$	−210.836			−0.814038
$260$	−19.6653	+	28.3921i	−0.0756356	+	0.109200i
$261$		0			0
$262$		−	105.497i		−	0.402661i
$263$	302.639			1.15072			0.575359	−	0.817901i	$-0.304862\pi$
$263$	302.639			1.15072			0.575359	+	0.817901i	$0.304862\pi$
$264$		0			0
$265$	193.288	+	133.877i	0.729389	+	0.505197i
$266$		−	136.750i		−	0.514097i
$267$		0			0
$268$		−	64.5642i		−	0.240911i
$269$		−	167.787i		−	0.623742i	−0.950124	−	0.311871i	$-0.899044\pi$
$269$		−	167.787i		−	0.623742i	0.950124	−	0.311871i	$-0.100956\pi$
$270$		0			0
$271$	−77.9380			−0.287594			−0.143797	−	0.989607i	$-0.545931\pi$
$271$	−77.9380			−0.287594			−0.143797	+	0.989607i	$0.545931\pi$
$272$	−122.092			−0.448866
$273$		0			0
$274$	33.2312			0.121282
$275$	−238.869	+	89.7116i	−0.868613	+	0.326224i
$276$		0			0
$277$		−	56.2764i		−	0.203164i	−0.994827	−	0.101582i	$-0.967610\pi$
$277$		−	56.2764i		−	0.203164i	0.994827	−	0.101582i	$-0.0323904\pi$
$278$	305.789			1.09996
$279$		0			0
$280$	−77.2023	+	111.462i	−0.275723	+	0.398080i
$281$			43.0802i			0.153310i	0.997058	+	0.0766552i	$0.0244241\pi$
$281$			43.0802i			0.153310i	−0.997058	+	0.0766552i	$0.975576\pi$
$282$		0			0
$283$			325.457i			1.15002i	0.818145	+	0.575012i	$0.195003\pi$
$283$			325.457i			1.15002i	−0.818145	+	0.575012i	$0.804997\pi$
$284$		−	131.835i		−	0.464207i
$285$		0			0
$286$	−49.8513			−0.174305
$287$	380.274			1.32500
$288$		0			0
$289$	642.647			2.22369
$290$	169.120	−	244.171i	0.583173	−	0.841967i
$291$		0			0
$292$		−	108.340i		−	0.371028i
$293$	149.002			0.508539			0.254269	−	0.967133i	$-0.418165\pi$
$293$	149.002			0.508539			0.254269	+	0.967133i	$0.418165\pi$
$294$		0			0
$295$	92.2102	−	133.130i	0.312577	−	0.451289i
$296$		−	62.1990i		−	0.210132i
$297$		0			0
$298$			317.066i			1.06398i
$299$		−	105.715i		−	0.353563i
$300$		0			0
$301$	207.684			0.689978
$302$	−3.91357			−0.0129589
$303$		0			0
$304$	40.3428			0.132707
$305$	469.586	+	325.250i	1.53963	+	1.06639i
$306$		0			0
$307$		−	559.780i		−	1.82339i	−0.410869	−	0.911694i	$-0.634775\pi$
$307$		−	559.780i		−	1.82339i	0.410869	−	0.911694i	$-0.365225\pi$
$308$	−195.707			−0.635414
$309$		0			0
$310$	−58.3582	−	40.4207i	−0.188252	−	0.130389i
$311$			414.549i			1.33295i	0.745526	+	0.666477i	$0.232198\pi$
$311$			414.549i			1.33295i	−0.745526	+	0.666477i	$0.767802\pi$
$312$		0			0
$313$			96.9061i			0.309604i	0.987946	+	0.154802i	$0.0494740\pi$
$313$			96.9061i			0.309604i	−0.987946	+	0.154802i	$0.950526\pi$
$314$			253.916i			0.808650i
$315$		0			0
$316$	176.252			0.557759
$317$	546.792			1.72490			0.862448	−	0.506146i	$-0.168930\pi$
$317$	546.792			1.72490			0.862448	+	0.506146i	$0.168930\pi$
$318$		0			0
$319$	428.719			1.34395
$320$	−32.8827	−	22.7756i	−0.102758	−	0.0711737i
$321$		0			0
$322$		−	415.020i		−	1.28888i
$323$	−307.845			−0.953080
$324$		0			0
$325$	80.8309	−	30.3576i	0.248710	−	0.0934079i
$326$		−	89.4564i		−	0.274406i
$327$		0			0
$328$			112.185i			0.342028i
$329$		−	120.577i		−	0.366494i
$330$		0			0
$331$	−52.0463			−0.157239			−0.0786197	−	0.996905i	$-0.525051\pi$
$331$	−52.0463			−0.157239			−0.0786197	+	0.996905i	$0.525051\pi$
$332$	−82.2003			−0.247591
$333$		0			0
$334$	−104.568			−0.313078
$335$	−91.9055	+	132.690i	−0.274345	+	0.396091i
$336$		0			0
$337$			275.238i			0.816729i	0.912819	+	0.408364i	$0.133901\pi$
$337$			275.238i			0.816729i	−0.912819	+	0.408364i	$0.866099\pi$
$338$	−222.133			−0.657198
$339$		0			0
$340$	250.919	+	173.794i	0.737996	+	0.511160i
$341$		−	102.466i		−	0.300487i
$342$		0			0
$343$			58.2899i			0.169941i
$344$			61.2691i			0.178108i
$345$		0			0
$346$	17.7862			0.0514051
$347$	60.3048			0.173789			0.0868945	−	0.996218i	$-0.472306\pi$
$347$	60.3048			0.173789			0.0868945	+	0.996218i	$0.472306\pi$
$348$		0			0
$349$	−166.466			−0.476980			−0.238490	−	0.971145i	$-0.576652\pi$
$349$	−166.466			−0.476980			−0.238490	+	0.971145i	$0.576652\pi$
$350$	317.328	−	119.178i	0.906650	−	0.340510i
$351$		0			0
$352$		−	57.7360i		−	0.164023i
$353$	−496.272			−1.40587			−0.702935	−	0.711254i	$-0.748128\pi$
$353$	−496.272			−1.40587			−0.702935	+	0.711254i	$0.748128\pi$
$354$		0			0
$355$	−187.663	+	270.943i	−0.528629	+	0.763219i
$356$		−	77.0606i		−	0.216462i
$357$		0			0
$358$		−	317.515i		−	0.886912i
