LMFDB - Embedded newform 825.3.h.b.274.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [825,3,Mod(274,825)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("825.274"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(825, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	825.h (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$22.4796218097$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.13
Character	$\chi$	$=$	825.274
Dual form			825.3.h.b.274.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.664903 q^{2} -1.73205i q^{3} -3.55790 q^{4} +1.15165i q^{6} -8.36247 q^{7} +5.02527 q^{8} -3.00000 q^{9} +(7.04830 - 8.44521i) q^{11} +6.16247i q^{12} +16.0778 q^{13} +5.56023 q^{14} +10.8903 q^{16} +22.0359 q^{17} +1.99471 q^{18} +6.10810i q^{19} +14.4842i q^{21} +(-4.68643 + 5.61524i) q^{22} -6.43313i q^{23} -8.70402i q^{24} -10.6902 q^{26} +5.19615i q^{27} +29.7529 q^{28} -20.7699i q^{29} -52.4060 q^{31} -27.3421 q^{32} +(-14.6275 - 12.2080i) q^{33} -14.6517 q^{34} +10.6737 q^{36} +23.9112i q^{37} -4.06129i q^{38} -27.8476i q^{39} -66.7913i q^{41} -9.63059i q^{42} -56.5789 q^{43} +(-25.0772 + 30.0472i) q^{44} +4.27741i q^{46} -35.9964i q^{47} -18.8626i q^{48} +20.9309 q^{49} -38.1672i q^{51} -57.2034 q^{52} +83.7803i q^{53} -3.45494i q^{54} -42.0237 q^{56} +10.5795 q^{57} +13.8099i q^{58} +13.5741 q^{59} -120.042i q^{61} +34.8449 q^{62} +25.0874 q^{63} -25.3814 q^{64} +(9.72588 + 8.11714i) q^{66} +69.5457i q^{67} -78.4015 q^{68} -11.1425 q^{69} -69.1708 q^{71} -15.0758 q^{72} +78.0255 q^{73} -15.8986i q^{74} -21.7320i q^{76} +(-58.9412 + 70.6228i) q^{77} +18.5159i q^{78} +7.65867i q^{79} +9.00000 q^{81} +44.4097i q^{82} -5.69286 q^{83} -51.5335i q^{84} +37.6195 q^{86} -35.9745 q^{87} +(35.4196 - 42.4394i) q^{88} -73.0710 q^{89} -134.450 q^{91} +22.8885i q^{92} +90.7699i q^{93} +23.9341i q^{94} +47.3579i q^{96} -37.9109i q^{97} -13.9170 q^{98} +(-21.1449 + 25.3356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 96 q^{9} - 56 q^{11} - 32 q^{16} - 176 q^{26} - 192 q^{31} + 400 q^{34} - 48 q^{36} - 600 q^{44} + 992 q^{49} - 64 q^{56} + 272 q^{59} - 912 q^{64} - 360 q^{66} - 336 q^{69} + 432 q^{71}+ \cdots + 168 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 96 * q^9 - 56 * q^11 - 32 * q^16 - 176 * q^26 - 192 * q^31 + 400 * q^34 - 48 * q^36 - 600 * q^44 + 992 * q^49 - 64 * q^56 + 272 * q^59 - 912 * q^64 - 360 * q^66 - 336 * q^69 + 432 * q^71 + 288 * q^81 + 384 * q^86 + 672 * q^89 + 512 * q^91 + 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.664903			−0.332451			−0.166226	−	0.986088i	$-0.553158\pi$
$2$	−0.664903			−0.332451			−0.166226	+	0.986088i	$0.553158\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.55790			−0.889476
$5$		0			0
$5$		0			0
$6$			1.15165i			0.191941i
$7$	−8.36247			−1.19464			−0.597319	−	0.802004i	$-0.703767\pi$
$7$	−8.36247			−1.19464			−0.597319	+	0.802004i	$0.703767\pi$
$8$	5.02527			0.628159
$9$	−3.00000			−0.333333
$10$		0			0
$11$	7.04830	−	8.44521i	0.640754	−	0.767746i
$11$	7.04830	−	8.44521i	0.640754	−	0.767746i
$12$			6.16247i			0.513539i
$13$	16.0778			1.23676			0.618378	−	0.785881i	$-0.287790\pi$
$13$	16.0778			1.23676			0.618378	+	0.785881i	$0.287790\pi$
$14$	5.56023			0.397159
$15$		0			0
$16$	10.8903			0.680644
$17$	22.0359			1.29623			0.648114	−	0.761544i	$-0.275558\pi$
$17$	22.0359			1.29623			0.648114	+	0.761544i	$0.275558\pi$
$18$	1.99471			0.110817
$19$			6.10810i			0.321479i	0.986997	+	0.160739i	$0.0513879\pi$
$19$			6.10810i			0.321479i	−0.986997	+	0.160739i	$0.948612\pi$
$20$		0			0
$21$			14.4842i			0.689725i
$22$	−4.68643	+	5.61524i	−0.213020	+	0.255238i
$23$		−	6.43313i		−	0.279701i	−0.990173	−	0.139851i	$-0.955338\pi$
$23$		−	6.43313i		−	0.279701i	0.990173	−	0.139851i	$-0.0446622\pi$
$24$		−	8.70402i		−	0.362668i
$25$		0			0
$26$	−10.6902			−0.411161
$27$			5.19615i			0.192450i
$28$	29.7529			1.06260
$29$		−	20.7699i		−	0.716202i	−0.933683	−	0.358101i	$-0.883424\pi$
$29$		−	20.7699i		−	0.716202i	0.933683	−	0.358101i	$-0.116576\pi$
$30$		0			0
$31$	−52.4060			−1.69052			−0.845258	−	0.534358i	$-0.820554\pi$
$31$	−52.4060			−1.69052			−0.845258	+	0.534358i	$0.820554\pi$
$32$	−27.3421			−0.854440
$33$	−14.6275	−	12.2080i	−0.443258	−	0.369940i
$34$	−14.6517			−0.430932
$35$		0			0
$36$	10.6737			0.296492
$37$			23.9112i			0.646249i	0.946356	+	0.323124i	$0.104733\pi$
$37$			23.9112i			0.646249i	−0.946356	+	0.323124i	$0.895267\pi$
$38$		−	4.06129i		−	0.106876i
$39$		−	27.8476i		−	0.714041i
$40$		0			0