$359$		−	508.248i		−	1.41573i	−0.706347	−	0.707866i	$-0.749658\pi$
$359$		−	508.248i		−	1.41573i	0.706347	−	0.707866i	$-0.250342\pi$
$360$		0			0
$361$	−259.279			−0.718223
$362$	63.3918			0.175115
$363$		0			0
$364$	66.2255			0.181938
$365$	−154.219	+	222.657i	−0.422519	+	0.610020i
$366$		0			0
$367$			115.919i			0.315856i	0.987451	+	0.157928i	$0.0504813\pi$
$367$			115.919i			0.315856i	−0.987451	+	0.157928i	$0.949519\pi$
$368$	122.436			0.332706
$369$		0			0
$370$	−88.5388	+	127.830i	−0.239294	+	0.345485i
$371$		−	450.851i		−	1.21523i
$372$		0			0
$373$			322.072i			0.863465i	0.902002	+	0.431733i	$0.142098\pi$
$373$			322.072i			0.863465i	−0.902002	+	0.431733i	$0.857902\pi$
$374$			440.567i			1.17799i
$375$		0			0
$376$	35.5715			0.0946051
$377$	−145.074			−0.384813
$378$		0			0
$379$	−393.644			−1.03864			−0.519319	−	0.854581i	$-0.673814\pi$
$379$	−393.644			−1.03864			−0.519319	+	0.854581i	$0.673814\pi$
$380$	−82.9113	−	57.4269i	−0.218188	−	0.151124i
$381$		0			0
$382$		−	394.057i		−	1.03156i
$383$	−133.515			−0.348604			−0.174302	−	0.984692i	$-0.555767\pi$
$383$	−133.515			−0.348604			−0.174302	+	0.984692i	$0.555767\pi$
$384$		0			0
$385$	402.212	+	278.585i	1.04471	+	0.723596i
$386$			462.572i			1.19837i
$387$		0			0
$388$		−	256.514i		−	0.661119i
$389$			646.213i			1.66121i	0.556859	+	0.830607i	$0.312007\pi$
$389$			646.213i			1.66121i	−0.556859	+	0.830607i	$0.687993\pi$
$390$		0			0
$391$	−934.274			−2.38945
$392$	121.397			0.309686
$393$		0			0
$394$	−276.124			−0.700822
$395$	−362.227	−	250.890i	−0.917032	−	0.635165i
$396$		0			0
$397$			93.2322i			0.234842i	0.993082	+	0.117421i	$0.0374626\pi$
$397$			93.2322i			0.234842i	−0.993082	+	0.117421i	$0.962537\pi$
$398$	166.505			0.418355
$399$		0			0
$400$	35.1590	+	93.6154i	0.0878976	+	0.234038i
$401$			364.865i			0.909889i	0.890520	+	0.454944i	$0.150341\pi$
$401$			364.865i			0.909889i	−0.890520	+	0.454944i	$0.849659\pi$
$402$		0			0
$403$			34.6736i			0.0860387i
$404$			122.244i			0.302584i
$405$		0			0
$406$	−569.536			−1.40280
$407$	−224.445			−0.551463
$408$		0			0
$409$	343.973			0.841009			0.420505	−	0.907290i	$-0.361853\pi$
$409$	343.973			0.841009			0.420505	+	0.907290i	$0.361853\pi$
$410$	159.693	−	230.560i	0.389495	−	0.562341i
$411$		0			0
$412$		−	164.898i		−	0.400239i
$413$	−310.531			−0.751891
$414$		0			0
$415$	168.935	+	117.010i	0.407073	+	0.281952i
$416$			19.5373i			0.0469647i
$417$		0			0
$418$		−	145.577i		−	0.348270i
$419$		−	696.315i		−	1.66185i	−0.556385	−	0.830924i	$-0.687812\pi$
$419$		−	696.315i		−	1.66185i	0.556385	−	0.830924i	$-0.312188\pi$
$420$		0			0
$421$	−335.998			−0.798094			−0.399047	−	0.916931i	$-0.630659\pi$
$421$	−335.998			−0.798094			−0.399047	+	0.916931i	$0.630659\pi$
$422$	−99.1634			−0.234984
$423$		0			0
$424$	133.006			0.313694
$425$	−268.289	−	714.353i	−0.631268	−	1.68083i
$426$		0			0
$427$		−	1095.33i		−	2.56517i
$428$	−120.807			−0.282259
$429$		0			0
$430$	87.2150	−	125.918i	0.202826	−	0.292833i
$431$			161.905i			0.375649i	0.982203	+	0.187825i	$0.0601436\pi$
$431$			161.905i			0.375649i	−0.982203	+	0.187825i	$0.939856\pi$
$432$		0			0
$433$			311.373i			0.719107i	0.933125	+	0.359553i	$0.117071\pi$
$433$			311.373i			0.719107i	−0.933125	+	0.359553i	$0.882929\pi$
$434$			136.122i			0.313646i
$435$		0			0
$436$	−290.991			−0.667411
$437$	308.713			0.706436
$438$		0			0
$439$	−757.398			−1.72528			−0.862640	−	0.505818i	$-0.831191\pi$
$439$	−757.398			−1.72528			−0.862640	+	0.505818i	$0.831191\pi$
$440$	−82.1857	+	118.657i	−0.186786	+	0.269676i
$441$		0			0
$442$		−	149.084i		−	0.337294i
$443$	39.4967			0.0891573			0.0445787	−	0.999006i	$-0.485805\pi$
$443$	39.4967			0.0891573			0.0445787	+	0.999006i	$0.485805\pi$
$444$		0			0
$445$	−109.694	+	158.373i	−0.246503	+	0.355893i
$446$		−	206.741i		−	0.463544i
$447$		0			0
$448$			76.7000i			0.171205i
$449$		−	329.154i		−	0.733083i	−0.930402	−	0.366541i	$-0.880542\pi$
$449$		−	329.154i		−	0.733083i	0.930402	−	0.366541i	$-0.119458\pi$
$450$		0			0
$451$	404.821			0.897607
$452$	−158.086			−0.349747
$453$		0			0
$454$	228.360			0.502996
$455$	−136.105	−	94.2704i	−0.299131	−	0.207188i
$456$		0			0
$457$		−	682.795i		−	1.49408i	−0.664779	−	0.747041i	$-0.731474\pi$
$457$		−	682.795i		−	1.49408i	0.664779	−	0.747041i	$-0.268526\pi$
$458$	−36.2952			−0.0792471
$459$		0			0
$460$	−251.626	−	174.284i	−0.547014	−	0.378879i
$461$			200.713i			0.435387i	0.976017	+	0.217693i	$0.0698533\pi$
$461$			200.713i			0.435387i	−0.976017	+	0.217693i	$0.930147\pi$
$462$		0			0
$463$		−	490.118i		−	1.05857i	−0.848444	−	0.529285i	$-0.822460\pi$
$463$		−	490.118i		−	1.05857i	0.848444	−	0.529285i	$-0.177540\pi$
$464$		−	168.020i		−	0.362112i
$465$		0			0
$466$	146.071			0.313457
$467$	−499.296			−1.06916			−0.534579	−	0.845119i	$-0.679530\pi$
$467$	−499.296			−1.06916			−0.534579	+	0.845119i	$0.679530\pi$
$468$		0			0
$469$	309.505			0.659925
$470$	−73.1055	−	50.6351i	−0.155544	−	0.107734i
$471$		0			0
$472$		−	91.6103i		−	0.194090i
$473$	221.090			0.467420
$474$		0			0
$475$	88.6509	+	236.044i	0.186633	+	0.496935i
$476$		−	585.277i		−	1.22957i
$477$		0			0
$478$		−	404.289i		−	0.845793i
$479$			289.819i			0.605049i	0.953142	+	0.302525i	$0.0978294\pi$
$479$			289.819i			0.605049i	−0.953142	+	0.302525i	$0.902171\pi$
$480$		0			0
$481$	75.9502			0.157901
$482$	−348.870			−0.723796
$483$		0			0
$484$	33.6596			0.0695445
$485$	−365.141	+	527.180i	−0.752869	+	1.08697i
$486$		0			0
$487$			130.758i			0.268497i	0.990948	+	0.134249i	$0.0428621\pi$
$487$			130.758i			0.268497i	−0.990948	+	0.134249i	$0.957138\pi$
$488$	323.134			0.662160
$489$		0			0
$490$	−249.491	−	172.805i	−0.509165	−	0.352664i
$491$		−	806.195i		−	1.64194i	−0.570968	−	0.820972i	$-0.693432\pi$
$491$		−	806.195i		−	1.64194i	0.570968	−	0.820972i	$-0.306568\pi$
$492$		0			0
$493$			1282.11i			2.60064i
$494$			49.2619i			0.0997204i
$495$		0			0
$496$	−40.1577			−0.0809631
$497$	631.983			1.27160
$498$		0			0
$499$	−248.367			−0.497730			−0.248865	−	0.968538i	$-0.580058\pi$
$499$	−248.367			−0.497730			−0.248865	+	0.968538i	$0.580058\pi$
$500$	61.0014	−	242.443i	0.122003	−	0.484887i
$501$		0			0
$502$		−	39.3359i		−	0.0783583i
$503$	713.802			1.41909			0.709545	−	0.704661i	$-0.248901\pi$
$503$	713.802			1.41909			0.709545	+	0.704661i	$0.248901\pi$
$504$		0			0
$505$	174.011	−	251.232i	0.344576	−	0.497489i
$506$		−	441.810i		−	0.873142i
$507$		0			0
$508$		−	466.021i		−	0.917365i
$509$		−	394.430i		−	0.774911i	−0.921888	−	0.387456i	$-0.873354\pi$
$509$		−	394.430i		−	0.774911i	0.921888	−	0.387456i	$-0.126646\pi$
$510$		0			0
$511$	519.356			1.01635
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	214.765			0.417831
$515$	−234.729	+	338.894i	−0.455784	+	0.658047i
$516$		0			0
$517$		−	128.360i		−	0.248278i
$518$	298.167			0.575612
$519$		0			0
$520$	27.8109	−	40.1525i	0.0534825	−	0.0772163i
$521$		−	75.4415i		−	0.144801i	−0.997376	−	0.0724007i	$-0.976934\pi$
$521$		−	75.4415i		−	0.144801i	0.997376	−	0.0724007i	$-0.0230660\pi$
$522$		0			0
$523$		−	320.198i		−	0.612232i	−0.951994	−	0.306116i	$-0.900970\pi$
$523$		−	320.198i		−	0.612232i	0.951994	−	0.306116i	$-0.0990296\pi$
$524$			149.196i			0.284724i
$525$		0			0
$526$	−427.996			−0.813680
$527$	306.432			0.581466
$528$		0			0
$529$	407.908			0.771092
$530$	−273.351	−	189.331i	−0.515756	−	0.357229i
$531$		0			0
$532$			193.393i			0.363521i
$533$	−136.987			−0.257012
$534$		0			0
$535$	248.279	+	171.966i	0.464072	+	0.321431i
$536$			91.3076i			0.170350i
$537$		0			0
$538$			237.286i			0.441052i
$539$		−	438.060i		−	0.812728i
$540$		0			0
$541$	8.73058			0.0161379			0.00806893	−	0.999967i	$-0.497432\pi$
$541$	8.73058			0.0161379			0.00806893	+	0.999967i	$0.497432\pi$
$542$	110.221			0.203360
$543$		0			0
$544$	172.664			0.317396
$545$	598.036	+	414.218i	1.09731	+	0.760034i
$546$		0			0
$547$		−	496.549i		−	0.907768i	−0.891061	−	0.453884i	$-0.850038\pi$
$547$		−	496.549i		−	0.907768i	0.891061	−	0.453884i	$-0.149962\pi$
$548$	−46.9960			−0.0857592
$549$		0			0
$550$	337.811	−	126.871i	0.614202	−	0.230675i
$551$		−	423.650i		−	0.768874i
$552$		0			0
$553$			844.908i			1.52786i
$554$			79.5868i			0.143658i
$555$		0			0
$556$	−432.451			−0.777789
$557$	−81.4006			−0.146141			−0.0730706	−	0.997327i	$-0.523280\pi$
$557$	−81.4006			−0.146141			−0.0730706	+	0.997327i	$0.523280\pi$
$558$		0			0
$559$	−74.8146			−0.133837
$560$	109.181	−	157.632i	0.194965	−	0.281485i
$561$		0			0
$562$		−	60.9247i		−	0.108407i
$563$	−633.842			−1.12583			−0.562915	−	0.826515i	$-0.690320\pi$
$563$	−633.842			−1.12583			−0.562915	+	0.826515i	$0.690320\pi$