$41$		−	66.7913i		−	1.62906i	−0.580124	−	0.814528i	$-0.696996\pi$
$41$		−	66.7913i		−	1.62906i	0.580124	−	0.814528i	$-0.303004\pi$
$42$		−	9.63059i		−	0.229300i
$43$	−56.5789			−1.31579			−0.657894	−	0.753110i	$-0.728553\pi$
$43$	−56.5789			−1.31579			−0.657894	+	0.753110i	$0.728553\pi$
$44$	−25.0772	+	30.0472i	−0.569936	+	0.682892i
$45$		0			0
$46$			4.27741i			0.0929871i
$47$		−	35.9964i		−	0.765881i	−0.923773	−	0.382940i	$-0.874911\pi$
$47$		−	35.9964i		−	0.765881i	0.923773	−	0.382940i	$-0.125089\pi$
$48$		−	18.8626i		−	0.392970i
$49$	20.9309			0.427160
$50$		0			0
$51$		−	38.1672i		−	0.748377i
$52$	−57.2034			−1.10006
$53$			83.7803i			1.58076i	0.612616	+	0.790381i	$0.290117\pi$
$53$			83.7803i			1.58076i	−0.612616	+	0.790381i	$0.709883\pi$
$54$		−	3.45494i		−	0.0639803i
$55$		0			0
$56$	−42.0237			−0.750422
$57$	10.5795			0.185606
$58$			13.8099i			0.238102i
$59$	13.5741			0.230070			0.115035	−	0.993361i	$-0.463302\pi$
$59$	13.5741			0.230070			0.115035	+	0.993361i	$0.463302\pi$
$60$		0			0
$61$		−	120.042i		−	1.96790i	−0.178455	−	0.983948i	$-0.557110\pi$
$61$		−	120.042i		−	1.96790i	0.178455	−	0.983948i	$-0.442890\pi$
$62$	34.8449			0.562015
$63$	25.0874			0.398213
$64$	−25.3814			−0.396584
$65$		0			0
$66$	9.72588	+	8.11714i	0.147362	+	0.122987i
$67$			69.5457i			1.03799i	0.854776	+	0.518997i	$0.173695\pi$
$67$			69.5457i			1.03799i	−0.854776	+	0.518997i	$0.826305\pi$
$68$	−78.4015			−1.15296
$69$	−11.1425			−0.161486
$70$		0			0
$71$	−69.1708			−0.974237			−0.487119	−	0.873336i	$-0.661952\pi$
$71$	−69.1708			−0.974237			−0.487119	+	0.873336i	$0.661952\pi$
$72$	−15.0758			−0.209386
$73$	78.0255			1.06884			0.534421	−	0.845218i	$-0.320530\pi$
$73$	78.0255			1.06884			0.534421	+	0.845218i	$0.320530\pi$
$74$		−	15.8986i		−	0.214846i
$75$		0			0
$76$		−	21.7320i		−	0.285948i
$77$	−58.9412	+	70.6228i	−0.765470	+	0.917179i
$78$			18.5159i			0.237384i
$79$			7.65867i			0.0969451i	0.998825	+	0.0484726i	$0.0154353\pi$
$79$			7.65867i			0.0969451i	−0.998825	+	0.0484726i	$0.984565\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			44.4097i			0.541582i
$83$	−5.69286			−0.0685887			−0.0342943	−	0.999412i	$-0.510918\pi$
$83$	−5.69286			−0.0685887			−0.0342943	+	0.999412i	$0.510918\pi$
$84$		−	51.5335i		−	0.613494i
$85$		0			0
$86$	37.6195			0.437436
$87$	−35.9745			−0.413500
$88$	35.4196	−	42.4394i	0.402495	−	0.482266i
$89$	−73.0710			−0.821023			−0.410512	−	0.911855i	$-0.634650\pi$
$89$	−73.0710			−0.821023			−0.410512	+	0.911855i	$0.634650\pi$
$90$		0			0
$91$	−134.450			−1.47748
$92$			22.8885i			0.248788i
$93$			90.7699i			0.976020i
$94$			23.9341i			0.254618i
$95$		0			0
$96$			47.3579i			0.493311i
$97$		−	37.9109i		−	0.390834i	−0.980720	−	0.195417i	$-0.937394\pi$
$97$		−	37.9109i		−	0.390834i	0.980720	−	0.195417i	$-0.0626060\pi$
$98$	−13.9170			−0.142010
$99$	−21.1449	+	25.3356i	−0.213585	+	0.255915i
$100$		0			0
$101$		−	21.2764i		−	0.210658i	−0.994437	−	0.105329i	$-0.966411\pi$
$101$		−	21.2764i		−	0.210658i	0.994437	−	0.105329i	$-0.0335895\pi$
$102$			25.3775i			0.248799i
$103$		−	147.861i		−	1.43555i	−0.696277	−	0.717773i	$-0.745162\pi$
$103$		−	147.861i		−	1.43555i	0.696277	−	0.717773i	$-0.254838\pi$
$104$	80.7954			0.776879
$105$		0			0
$106$		−	55.7058i		−	0.525526i
$107$	−115.599			−1.08037			−0.540183	−	0.841548i	$-0.681645\pi$
$107$	−115.599			−1.08037			−0.540183	+	0.841548i	$0.681645\pi$
$108$		−	18.4874i		−	0.171180i
$109$		−	138.985i		−	1.27510i	−0.770411	−	0.637548i	$-0.779949\pi$
$109$		−	138.985i		−	1.27510i	0.770411	−	0.637548i	$-0.220051\pi$
$110$		0			0
$111$	41.4154			0.373112
$112$	−91.0698			−0.813123
$113$			37.9798i			0.336104i	0.985778	+	0.168052i	$0.0537477\pi$
$113$			37.9798i			0.336104i	−0.985778	+	0.168052i	$0.946252\pi$
$114$	−7.03436			−0.0617049
$115$		0			0
$116$			73.8972i			0.637045i
$117$	−48.2335			−0.412252
$118$	−9.02546			−0.0764869
$119$	−184.274			−1.54852
$120$		0			0
$121$	−21.6430	−	119.049i	−0.178868	−	0.983873i
$122$			79.8160i			0.654230i
$123$	−115.686			−0.940536
$124$	186.456			1.50367
$125$		0			0
$126$	−16.6807			−0.132386
$127$	8.43502			0.0664175			0.0332087	−	0.999448i	$-0.489427\pi$
$127$	8.43502			0.0664175			0.0332087	+	0.999448i	$0.489427\pi$
$128$	126.244			0.986285
$129$			97.9975i			0.759671i
$130$		0			0
$131$			186.122i			1.42078i	0.703811	+	0.710388i	$0.251480\pi$
$131$			186.122i			1.42078i	−0.703811	+	0.710388i	$0.748520\pi$
$132$	52.0433	+	43.4349i	0.394268	+	0.329053i
$133$		−	51.0788i		−	0.384051i
$134$		−	46.2411i		−	0.345083i