$564$		0			0
$565$	324.893	+	225.031i	0.575032	+	0.398285i
$566$		−	460.265i		−	0.813189i
$567$		0			0
$568$			186.442i			0.328244i
$569$		−	990.851i		−	1.74139i	−0.491824	−	0.870695i	$-0.663670\pi$
$569$		−	990.851i		−	1.74139i	0.491824	−	0.870695i	$-0.336330\pi$
$570$		0			0
$571$	864.747			1.51444			0.757222	−	0.653158i	$-0.226556\pi$
$571$	864.747			1.51444			0.757222	+	0.653158i	$0.226556\pi$
$572$	70.5004			0.123253
$573$		0			0
$574$	−537.788			−0.936913
$575$	269.045	+	716.367i	0.467905	+	1.24586i
$576$		0			0
$577$			475.177i			0.823530i	0.911290	+	0.411765i	$0.135088\pi$
$577$			475.177i			0.823530i	−0.911290	+	0.411765i	$0.864912\pi$
$578$	−908.840			−1.57239
$579$		0			0
$580$	−239.172	+	345.309i	−0.412366	+	0.595361i
$581$		−	394.048i		−	0.678223i
$582$		0			0
$583$		−	479.953i		−	0.823248i
$584$			153.216i			0.262356i
$585$		0			0
$586$	−210.720			−0.359591
$587$	−893.206			−1.52165			−0.760823	−	0.648960i	$-0.775204\pi$
$587$	−893.206			−1.52165			−0.760823	+	0.648960i	$0.775204\pi$
$588$		0			0
$589$	−101.255			−0.171909
$590$	−130.405	+	188.275i	−0.221025	+	0.319110i
$591$		0			0
$592$			87.9627i			0.148586i
$593$	113.870			0.192024			0.0960121	−	0.995380i	$-0.469391\pi$
$593$	113.870			0.192024			0.0960121	+	0.995380i	$0.469391\pi$
$594$		0			0
$595$	−833.126	+	1202.84i	−1.40021	+	2.02158i
$596$		−	448.399i		−	0.752347i
$597$		0			0
$598$			149.504i			0.250007i
$599$			16.8382i			0.0281106i	0.999901	+	0.0140553i	$0.00447409\pi$
$599$			16.8382i			0.0281106i	−0.999901	+	0.0140553i	$0.995526\pi$
$600$		0			0
$601$	757.984			1.26120			0.630602	−	0.776106i	$-0.282808\pi$
$601$	757.984			1.26120			0.630602	+	0.776106i	$0.282808\pi$
$602$	−293.709			−0.487888
$603$		0			0
$604$	5.53463			0.00916329
$605$	−69.1761	−	47.9135i	−0.114341	−	0.0791959i
$606$		0			0
$607$			74.6302i			0.122949i	0.998109	+	0.0614746i	$0.0195803\pi$
$607$			74.6302i			0.122949i	−0.998109	+	0.0614746i	$0.980420\pi$
$608$	−57.0533			−0.0938377
$609$		0			0
$610$	−664.095	−	459.973i	−1.08868	−	0.754054i
$611$			43.4357i			0.0710896i
$612$		0			0
$613$		−	79.0426i		−	0.128944i	−0.997920	−	0.0644719i	$-0.979464\pi$
$613$		−	79.0426i		−	0.128944i	0.997920	−	0.0644719i	$-0.0205363\pi$
$614$			791.649i			1.28933i
$615$		0			0
$616$	276.772			0.449305
$617$	−639.650			−1.03671			−0.518355	−	0.855166i	$-0.673455\pi$
$617$	−639.650			−1.03671			−0.518355	+	0.855166i	$0.673455\pi$
$618$		0			0
$619$	684.319			1.10552			0.552762	−	0.833339i	$-0.313574\pi$
$619$	684.319			1.10552			0.552762	+	0.833339i	$0.313574\pi$
$620$	82.5309	+	57.1635i	0.133114	+	0.0921992i
$621$		0			0
$622$		−	586.260i		−	0.942541i
$623$	369.409			0.592953
$624$		0			0
$625$	−470.480	+	411.428i	−0.752768	+	0.658285i
$626$		−	137.046i		−	0.218923i
$627$		0			0
$628$		−	359.091i		−	0.571802i
$629$		−	671.219i		−	1.06712i
$630$		0			0
$631$	126.191			0.199985			0.0999926	−	0.994988i	$-0.468118\pi$
$631$	126.191			0.199985			0.0999926	+	0.994988i	$0.468118\pi$
$632$	−249.258			−0.394395
$633$		0			0
$634$	−773.281			−1.21969
$635$	−663.370	+	957.753i	−1.04468	+	1.50827i
$636$		0			0
$637$			148.235i			0.232709i
$638$	−606.300			−0.950313
$639$		0			0
$640$	46.5032	+	32.2096i	0.0726612	+	0.0503274i
$641$		−	581.233i		−	0.906760i	−0.891317	−	0.453380i	$-0.850218\pi$
$641$		−	581.233i		−	0.906760i	0.891317	−	0.453380i	$-0.149782\pi$
$642$		0			0
$643$		−	567.280i		−	0.882239i	−0.897448	−	0.441120i	$-0.854581\pi$
$643$		−	567.280i		−	0.882239i	0.897448	−	0.441120i	$-0.145419\pi$
$644$			586.927i			0.911377i
$645$		0			0
$646$	435.358			0.673929
$647$	−264.409			−0.408669			−0.204334	−	0.978901i	$-0.565503\pi$
$647$	−264.409			−0.408669			−0.204334	+	0.978901i	$0.565503\pi$
$648$		0			0
$649$	−330.576			−0.509362
$650$	−114.312	+	42.9321i	−0.175865	+	0.0660494i
$651$		0			0
$652$			126.510i			0.194034i
$653$	−995.446			−1.52442			−0.762210	−	0.647330i	$-0.775886\pi$
$653$	−995.446			−1.52442			−0.762210	+	0.647330i	$0.775886\pi$
$654$		0			0
$655$	212.376	−	306.622i	0.324238	−	0.468125i
$656$		−	158.654i		−	0.241850i
$657$		0			0
$658$			170.521i			0.259150i
$659$		−	437.458i		−	0.663820i	−0.943311	−	0.331910i	$-0.892307\pi$
$659$		−	437.458i		−	0.663820i	0.943311	−	0.331910i	$-0.107693\pi$