$135$		0			0
$136$	110.736			0.814237
$137$			40.5816i			0.296216i	0.988971	+	0.148108i	$0.0473183\pi$
$137$			40.5816i			0.296216i	−0.988971	+	0.148108i	$0.952682\pi$
$138$	7.40868			0.0536861
$139$			88.1363i			0.634074i	0.948413	+	0.317037i	$0.102688\pi$
$139$			88.1363i			0.634074i	−0.948413	+	0.317037i	$0.897312\pi$
$140$		0			0
$141$	−62.3476			−0.442182
$142$	45.9919			0.323886
$143$	113.321	−	135.781i	0.792457	−	0.949514i
$144$	−32.6709			−0.226881
$145$		0			0
$146$	−51.8793			−0.355338
$147$		−	36.2533i		−	0.246621i
$148$		−	85.0738i		−	0.574823i
$149$		−	90.6013i		−	0.608062i	−0.952662	−	0.304031i	$-0.901667\pi$
$149$		−	90.6013i		−	0.608062i	0.952662	−	0.304031i	$-0.0983327\pi$
$150$		0			0
$151$		−	38.1059i		−	0.252357i	−0.992008	−	0.126178i	$-0.959729\pi$
$151$		−	38.1059i		−	0.252357i	0.992008	−	0.126178i	$-0.0402712\pi$
$152$			30.6948i			0.201940i
$153$	−66.1076			−0.432076
$154$	39.1901	−	46.9573i	0.254481	−	0.304917i
$155$		0			0
$156$			99.0791i			0.635123i
$157$		−	271.722i		−	1.73071i	−0.501157	−	0.865356i	$-0.667092\pi$
$157$		−	271.722i		−	1.73071i	0.501157	−	0.865356i	$-0.332908\pi$
$158$		−	5.09227i		−	0.0322295i
$159$	145.112			0.912653
$160$		0			0
$161$			53.7968i			0.334142i
$162$	−5.98412			−0.0369390
$163$		−	128.405i		−	0.787759i	−0.919162	−	0.393879i	$-0.871133\pi$
$163$		−	128.405i		−	0.787759i	0.919162	−	0.393879i	$-0.128867\pi$
$164$			237.637i			1.44901i
$165$		0			0
$166$	3.78520			0.0228024
$167$	−172.263			−1.03152			−0.515758	−	0.856734i	$-0.672490\pi$
$167$	−172.263			−1.03152			−0.515758	+	0.856734i	$0.672490\pi$
$168$			72.7871i			0.433257i
$169$	89.4964			0.529565
$170$		0			0
$171$		−	18.3243i		−	0.107160i
$172$	201.302			1.17036
$173$	−125.237			−0.723914			−0.361957	−	0.932195i	$-0.617891\pi$
$173$	−125.237			−0.723914			−0.361957	+	0.932195i	$0.617891\pi$
$174$	23.9195			0.137469
$175$		0			0
$176$	76.7581	−	91.9709i	0.436126	−	0.522562i
$177$		−	23.5110i		−	0.132831i
$178$	48.5851			0.272950
$179$	−75.0674			−0.419371			−0.209685	−	0.977769i	$-0.567244\pi$
$179$	−75.0674			−0.419371			−0.209685	+	0.977769i	$0.567244\pi$
$180$		0			0
$181$	−285.524			−1.57748			−0.788740	−	0.614727i	$-0.789266\pi$
$181$	−285.524			−1.57748			−0.788740	+	0.614727i	$0.789266\pi$
$182$	89.3963			0.491189
$183$	−207.918			−1.13617
$184$		−	32.3282i		−	0.175697i
$185$		0			0
$186$		−	60.3531i		−	0.324479i
$187$	155.315	−	186.097i	0.830563	−	0.995173i
$188$			128.072i			0.681233i
$189$		−	43.4527i		−	0.229908i
$190$		0			0
$191$	256.484			1.34285			0.671423	−	0.741074i	$-0.265683\pi$
$191$	256.484			1.34285			0.671423	+	0.741074i	$0.265683\pi$
$192$			43.9619i			0.228968i
$193$	157.978			0.818541			0.409271	−	0.912413i	$-0.365783\pi$
$193$	157.978			0.818541			0.409271	+	0.912413i	$0.365783\pi$
$194$			25.2070i			0.129933i
$195$		0			0
$196$	−74.4700			−0.379949
$197$	203.131			1.03112			0.515562	−	0.856852i	$-0.327583\pi$
$197$	203.131			1.03112			0.515562	+	0.856852i	$0.327583\pi$
$198$	14.0593	−	16.8457i	0.0710065	−	0.0850794i
$199$	−286.490			−1.43965			−0.719823	−	0.694158i	$-0.755777\pi$
$199$	−286.490			−1.43965			−0.719823	+	0.694158i	$0.755777\pi$
$200$		0			0
$201$	120.457			0.599287
$202$			14.1467i			0.0700334i
$203$			173.687i			0.855603i
$204$			135.795i			0.665664i
$205$		0			0
$206$			98.3133i			0.477249i
$207$			19.2994i			0.0932338i
$208$	175.092			0.841790
$209$	51.5841	+	43.0517i	0.246814	+	0.205989i
$210$		0			0
$211$			138.840i			0.658012i	0.944328	+	0.329006i	$0.106714\pi$
$211$			138.840i			0.658012i	−0.944328	+	0.329006i	$0.893286\pi$
$212$		−	298.082i		−	1.40605i
$213$			119.807i			0.562476i
$214$	76.8621			0.359169
$215$		0			0
$216$			26.1121i			0.120889i
$217$	438.244			2.01956
$218$			92.4117i			0.423907i
$219$		−	135.144i		−	0.617096i
$220$		0			0
$221$	354.289			1.60312
$222$	−27.5372			−0.124042
$223$			250.067i			1.12138i	0.828027	+	0.560688i	$0.189463\pi$
$223$			250.067i			1.12138i	−0.828027	+	0.560688i	$0.810537\pi$
$224$	228.647			1.02075
$225$		0			0
$226$		−	25.2528i		−	0.111738i
$227$	−247.410			−1.08991			−0.544955	−	0.838465i	$-0.683453\pi$
$227$	−247.410			−1.08991			−0.544955	+	0.838465i	$0.683453\pi$
$228$	−37.6410			−0.165092
$229$	−363.652			−1.58800			−0.794000	−	0.607918i	$-0.792005\pi$
$229$	−363.652			−1.58800			−0.794000	+	0.607918i	$0.792005\pi$
$230$		0			0
$231$	122.322	+	102.089i	0.529533	+	0.441944i
$232$		−	104.374i		−	0.449889i
$233$	−263.367			−1.13033			−0.565165	−	0.824978i	$-0.691188\pi$
$233$	−263.367			−1.13033			−0.565165	+	0.824978i	$0.691188\pi$
$234$	32.0706			0.137054
$235$		0			0
$236$	−48.2954			−0.204641
$237$	13.2652			0.0559713
$238$	122.524			0.514808
$239$		−	364.771i		−	1.52624i	−0.646257	−	0.763120i	$-0.723667\pi$
$239$		−	364.771i		−	1.52624i	0.646257	−	0.763120i	$-0.276333\pi$
$240$		0			0
$241$		−	149.640i		−	0.620912i	−0.950588	−	0.310456i	$-0.899518\pi$
$241$		−	149.640i		−	0.620912i	0.950588	−	0.310456i	$-0.100482\pi$
$242$	14.3905	+	79.1558i	0.0594649	+	0.327090i
$243$		−	15.5885i		−	0.0641500i
$244$			427.097i			1.75040i
$245$		0			0
$246$	76.9199			0.312682
$247$			98.2049i			0.397591i
$248$	−263.354			−1.06191
$249$			9.86032i			0.0395997i
$250$		0			0
$251$	−118.965			−0.473962			−0.236981	−	0.971514i	$-0.576158\pi$
$251$	−118.965			−0.473962			−0.236981	+	0.971514i	$0.576158\pi$
$252$	−89.2586			−0.354201
$253$	−54.3291	−	45.3426i	−0.214740	−	0.179220i
$254$	−5.60847			−0.0220806
$255$		0			0
$256$	17.5853			0.0686927
$257$		−	182.143i		−	0.708729i	−0.935107	−	0.354364i	$-0.884697\pi$
$257$		−	182.143i		−	0.708729i	0.935107	−	0.354364i	$-0.115303\pi$
$258$		−	65.1588i		−	0.252554i
$259$		−	199.957i		−	0.772034i
$260$		0			0
$261$			62.3096i			0.238734i
$262$		−	123.753i		−	0.472339i
$263$	55.7205			0.211865			0.105933	−	0.994373i	$-0.466217\pi$
$263$	55.7205			0.211865			0.105933	+	0.994373i	$0.466217\pi$
$264$	−73.5073	−	61.3485i	−0.278437	−	0.232381i
$265$		0			0
$266$			33.9624i			0.127678i
$267$			126.563i			0.474018i
$268$		−	247.437i		−	0.923272i
$269$	46.7482			0.173785			0.0868925	−	0.996218i	$-0.472306\pi$
$269$	46.7482			0.173785			0.0868925	+	0.996218i	$0.472306\pi$
$270$		0			0
$271$			81.2380i			0.299771i	0.988703	+	0.149886i	$0.0478906\pi$
$271$			81.2380i			0.299771i	−0.988703	+	0.149886i	$0.952109\pi$
$272$	239.977			0.882269
$273$			232.875i			0.853021i
$274$		−	26.9828i		−	0.0984774i
$275$		0			0
$276$	39.6440			0.143638
$277$	309.041			1.11567			0.557835	−	0.829952i	$-0.311632\pi$
$277$	309.041			1.11567			0.557835	+	0.829952i	$0.311632\pi$
$278$		−	58.6020i		−	0.210799i
$279$	157.218			0.563506
$280$		0			0
$281$			306.448i			1.09056i	0.838253	+	0.545282i	$0.183577\pi$
$281$			306.448i			1.09056i	−0.838253	+	0.545282i	$0.816423\pi$
$282$	41.4551			0.147004
$283$	495.935			1.75242			0.876210	−	0.481929i	$-0.160064\pi$
$283$	495.935			1.75242			0.876210	+	0.481929i	$0.160064\pi$
$284$	246.103			0.866561
$285$		0			0
$286$	−75.3476	+	90.2808i	−0.263453	+	0.315667i
$287$			558.540i			1.94613i
$288$	82.0262			0.284813
$289$	196.579			0.680205
$290$		0			0
$291$	−65.6636			−0.225648
$292$	−277.607			−0.950710
$293$	−391.532			−1.33629			−0.668144	−	0.744032i	$-0.732911\pi$
$293$	−391.532			−1.33629			−0.668144	+	0.744032i	$0.732911\pi$
$294$			24.1049i			0.0819895i
$295$		0			0
$296$			120.160i			0.405947i
$297$	43.8826	+	36.6240i	0.147753	+	0.123313i
$298$			60.2410i			0.202151i
$299$		−	103.431i		−	0.345922i
$300$		0			0
$301$	473.139			1.57189
$302$			25.3367i			0.0838964i
$303$	−36.8518			−0.121623
$304$			66.5190i			0.218813i
$305$		0			0
$306$	43.9551			0.143644
$307$	−92.7037			−0.301966			−0.150983	−	0.988536i	$-0.548244\pi$
$307$	−92.7037			−0.301966			−0.150983	+	0.988536i	$0.548244\pi$
$308$	209.707	−	251.269i	0.680867	−	0.815809i
$309$	−256.103			−0.828813
$310$		0			0
$311$	442.851			1.42396			0.711980	−	0.702200i	$-0.247799\pi$
$311$	442.851			1.42396			0.711980	+	0.702200i	$0.247799\pi$
$312$		−	139.942i		−	0.448531i
$313$		−	97.9824i		−	0.313043i	−0.987675	−	0.156521i	$-0.949972\pi$
$313$		−	97.9824i		−	0.313043i	0.987675	−	0.156521i	$-0.0500280\pi$
$314$			180.669i			0.575378i
$315$		0			0
$316$		−	27.2488i		−	0.0862304i
$317$		−	433.796i		−	1.36844i	−0.729275	−	0.684221i	$-0.760143\pi$
$317$		−	433.796i		−	1.36844i	0.729275	−	0.684221i	$-0.239857\pi$
$318$	−96.4852			−0.303413
$319$	−175.406	−	146.392i	−0.549862	−	0.458910i
$320$		0			0
$321$			200.223i			0.623749i
$322$		−	35.7697i		−	0.111086i
$323$			134.597i			0.416710i
$324$	−32.0211			−0.0988307
$325$		0			0
$326$			85.3766i			0.261891i
$327$	−240.730			−0.736176
$328$		−	335.644i		−	1.02331i
$329$			301.019i			0.914950i
$330$		0			0
$331$	−270.505			−0.817235			−0.408618	−	0.912706i	$-0.633989\pi$
$331$	−270.505			−0.817235			−0.408618	+	0.912706i	$0.633989\pi$
$332$	20.2547			0.0610080
$333$		−	71.7336i		−	0.215416i
$334$	114.538			0.342929
$335$		0			0
$336$			157.738i			0.469457i
$337$	−80.7287			−0.239551			−0.119775	−	0.992801i	$-0.538217\pi$