$660$		0			0
$661$	260.560			0.394190			0.197095	−	0.980384i	$-0.436849\pi$
$661$	260.560			0.394190			0.197095	+	0.980384i	$0.436849\pi$
$662$	73.6045			0.111185
$663$		0			0
$664$	116.249			0.175073
$665$	275.291	−	397.456i	0.413971	−	0.597678i
$666$		0			0
$667$		−	1285.73i		−	1.92763i
$668$	147.882			0.221380
$669$		0			0
$670$	129.974	−	187.653i	0.193991	−	0.280078i
$671$		−	1166.03i		−	1.73775i
$672$		0			0
$673$		−	780.670i		−	1.15998i	−0.814622	−	0.579992i	$-0.803055\pi$
$673$		−	780.670i		−	1.15998i	0.814622	−	0.579992i	$-0.196945\pi$
$674$		−	389.245i		−	0.577515i
$675$		0			0
$676$	314.143			0.464709
$677$	−272.656			−0.402741			−0.201371	−	0.979515i	$-0.564540\pi$
$677$	−272.656			−0.402741			−0.201371	+	0.979515i	$0.564540\pi$
$678$		0			0
$679$	1229.67			1.81099
$680$	−354.853	−	245.782i	−0.521842	−	0.361444i
$681$		0			0
$682$			144.909i			0.212477i
$683$	292.767			0.428649			0.214325	−	0.976763i	$-0.431245\pi$
$683$	292.767			0.428649			0.214325	+	0.976763i	$0.431245\pi$
$684$		0			0
$685$	96.5848	+	66.8976i	0.141000	+	0.0976608i
$686$		−	82.4343i		−	0.120167i
$687$		0			0
$688$		−	86.6476i		−	0.125941i
$689$			162.412i			0.235721i
$690$		0			0
$691$	−1190.20			−1.72243			−0.861213	−	0.508245i	$-0.830294\pi$
$691$	−1190.20			−1.72243			−0.861213	+	0.508245i	$0.830294\pi$
$692$	−25.1534			−0.0363489
$693$		0			0
$694$	−85.2838			−0.122887
$695$	888.759	+	615.583i	1.27879	+	0.885730i
$696$		0			0
$697$			1210.64i			1.73694i
$698$	235.419			0.337276
$699$		0			0
$700$	−448.769	+	168.544i	−0.641099	+	0.240777i
$701$		−	178.121i		−	0.254095i	−0.991897	−	0.127048i	$-0.959450\pi$
$701$		−	178.121i		−	0.254095i	0.991897	−	0.127048i	$-0.0405501\pi$
$702$		0			0
$703$			221.791i			0.315493i
$704$			81.6511i			0.115982i
$705$		0			0
$706$	701.835			0.994100
$707$	−586.007			−0.828864
$708$		0			0
$709$	−1052.92			−1.48508			−0.742542	−	0.669800i	$-0.766380\pi$
$709$	−1052.92			−1.48508			−0.742542	+	0.669800i	$0.766380\pi$
$710$	265.396	−	383.171i	0.373797	−	0.539677i
$711$		0			0
$712$			108.980i			0.153062i
$713$	−307.296			−0.430991
$714$		0			0
$715$	−144.890	−	100.356i	−0.202644	−	0.140357i
$716$			449.033i			0.627142i
$717$		0			0
$718$			718.771i			1.00107i
$719$			611.205i			0.850076i	0.905175	+	0.425038i	$0.139739\pi$
$719$			611.205i			0.850076i	−0.905175	+	0.425038i	$0.860261\pi$
$720$		0			0
$721$	790.482			1.09637
$722$	366.675			0.507861
$723$		0			0
$724$	−89.6495			−0.123825
$725$	983.078	−	369.214i	1.35597	−	0.509260i
$726$		0			0
$727$			1446.91i			1.99025i	0.0986043	+	0.995127i	$0.468562\pi$
$727$			1446.91i			1.99025i	−0.0986043	+	0.995127i	$0.531438\pi$
$728$	−93.6571			−0.128650
$729$		0			0
$730$	218.099	−	314.885i	0.298766	−	0.431349i
$731$			661.184i			0.904492i
$732$		0			0
$733$			904.308i			1.23371i	0.787078	+	0.616854i	$0.211593\pi$
$733$			904.308i			1.23371i	−0.787078	+	0.616854i	$0.788407\pi$
$734$		−	163.934i		−	0.223344i
$735$		0			0
$736$	−173.150			−0.235259
$737$	329.483			0.447060
$738$		0			0
$739$	−287.255			−0.388708			−0.194354	−	0.980931i	$-0.562261\pi$
$739$	−287.255			−0.388708			−0.194354	+	0.980931i	$0.562261\pi$
$740$	125.213	−	180.778i	0.169206	−	0.244295i
$741$		0			0
$742$			637.599i			0.859298i
$743$	150.228			0.202191			0.101095	−	0.994877i	$-0.467765\pi$
$743$	150.228			0.202191			0.101095	+	0.994877i	$0.467765\pi$
$744$		0			0
$745$	−638.284	+	921.535i	−0.856758	+	1.23696i
$746$		−	455.479i		−	0.610562i
$747$		0			0
$748$		−	623.057i		−	0.832963i
$749$		−	579.118i		−	0.773189i
$750$		0			0
$751$	338.180			0.450306			0.225153	−	0.974323i	$-0.427712\pi$
$751$	338.180			0.450306			0.225153	+	0.974323i	$0.427712\pi$
$752$	−50.3057			−0.0668959
$753$		0			0
$754$	205.166			0.272104
$755$	−11.3746	−	7.87840i	−0.0150657	−	0.0104350i
$756$		0			0
$757$			1070.64i			1.41432i	0.707053	+	0.707160i	$0.250024\pi$
$757$			1070.64i			1.41432i	−0.707053	+	0.707160i	$0.749976\pi$
$758$	556.696			0.734428
$759$		0			0
$760$	117.254	+	81.2140i	0.154282	+	0.106860i
$761$			810.405i			1.06492i	0.846455	+	0.532460i	$0.178732\pi$
$761$			810.405i			1.06492i	−0.846455	+	0.532460i	$0.821268\pi$
$762$		0			0
$763$		−	1394.94i		−	1.82823i
$764$			557.280i			0.729425i
$765$		0			0
$766$	188.819			0.246500