$337$	−80.7287			−0.239551			−0.119775	+	0.992801i	$0.538217\pi$
$338$	−59.5064			−0.176054
$339$	65.7829			0.194050
$340$		0			0
$341$	−369.373	+	442.580i	−1.08321	+	1.29789i
$342$			12.1839i			0.0356254i
$343$	234.727			0.684336
$344$	−284.324			−0.826524
$345$		0			0
$346$	83.2705			0.240666
$347$	105.638			0.304433			0.152217	−	0.988347i	$-0.451359\pi$
$347$	105.638			0.304433			0.152217	+	0.988347i	$0.451359\pi$
$348$	127.994			0.367798
$349$			515.712i			1.47769i	0.673878	+	0.738843i	$0.264627\pi$
$349$			515.712i			1.47769i	−0.673878	+	0.738843i	$0.735373\pi$
$350$		0			0
$351$			83.5428i			0.238014i
$352$	−192.715	+	230.909i	−0.547486	+	0.655993i
$353$			467.858i			1.32538i	0.748896	+	0.662688i	$0.230584\pi$
$353$			467.858i			1.32538i	−0.748896	+	0.662688i	$0.769416\pi$
$354$			15.6325i			0.0441597i
$355$		0			0
$356$	259.980			0.730280
$357$			319.172i			0.894040i
$358$	49.9125			0.139420
$359$			274.186i			0.763751i	0.924214	+	0.381875i	$0.124722\pi$
$359$			274.186i			0.763751i	−0.924214	+	0.381875i	$0.875278\pi$
$360$		0			0
$361$	323.691			0.896651
$362$	189.846			0.524435
$363$	−206.198	+	37.4868i	−0.568039	+	0.103269i
$364$	478.361			1.31418
$365$		0			0
$366$	138.245			0.377720
$367$		−	285.758i		−	0.778631i	−0.921104	−	0.389316i	$-0.872712\pi$
$367$		−	285.758i		−	0.778631i	0.921104	−	0.389316i	$-0.127288\pi$
$368$		−	70.0587i		−	0.190377i
$369$			200.374i			0.543019i
$370$		0			0
$371$		−	700.610i		−	1.88844i
$372$		−	322.951i		−	0.868147i
$373$	−18.2467			−0.0489188			−0.0244594	−	0.999701i	$-0.507786\pi$
$373$	−18.2467			−0.0489188			−0.0244594	+	0.999701i	$0.507786\pi$
$374$	−103.270	+	123.737i	−0.276122	+	0.330847i
$375$		0			0
$376$		−	180.892i		−	0.481095i
$377$		−	333.934i		−	0.885767i
$378$			28.8918i			0.0764333i
$379$	336.559			0.888018			0.444009	−	0.896022i	$-0.353556\pi$
$379$	336.559			0.888018			0.444009	+	0.896022i	$0.353556\pi$
$380$		0			0
$381$		−	14.6099i		−	0.0383461i
$382$	−170.537			−0.446431
$383$			212.241i			0.554154i	0.960848	+	0.277077i	$0.0893657\pi$
$383$			212.241i			0.554154i	−0.960848	+	0.277077i	$0.910634\pi$
$384$		−	218.662i		−	0.569432i
$385$		0			0
$386$	−105.040			−0.272125
$387$	169.737			0.438596
$388$			134.883i			0.347637i
$389$	530.891			1.36476			0.682379	−	0.730999i	$-0.260946\pi$
$389$	530.891			1.36476			0.682379	+	0.730999i	$0.260946\pi$
$390$		0			0
$391$		−	141.760i		−	0.362556i
$392$	105.183			0.268324
$393$	322.372			0.820285
$394$	−135.063			−0.342798
$395$		0			0
$396$	75.2315	−	90.1417i	0.189979	−	0.227631i
$397$		−	616.868i		−	1.55382i	−0.629610	−	0.776911i	$-0.716785\pi$
$397$		−	616.868i		−	1.55382i	0.629610	−	0.776911i	$-0.283215\pi$
$398$	190.488			0.478612
$399$	−88.4710			−0.221732
$400$		0			0
$401$	−300.579			−0.749574			−0.374787	−	0.927111i	$-0.622284\pi$
$401$	−300.579			−0.749574			−0.374787	+	0.927111i	$0.622284\pi$
$402$	−80.0919			−0.199234
$403$	−842.575			−2.09076
$404$			75.6994i			0.187375i
$405$		0			0
$406$		−	115.485i		−	0.284446i
$407$	201.935	+	168.533i	0.496155	+	0.414087i
$408$		−	191.801i		−	0.470100i
$409$		−	696.288i		−	1.70242i	−0.524828	−	0.851208i	$-0.675870\pi$
$409$		−	696.288i		−	1.70242i	0.524828	−	0.851208i	$-0.324130\pi$
$410$		0			0
$411$	70.2894			0.171020
$412$			526.076i			1.27688i
$413$	−113.513			−0.274850
$414$		−	12.8322i		−	0.0309957i
$415$		0			0
$416$	−439.601			−1.05673
$417$	152.656			0.366083
$418$	−34.2984	−	28.6252i	−0.0820537	−	0.0684813i
$419$	326.612			0.779504			0.389752	−	0.920920i	$-0.372561\pi$
$419$	326.612			0.779504			0.389752	+	0.920920i	$0.372561\pi$
$420$		0			0
$421$	23.5479			0.0559333			0.0279666	−	0.999609i	$-0.491097\pi$
$421$	23.5479			0.0559333			0.0279666	+	0.999609i	$0.491097\pi$
$422$		−	92.3154i		−	0.218757i
$423$			107.989i			0.255294i
$424$			421.019i			0.992969i
$425$		0			0
$426$		−	79.6602i		−	0.186996i
$427$			1003.84i			2.35092i
$428$	411.290			0.960959
$429$	−235.179	−	196.278i	−0.548202	−	0.457525i
$430$		0			0
$431$		−	223.614i		−	0.518825i	−0.965767	−	0.259413i	$-0.916471\pi$
$431$		−	223.614i		−	0.518825i	0.965767	−	0.259413i	$-0.0835290\pi$
$432$			56.5877i			0.130990i
$433$			181.032i			0.418087i	0.977906	+	0.209044i	$0.0670350\pi$
$433$			181.032i			0.418087i	−0.977906	+	0.209044i	$0.932965\pi$
$434$	−291.389			−0.671404
$435$		0			0
$436$			494.497i			1.13417i
$437$	39.2942			0.0899181
$438$			89.8577i			0.205154i
$439$			66.4465i			0.151359i	0.997132	+	0.0756794i	$0.0241125\pi$
$439$			66.4465i			0.151359i	−0.997132	+	0.0756794i	$0.975887\pi$
$440$		0			0
$441$	−62.7926			−0.142387
$442$	−235.567			−0.532958
$443$		−	430.438i		−	0.971642i	−0.874058	−	0.485821i	$-0.838521\pi$
$443$		−	430.438i		−	0.971642i	0.874058	−	0.485821i	$-0.161479\pi$
$444$	−147.352			−0.331874
$445$		0			0
$446$		−	166.270i		−	0.372803i
$447$	−156.926			−0.351065
$448$	212.251			0.473775
$449$	−261.662			−0.582766			−0.291383	−	0.956607i	$-0.594115\pi$
$449$	−261.662			−0.582766			−0.291383	+	0.956607i	$0.594115\pi$
$450$		0			0
$451$	−564.066	−	470.765i	−1.25070	−	1.04382i
$452$		−	135.128i		−	0.298957i
$453$	−66.0013			−0.145698
$454$	164.503			0.362342
$455$		0			0
$456$	53.1650			0.116590
$457$	187.453			0.410181			0.205090	−	0.978743i	$-0.434251\pi$
$457$	187.453			0.410181			0.205090	+	0.978743i	$0.434251\pi$
$458$	241.793			0.527932
$459$			114.502i			0.249459i
$460$		0			0
$461$		−	683.006i		−	1.48157i	−0.671740	−	0.740787i	$-0.734453\pi$
$461$		−	683.006i		−	1.48157i	0.671740	−	0.740787i	$-0.265547\pi$
$462$	−81.3324	−	67.8793i	−0.176044	−	0.146925i
$463$		−	72.4460i		−	0.156471i	−0.996935	−	0.0782354i	$-0.975071\pi$
$463$		−	72.4460i		−	0.156471i	0.996935	−	0.0782354i	$-0.0249286\pi$
$464$		−	226.190i		−	0.487479i
$465$		0			0
$466$	175.113			0.375780
$467$			401.507i			0.859759i	0.902886	+	0.429879i	$0.141444\pi$
$467$			401.507i			0.859759i	−0.902886	+	0.429879i	$0.858556\pi$
$468$	171.610			0.366688
$469$		−	581.573i		−	1.24003i
$470$		0			0
$471$	−470.636			−0.999228
$472$	68.2135			0.144520
$473$	−398.785	+	477.820i	−0.843097	+	1.01019i
$474$	−8.82007			−0.0186077
$475$		0			0
$476$	655.630			1.37737
$477$		−	251.341i		−	0.526920i
$478$			242.537i			0.507400i
$479$		−	620.609i		−	1.29563i	−0.761796	−	0.647817i	$-0.775682\pi$
$479$		−	620.609i		−	1.29563i	0.761796	−	0.647817i	$-0.224318\pi$
$480$		0			0
$481$			384.440i			0.799252i
$482$			99.4958i			0.206423i
$483$	93.1789			0.192917
$484$	77.0038	+	423.564i	0.159099	+	0.875132i
$485$		0			0
$486$			10.3648i			0.0213268i
$487$		−	539.097i		−	1.10697i	−0.832857	−	0.553487i	$-0.813297\pi$
$487$		−	539.097i		−	1.10697i	0.832857	−	0.553487i	$-0.186703\pi$
$488$		−	603.242i		−	1.23615i
$489$	−222.403			−0.454813
$490$		0			0
$491$			480.768i			0.979161i	0.871958	+	0.489580i	$0.162850\pi$
$491$			480.768i			0.979161i	−0.871958	+	0.489580i	$0.837150\pi$
$492$	411.600			0.836585
$493$		−	457.682i		−	0.928361i
$494$		−	65.2967i		−	0.132180i
$495$		0			0
$496$	−570.717			−1.15064
$497$	578.439			1.16386
$498$		−	6.55615i		−	0.0131650i
$499$	−566.286			−1.13484			−0.567421	−	0.823428i	$-0.692059\pi$
$499$	−566.286			−1.13484			−0.567421	+	0.823428i	$0.692059\pi$
$500$		0			0
$501$			298.369i			0.595547i
$502$	79.0998			0.157569
$503$	−622.513			−1.23760			−0.618800	−	0.785549i	$-0.712381\pi$
$503$	−622.513			−1.23760			−0.618800	+	0.785549i	$0.712381\pi$
$504$	126.071			0.250141
$505$		0			0
$506$	36.1236	+	30.1484i	0.0713905	+	0.0595819i
$507$		−	155.012i		−	0.305744i
$508$	−30.0110			−0.0590768
$509$	−506.799			−0.995677			−0.497838	−	0.867270i	$-0.665873\pi$
$509$	−506.799			−0.995677			−0.497838	+	0.867270i	$0.665873\pi$
$510$		0			0
$511$	−652.485			−1.27688
$512$	−516.670			−1.00912
$513$	−31.7386			−0.0618686
$514$			121.108i			0.235618i
$515$		0			0
$516$		−	348.666i		−	0.675709i
$517$	−303.997	−	253.713i	−0.588002	−	0.490741i
$518$			132.952i			0.256664i
$519$			216.917i			0.417952i
$520$		0			0
$521$	−486.736			−0.934233			−0.467117	−	0.884196i	$-0.654707\pi$
$521$	−486.736			−0.934233			−0.467117	+	0.884196i	$0.654707\pi$
$522$		−	41.4298i		−	0.0793675i
$523$	−390.347			−0.746362			−0.373181	−	0.927759i	$-0.621733\pi$
$523$	−390.347			−0.746362			−0.373181	+	0.927759i	$0.621733\pi$
$524$		−	662.203i		−	1.26375i
$525$		0			0
$526$	−37.0487			−0.0704348
$527$	−1154.81			−2.19129
$528$	−159.298	−	132.949i	−0.301701	−	0.251797i
$529$	487.615			0.921767
$530$		0			0
$531$	−40.7223			−0.0766898
$532$			181.733i			0.341604i
$533$		−	1073.86i		−	2.01474i
$534$		−	84.1519i		−	0.157588i
$535$		0			0
$536$			349.486i			0.652026i
$537$			130.021i			0.242124i
$538$	−31.0830			−0.0577751
$539$	147.527	−	176.765i	0.273705	−	0.327951i
$540$		0			0
$541$		−	43.4279i		−	0.0802735i	−0.999194	−	0.0401367i	$-0.987221\pi$
$541$		−	43.4279i		−	0.0802735i	0.999194	−	0.0401367i	$-0.0127794\pi$
$542$		−	54.0154i		−	0.0996594i
$543$			494.542i			0.910759i
$544$	−602.506			−1.10755
$545$		0			0
$546$		−	154.839i		−	0.283588i
$547$	−298.284			−0.545309			−0.272655	−	0.962112i	$-0.587902\pi$