$767$	111.864			0.145846
$768$		0			0
$769$	−957.950			−1.24571			−0.622854	−	0.782338i	$-0.714027\pi$
$769$	−957.950			−1.24571			−0.622854	+	0.782338i	$0.714027\pi$
$770$	−568.814	−	393.978i	−0.738719	−	0.511660i
$771$		0			0
$772$		−	654.175i		−	0.847377i
$773$	−35.2002			−0.0455371			−0.0227686	−	0.999741i	$-0.507248\pi$
$773$	−35.2002			−0.0455371			−0.0227686	+	0.999741i	$0.507248\pi$
$774$		0			0
$775$	−88.2442	−	234.961i	−0.113863	−	0.303176i
$776$			362.766i			0.467482i
$777$		0			0
$778$		−	913.883i		−	1.17466i
$779$		−	400.034i		−	0.513522i
$780$		0			0
$781$	672.778			0.861431
$782$	1321.26			1.68959
$783$		0			0
$784$	−171.681			−0.218981
$785$	−511.157	+	737.994i	−0.651156	+	0.940119i
$786$		0			0
$787$		−	539.697i		−	0.685765i	−0.939378	−	0.342882i	$-0.888597\pi$
$787$		−	539.697i		−	0.685765i	0.939378	−	0.342882i	$-0.111403\pi$
$788$	390.498			0.495556
$789$		0			0
$790$	512.267	+	354.812i	0.648439	+	0.449129i
$791$		−	757.824i		−	0.958058i
$792$		0			0
$793$			394.573i			0.497570i
$794$		−	131.850i		−	0.166058i
$795$		0			0
$796$	−235.474			−0.295821
$797$	−439.824			−0.551850			−0.275925	−	0.961179i	$-0.588984\pi$
$797$	−439.824			−0.551850			−0.275925	+	0.961179i	$0.588984\pi$
$798$		0			0
$799$	383.869			0.480437
$800$	−49.7224	−	132.392i	−0.0621530	−	0.165490i
$801$		0			0
$802$		−	515.998i		−	0.643389i
$803$	552.880			0.688519
$804$		0			0
$805$	835.475	−	1206.23i	1.03786	−	1.49843i
$806$		−	49.0359i		−	0.0608386i
$807$		0			0
$808$		−	172.879i		−	0.213959i
$809$			908.178i			1.12259i	0.827615	+	0.561296i	$0.189697\pi$
$809$			908.178i			1.12259i	−0.827615	+	0.561296i	$0.810303\pi$
$810$		0			0
$811$	−1109.07			−1.36753			−0.683766	−	0.729701i	$-0.739659\pi$
$811$	−1109.07			−1.36753			−0.683766	+	0.729701i	$0.739659\pi$
$812$	805.446			0.991928
$813$		0			0
$814$	317.414			0.389943
$815$	180.084	−	260.000i	0.220962	−	0.319019i
$816$		0			0
$817$		−	218.475i		−	0.267412i
$818$	−486.451			−0.594683
$819$		0			0
$820$	−225.840	+	326.061i	−0.275414	+	0.397635i
$821$			501.720i			0.611109i	0.952175	+	0.305554i	$0.0988418\pi$
$821$			501.720i			0.611109i	−0.952175	+	0.305554i	$0.901158\pi$
$822$		0			0
$823$			767.865i			0.933008i	0.884519	+	0.466504i	$0.154487\pi$
$823$			767.865i			0.933008i	−0.884519	+	0.466504i	$0.845513\pi$
$824$			233.201i			0.283012i
$825$		0			0
$826$	439.157			0.531667
$827$	1016.13			1.22870			0.614349	−	0.789034i	$-0.289419\pi$
$827$	1016.13			1.22870			0.614349	+	0.789034i	$0.289419\pi$
$828$		0			0
$829$	699.908			0.844279			0.422140	−	0.906531i	$-0.361279\pi$
$829$	699.908			0.844279			0.422140	+	0.906531i	$0.361279\pi$
$830$	−238.911	−	165.477i	−0.287844	−	0.199370i
$831$		0			0
$832$		−	27.6299i		−	0.0332091i
$833$	1310.05			1.57269
$834$		0			0
$835$	−303.922	−	210.506i	−0.363978	−	0.252103i
$836$			205.877i			0.246264i
$837$		0			0
$838$			984.738i			1.17510i
$839$		−	156.865i		−	0.186967i	−0.995621	−	0.0934835i	$-0.970200\pi$
$839$		−	156.865i		−	0.186967i	0.995621	−	0.0934835i	$-0.0298002\pi$
$840$		0			0
$841$	−923.418			−1.09800
$842$	475.172			0.564338
$843$		0			0
$844$	140.238			0.166159
$845$	−645.618	−	447.175i	−0.764045	−	0.529201i
$846$		0			0
$847$			161.356i			0.190502i
$848$	−188.099			−0.221815
$849$		0			0
$850$	379.418	+	1010.25i	0.446374	+	1.18853i
$851$			673.112i			0.790966i
$852$		0			0
$853$			823.797i			0.965765i	0.875685	+	0.482882i	$0.160410\pi$
$853$			823.797i			0.965765i	−0.875685	+	0.482882i	$0.839590\pi$
$854$			1549.02i			1.81385i
$855$		0			0
$856$	170.847			0.199587
$857$	−1048.57			−1.22353			−0.611766	−	0.791039i	$-0.709541\pi$
$857$	−1048.57			−1.22353			−0.611766	+	0.791039i	$0.709541\pi$
$858$		0			0
$859$	−1281.59			−1.49196			−0.745978	−	0.665970i	$-0.768018\pi$
$859$	−1281.59			−1.49196			−0.745978	+	0.665970i	$0.768018\pi$
$860$	−123.341	+	178.075i	−0.143419	+	0.207064i
$861$		0			0
$862$		−	228.968i		−	0.265624i
$863$	−1035.47			−1.19985			−0.599923	−	0.800058i	$-0.704802\pi$
$863$	−1035.47			−1.19985			−0.599923	+	0.800058i	$0.704802\pi$
$864$		0			0
$865$	51.6946	+	35.8053i	0.0597625	+	0.0413934i
$866$		−	440.348i		−	0.508485i
$867$		0			0
$868$		−	192.506i		−	0.221781i
$869$			899.447i			1.03504i
$870$		0			0
$871$	−111.494			−0.128007
$872$	411.524			0.471931