$547$	−298.284			−0.545309			−0.272655	+	0.962112i	$0.587902\pi$
$548$		−	144.386i		−	0.263477i
$549$			360.125i			0.655965i
$550$		0			0
$551$	126.864			0.230244
$552$	−55.9941			−0.101439
$553$		−	64.0453i		−	0.115814i
$554$	−205.482			−0.370906
$555$		0			0
$556$		−	313.580i		−	0.563994i
$557$	−401.329			−0.720520			−0.360260	−	0.932852i	$-0.617312\pi$
$557$	−401.329			−0.720520			−0.360260	+	0.932852i	$0.617312\pi$
$558$	−104.535			−0.187338
$559$	−909.666			−1.62731
$560$		0			0
$561$	−322.330	−	269.014i	−0.574564	−	0.479526i
$562$		−	203.758i		−	0.362559i
$563$	190.526			0.338412			0.169206	−	0.985581i	$-0.445880\pi$
$563$	190.526			0.338412			0.169206	+	0.985581i	$0.445880\pi$
$564$	221.827			0.393310
$565$		0			0
$566$	−329.749			−0.582595
$567$	−75.2622			−0.132738
$568$	−347.602			−0.611976
$569$		−	718.614i		−	1.26294i	−0.775400	−	0.631471i	$-0.782452\pi$
$569$		−	718.614i		−	1.26294i	0.775400	−	0.631471i	$-0.217548\pi$
$570$		0			0
$571$		−	324.008i		−	0.567440i	−0.958907	−	0.283720i	$-0.908431\pi$
$571$		−	324.008i		−	0.567440i	0.958907	−	0.283720i	$-0.0915686\pi$
$572$	−403.186	+	483.094i	−0.704871	+	0.844570i
$573$		−	444.243i		−	0.775293i
$574$		−	371.375i		−	0.646994i
$575$		0			0
$576$	76.1442			0.132195
$577$			1131.01i			1.96016i	0.198606	+	0.980079i	$0.436358\pi$
$577$			1131.01i			1.96016i	−0.198606	+	0.980079i	$0.563642\pi$
$578$	−130.706			−0.226135
$579$		−	273.627i		−	0.472585i
$580$		0			0
$581$	47.6064			0.0819387
$582$	43.6599			0.0750170
$583$	707.542	+	590.509i	1.21362	+	1.01288i
$584$	392.099			0.671403
$585$		0			0
$586$	260.331			0.444251
$587$		−	856.901i		−	1.45980i	−0.683556	−	0.729898i	$-0.739567\pi$
$587$		−	856.901i		−	1.45980i	0.683556	−	0.729898i	$-0.260433\pi$
$588$			128.986i			0.219364i
$589$		−	320.101i		−	0.543465i
$590$		0			0
$591$		−	351.834i		−	0.595320i
$592$			260.400i			0.439865i
$593$	712.663			1.20179			0.600896	−	0.799327i	$-0.294810\pi$
$593$	712.663			1.20179			0.600896	+	0.799327i	$0.294810\pi$
$594$	−29.1776	−	24.3514i	−0.0491206	−	0.0409956i
$595$		0			0
$596$			322.351i			0.540857i
$597$			496.214i			0.831180i
$598$			68.7714i			0.115002i
$599$	−822.850			−1.37371			−0.686853	−	0.726796i	$-0.741008\pi$
$599$	−822.850			−1.37371			−0.686853	+	0.726796i	$0.741008\pi$
$600$		0			0
$601$		−	350.575i		−	0.583319i	−0.956522	−	0.291659i	$-0.905793\pi$
$601$		−	350.575i		−	0.583319i	0.956522	−	0.291659i	$-0.0942074\pi$
$602$	−314.591			−0.522577
$603$		−	208.637i		−	0.345998i
$604$			135.577i			0.224465i
$605$		0			0
$606$	24.5029			0.0404338
$607$	−358.620			−0.590808			−0.295404	−	0.955372i	$-0.595454\pi$
$607$	−358.620			−0.590808			−0.295404	+	0.955372i	$0.595454\pi$
$608$		−	167.008i		−	0.274684i
$609$	300.835			0.493982
$610$		0			0
$611$		−	578.744i		−	0.947208i
$612$	235.204			0.384321
$613$	28.2177			0.0460322			0.0230161	−	0.999735i	$-0.492673\pi$
$613$	28.2177			0.0460322			0.0230161	+	0.999735i	$0.492673\pi$
$614$	61.6389			0.100389
$615$		0			0
$616$	−296.195	+	354.898i	−0.480836	+	0.576134i
$617$			550.410i			0.892074i	0.895014	+	0.446037i	$0.147165\pi$
$617$			550.410i			0.892074i	−0.895014	+	0.446037i	$0.852835\pi$
$618$	170.284			0.275540
$619$	373.784			0.603852			0.301926	−	0.953331i	$-0.402371\pi$
$619$	373.784			0.603852			0.301926	+	0.953331i	$0.402371\pi$
$620$		0			0
$621$	33.4275			0.0538285
$622$	−294.453			−0.473397
$623$	611.054			0.980825
$624$		−	303.269i		−	0.486008i
$625$		0			0
$626$			65.1488i			0.104072i
$627$	74.5677	−	89.3464i	0.118928	−	0.142498i
$628$			966.761i			1.53943i
$629$			526.904i			0.837685i
$630$		0			0
$631$	1100.42			1.74393			0.871965	−	0.489568i	$-0.162846\pi$
$631$	1100.42			1.74393			0.871965	+	0.489568i	$0.162846\pi$
$632$			38.4869i			0.0608969i
$633$	240.479			0.379903
$634$			288.432i			0.454940i
$635$		0			0
$636$	−516.294			−0.811783
$637$	336.523			0.528293
$638$	116.628	+	97.3366i	0.182802	+	0.152565i
$639$	207.512			0.324746
$640$		0			0
$641$	653.649			1.01973			0.509867	−	0.860253i	$-0.329695\pi$
$641$	653.649			1.01973			0.509867	+	0.860253i	$0.329695\pi$
$642$		−	133.129i		−	0.207366i
$643$			502.794i			0.781950i	0.920401	+	0.390975i	$0.127862\pi$
$643$			502.794i			0.781950i	−0.920401	+	0.390975i	$0.872138\pi$
$644$		−	191.404i		−	0.297211i
$645$		0			0
$646$		−	89.4940i		−	0.138536i
$647$			897.406i			1.38703i	0.720444	+	0.693513i	$0.243938\pi$
$647$			897.406i			1.38703i	−0.720444	+	0.693513i	$0.756062\pi$
$648$	45.2274			0.0697954
$649$	95.6743	−	114.636i	0.147418	−	0.176635i
$650$		0			0