$873$		0			0
$874$	−436.586			−0.499526
$875$	1162.21	+	292.425i	1.32824	+	0.334200i
$876$		0			0
$877$		−	365.375i		−	0.416619i	−0.978063	−	0.208310i	$-0.933204\pi$
$877$		−	365.375i		−	0.416619i	0.978063	−	0.208310i	$-0.0667962\pi$
$878$	1071.12			1.21996
$879$		0			0
$880$	116.228	−	167.807i	0.132077	−	0.190689i
$881$			743.814i			0.844284i	0.906530	+	0.422142i	$0.138722\pi$
$881$			743.814i			0.844284i	−0.906530	+	0.422142i	$0.861278\pi$
$882$		0			0
$883$			122.004i			0.138170i	0.997611	+	0.0690851i	$0.0220080\pi$
$883$			122.004i			0.138170i	−0.997611	+	0.0690851i	$0.977992\pi$
$884$			210.836i			0.238503i
$885$		0			0
$886$	−55.8568			−0.0630437
$887$	1346.82			1.51839			0.759197	−	0.650860i	$-0.225592\pi$
$887$	1346.82			1.51839			0.759197	+	0.650860i	$0.225592\pi$
$888$		0			0
$889$	2233.99			2.51293
$890$	155.130	−	223.973i	0.174304	−	0.251655i
$891$		0			0
$892$			292.376i			0.327775i
$893$	−126.842			−0.142040
$894$		0			0
$895$	639.188	−	922.840i	0.714176	−	1.03111i
$896$		−	108.470i		−	0.121061i
$897$		0			0
$898$			465.494i			0.518368i
$899$			421.706i			0.469083i
$900$		0			0
$901$	1435.33			1.59305
$902$	−572.503			−0.634704
$903$		0			0
$904$	223.567			0.247309
$905$	184.245	+	127.614i	0.203586	+	0.141010i
$906$		0			0
$907$			1401.15i			1.54482i	0.635124	+	0.772410i	$0.280949\pi$
$907$			1401.15i			1.54482i	−0.635124	+	0.772410i	$0.719051\pi$
$908$	−322.950			−0.355672
$909$		0			0
$910$	192.481	+	133.318i	0.211518	+	0.146504i
$911$			559.156i			0.613783i	0.951745	+	0.306891i	$0.0992888\pi$
$911$			559.156i			0.613783i	−0.951745	+	0.306891i	$0.900711\pi$
$912$		0			0
$913$		−	419.484i		−	0.459456i
$914$			965.618i			1.05647i
$915$		0			0
$916$	51.3291			0.0560361
$917$	−715.207			−0.779942
$918$		0			0
$919$	27.5595			0.0299886			0.0149943	−	0.999888i	$-0.495227\pi$
$919$	27.5595			0.0299886			0.0149943	+	0.999888i	$0.495227\pi$
$920$	355.853	+	246.475i	0.386797	+	0.267908i
$921$		0			0
$922$		−	283.851i		−	0.307865i
$923$	−227.662			−0.246654
$924$		0			0
$925$	−514.667	+	193.293i	−0.556396	+	0.208965i
$926$			693.132i			0.748522i
$927$		0			0
$928$			237.616i			0.256052i
$929$		−	965.487i		−	1.03928i	−0.854387	−	0.519638i	$-0.826067\pi$
$929$		−	965.487i		−	1.03928i	0.854387	−	0.519638i	$-0.173933\pi$
$930$		0			0
$931$	−432.880			−0.464963
$932$	−206.576			−0.221648
$933$		0			0
$934$	706.112			0.756008
$935$	−886.905	+	1280.49i	−0.948562	+	1.36950i
$936$		0			0
$937$		−	259.723i		−	0.277186i	−0.990349	−	0.138593i	$-0.955742\pi$
$937$		−	259.723i		−	0.277186i	0.990349	−	0.138593i	$-0.0442580\pi$
$938$	−437.706			−0.466637
$939$		0			0
$940$	103.387	+	71.6089i	0.109986	+	0.0761797i
$941$			377.903i			0.401597i	0.979633	+	0.200799i	$0.0643537\pi$
$941$			377.903i			0.401597i	−0.979633	+	0.200799i	$0.935646\pi$
$942$		0			0
$943$		−	1214.06i		−	1.28744i
$944$			129.557i			0.137242i
$945$		0			0
$946$	−312.668			−0.330516
$947$	−176.474			−0.186350			−0.0931752	−	0.995650i	$-0.529702\pi$
$947$	−176.474			−0.186350			−0.0931752	+	0.995650i	$0.529702\pi$
$948$		0			0
$949$	−187.089			−0.197144
$950$	−125.371	−	333.817i	−0.131970	−	0.351386i
$951$		0			0
$952$			827.706i			0.869439i
$953$	587.748			0.616734			0.308367	−	0.951267i	$-0.400218\pi$
$953$	587.748			0.616734			0.308367	+	0.951267i	$0.400218\pi$
$954$		0			0
$955$	793.274	−	1145.31i	0.830654	−	1.19927i
$956$			571.751i			0.598066i
$957$		0			0
$958$		−	409.865i		−	0.427834i
$959$		−	225.287i		−	0.234919i
$960$		0			0
$961$	−860.210			−0.895120
$962$	−107.410			−0.111653
$963$		0			0
$964$	493.376			0.511801
$965$	−931.202	+	1344.44i	−0.964976	+	1.39320i
$966$		0			0
$967$			508.192i			0.525535i	0.964859	+	0.262767i	$0.0846352\pi$
$967$			508.192i			0.525535i	−0.964859	+	0.262767i	$0.915365\pi$
$968$	−47.6018			−0.0491754
$969$		0			0
$970$	516.388	−	745.545i	0.532359	−	0.768603i
$971$			311.310i			0.320607i	0.987068	+	0.160304i	$0.0512474\pi$
$971$			311.310i			0.320607i	−0.987068	+	0.160304i	$0.948753\pi$
$972$		0			0
$973$		−	2073.06i		−	2.13059i
$974$		−	184.920i		−	0.189856i
$975$		0			0
$976$	−456.981			−0.468218
$977$	407.933			0.417536			0.208768	−	0.977965i	$-0.433055\pi$
$977$	407.933			0.417536			0.208768	+	0.977965i	$0.433055\pi$
$978$		0			0
$979$	393.255			0.401690
$980$	352.833	+	244.383i	0.360034	+	0.249371i
$981$		0			0
$982$			1140.13i			1.16103i
$983$	424.649			0.431992			0.215996	−	0.976394i	$-0.430700\pi$
$983$	424.649			0.431992			0.215996	+	0.976394i	$0.430700\pi$
$984$		0			0
$985$	−802.540	−	555.864i	−0.814761	−	0.564329i
$986$		−	1813.18i		−	1.83893i
$987$		0			0
$988$		−	69.6668i		−	0.0705130i
$989$		−	663.048i		−	0.670423i
$990$		0			0
$991$	−1303.27			−1.31510			−0.657552	−	0.753409i	$-0.728408\pi$
$991$	−1303.27			−1.31510			−0.657552	+	0.753409i	$0.728408\pi$
$992$	56.7916			0.0572496
$993$		0			0
$994$	−893.759			−0.899154
$995$	483.938	+	335.191i	0.486370	+	0.336875i
$996$		0			0
$997$		−	918.200i		−	0.920963i	−0.887669	−	0.460482i	$-0.847677\pi$
$997$		−	918.200i		−	0.920963i	0.887669	−	0.460482i	$-0.152323\pi$
$998$	351.244			0.351948
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.b.b.809.1		16
3.2	odd	2	inner	810.3.b.b.809.16		16
5.4	even	2	inner	810.3.b.b.809.15		16
9.2	odd	6		270.3.j.b.179.2		16
9.4	even	3		270.3.j.b.89.7		16
9.5	odd	6		90.3.j.b.29.3	✓	16
9.7	even	3		90.3.j.b.59.6	yes	16
15.14	odd	2	inner	810.3.b.b.809.2		16
45.2	even	12		1350.3.i.e.1151.8		16
45.4	even	6		270.3.j.b.89.2		16
45.7	odd	12		450.3.i.e.401.1		16
45.13	odd	12		1350.3.i.e.251.1		16
45.14	odd	6		90.3.j.b.29.6	yes	16
45.22	odd	12		1350.3.i.e.251.8		16
45.23	even	12		450.3.i.e.101.8		16
45.29	odd	6		270.3.j.b.179.7		16
45.32	even	12		450.3.i.e.101.1		16
45.34	even	6		90.3.j.b.59.3	yes	16
45.38	even	12		1350.3.i.e.1151.1		16
45.43	odd	12		450.3.i.e.401.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.j.b.29.3	✓	16	9.5	odd	6
90.3.j.b.29.6	yes	16	45.14	odd	6
90.3.j.b.59.3	yes	16	45.34	even	6
90.3.j.b.59.6	yes	16	9.7	even	3
270.3.j.b.89.2		16	45.4	even	6
270.3.j.b.89.7		16	9.4	even	3
270.3.j.b.179.2		16	9.2	odd	6
270.3.j.b.179.7		16	45.29	odd	6
450.3.i.e.101.1		16	45.32	even	12
450.3.i.e.101.8		16	45.23	even	12
450.3.i.e.401.1		16	45.7	odd	12
450.3.i.e.401.8		16	45.43	odd	12
810.3.b.b.809.1		16	1.1	even	1	trivial
810.3.b.b.809.2		16	15.14	odd	2	inner
810.3.b.b.809.15		16	5.4	even	2	inner
810.3.b.b.809.16		16	3.2	odd	2	inner
1350.3.i.e.251.1		16	45.13	odd	12
1350.3.i.e.251.8		16	45.22	odd	12
1350.3.i.e.1151.1		16	45.38	even	12
1350.3.i.e.1151.8		16	45.2	even	12

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} +(-4.11034 - 2.84695i) q^{5} +9.58750i q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q-1.41421 q^{2} +2.00000 q^{4} +(-4.11034 - 2.84695i) q^{5} +9.58750i q^{7} -2.82843 q^{8} +(5.81290 + 4.02619i) q^{10} +10.2064i q^{11} -3.45374i q^{13} -13.5588i q^{14} +4.00000 q^{16} -30.5229 q^{17} +10.0857 q^{19} +(-8.22068 - 5.69390i) q^{20} -14.4340i q^{22} +30.6089 q^{23} +(8.78976 + 23.4038i) q^{25} +4.88433i q^{26} +19.1750i q^{28} -42.0050i q^{29} -10.0394 q^{31} -5.65685 q^{32} +43.1659 q^{34} +(27.2951 - 39.4079i) q^{35} +21.9907i q^{37} -14.2633 q^{38} +(11.6258 + 8.05239i) q^{40} -39.6635i q^{41} -21.6619i q^{43} +20.4128i q^{44} -43.2876 q^{46} -12.5764 q^{47} -42.9202 q^{49} +(-12.4306 - 33.0980i) q^{50} -6.90749i q^{52} -47.0248 q^{53} +(29.0570 - 41.9517i) q^{55} -27.1176i q^{56} +59.4040i q^{58} +32.3891i q^{59} -114.245 q^{61} +14.1979 q^{62} +8.00000 q^{64} +(-9.83263 + 14.1961i) q^{65} -32.2821i q^{67} -61.0458 q^{68} +(-38.6012 + 55.7312i) q^{70} -65.9174i q^{71} -54.1701i q^{73} -31.0995i q^{74} +20.1714 q^{76} -97.8537 q^{77} +88.1260 q^{79} +(-16.4414 - 11.3878i) q^{80} +56.0926i q^{82} -41.1001 q^{83} +(125.459 + 86.8971i) q^{85} +30.6345i q^{86} -28.8680i q^{88} -38.5303i q^{89} +33.1128 q^{91} +61.2179 q^{92} +17.7858 q^{94} +(-41.4556 - 28.7135i) q^{95} -128.257i q^{97} +60.6984 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 16 q^{10} + 64 q^{16} + 144 q^{19} - 12 q^{25} - 56 q^{31} + 272 q^{34} - 32 q^{40} - 56 q^{46} - 24 q^{49} + 20 q^{55} - 136 q^{61} + 128 q^{64} + 224 q^{70} + 288 q^{76} - 840 q^{79} + 272 q^{85} - 168 q^{91} + 328 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 - 16 * q^10 + 64 * q^16 + 144 * q^19 - 12 * q^25 - 56 * q^31 + 272 * q^34 - 32 * q^40 - 56 * q^46 - 24 * q^49 + 20 * q^55 - 136 * q^61 + 128 * q^64 + 224 * q^70 + 288 * q^76 - 840 * q^79 + 272 * q^85 - 168 * q^91 + 328 * q^94

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