$651$		−	759.060i		−	1.16599i
$652$			456.852i			0.700693i
$653$			789.461i			1.20898i	0.796615	+	0.604488i	$0.206622\pi$
$653$			789.461i			1.20898i	−0.796615	+	0.604488i	$0.793378\pi$
$654$	160.062			0.244743
$655$		0			0
$656$		−	727.378i		−	1.10881i
$657$	−234.076			−0.356281
$658$		−	200.148i		−	0.304176i
$659$			127.662i			0.193721i	0.995298	+	0.0968607i	$0.0308801\pi$
$659$			127.662i			0.193721i	−0.995298	+	0.0968607i	$0.969120\pi$
$660$		0			0
$661$	525.245			0.794621			0.397311	−	0.917684i	$-0.369944\pi$
$661$	525.245			0.794621			0.397311	+	0.917684i	$0.369944\pi$
$662$	179.859			0.271691
$663$		−	613.646i		−	0.925560i
$664$	−28.6082			−0.0430846
$665$		0			0
$666$			47.6959i			0.0716154i
$667$	−133.615			−0.200323
$668$	612.896			0.917510
$669$	433.129			0.647427
$670$		0			0
$671$	−1013.78	−	846.089i	−1.51084	−	1.26094i
$672$		−	396.029i		−	0.589328i
$673$	−952.301			−1.41501			−0.707505	−	0.706709i	$-0.750179\pi$
$673$	−952.301			−1.41501			−0.707505	+	0.706709i	$0.750179\pi$
$674$	53.6767			0.0796390
$675$		0			0
$676$	−318.420			−0.471035
$677$	258.470			0.381788			0.190894	−	0.981611i	$-0.438861\pi$
$677$	258.470			0.381788			0.190894	+	0.981611i	$0.438861\pi$
$678$	−43.7392			−0.0645121
$679$			317.028i			0.466905i
$680$		0			0
$681$			428.526i			0.629260i
$682$	245.597	−	294.272i	0.360113	−	0.431484i
$683$		−	391.010i		−	0.572489i	−0.958157	−	0.286245i	$-0.907593\pi$
$683$		−	391.010i		−	0.572489i	0.958157	−	0.286245i	$-0.0924070\pi$
$684$			65.1961i			0.0953159i
$685$		0			0
$686$	−156.071			−0.227508
$687$			629.863i			0.916832i
$688$	−616.161			−0.895583
$689$			1347.01i			1.95502i
$690$		0			0
$691$	199.456			0.288648			0.144324	−	0.989531i	$-0.453899\pi$
$691$	199.456			0.288648			0.144324	+	0.989531i	$0.453899\pi$
$692$	445.582			0.643904
$693$	176.823	−	211.868i	0.255157	−	0.305726i
$694$	−70.2392			−0.101209
$695$		0			0
$696$	−180.781			−0.259743
$697$		−	1471.80i		−	2.11163i
$698$		−	342.898i		−	0.491258i
$699$			456.165i			0.652596i
$700$		0			0
$701$		−	181.684i		−	0.259179i	−0.991568	−	0.129589i	$-0.958634\pi$
$701$		−	181.684i		−	0.259179i	0.991568	−	0.129589i	$-0.0413659\pi$
$702$		−	55.5478i		−	0.0791280i
$703$	−146.052			−0.207755
$704$	−178.896	+	214.351i	−0.254113	+	0.304476i
$705$		0			0
$706$		−	311.080i		−	0.440623i
$707$			177.923i			0.251660i
$708$			83.6500i			0.118150i
$709$	−975.319			−1.37563			−0.687813	−	0.725888i	$-0.741429\pi$
$709$	−975.319			−1.37563			−0.687813	+	0.725888i	$0.741429\pi$
$710$		0			0
$711$		−	22.9760i		−	0.0323150i
$712$	−367.202			−0.515733
$713$			337.135i			0.472840i
$714$		−	212.218i		−	0.297225i
$715$		0			0
$716$	267.083			0.373020
$717$	−631.802			−0.881175
$718$		−	182.307i		−	0.253910i
$719$	1352.64			1.88128			0.940641	−	0.339402i	$-0.110225\pi$
$719$	1352.64			1.88128			0.940641	+	0.339402i	$0.110225\pi$
$720$		0			0
$721$			1236.48i			1.71496i
$722$	−215.223			−0.298093
$723$	−259.184			−0.358484
$724$	1015.87			1.40313
$725$		0			0
$726$	137.102	−	24.9251i	0.188845	−	0.0343320i
$727$		−	268.503i		−	0.369330i	−0.982801	−	0.184665i	$-0.940880\pi$
$727$		−	268.503i		−	0.369330i	0.982801	−	0.184665i	$-0.0591201\pi$
$728$	−675.649			−0.928089
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1246.76			−1.70556
$732$	739.753			1.01059
$733$	1111.10			1.51583			0.757915	−	0.652353i	$-0.226218\pi$
$733$	1111.10			1.51583			0.757915	+	0.652353i	$0.226218\pi$
$734$			190.001i			0.258857i
$735$		0			0
$736$			175.895i			0.238988i
$737$	587.327	+	490.178i	0.796916	+	0.665100i
$738$		−	133.229i		−	0.180527i
$739$			962.884i			1.30296i	0.758668	+	0.651478i	$0.225851\pi$
$739$			962.884i			1.30296i	−0.758668	+	0.651478i	$0.774149\pi$
$740$		0			0
$741$	170.096			0.229549
$742$			465.838i			0.627814i
$743$	674.012			0.907149			0.453574	−	0.891218i	$-0.350149\pi$
$743$	674.012			0.907149			0.453574	+	0.891218i	$0.350149\pi$
$744$			456.143i			0.613096i
$745$		0			0
$746$	12.1323			0.0162631
$747$	17.0786			0.0228629
$748$	−552.597	+	662.117i	−0.738766	+	0.885183i
$749$	966.693			1.29065
$750$		0			0
$751$	360.050			0.479428			0.239714	−	0.970844i	$-0.422946\pi$
$751$	360.050			0.479428			0.239714	+	0.970844i	$0.422946\pi$
$752$		−	392.012i		−	0.521292i
$753$			206.053i			0.273642i
$754$			222.034i			0.294475i
$755$		0			0
$756$			154.600i			0.204498i
$757$			573.607i			0.757737i	0.925450	+	0.378869i	$0.123687\pi$
$757$			573.607i			0.757737i	−0.925450	+	0.378869i	$0.876313\pi$
$758$	−223.779			−0.295223
$759$	−78.5357	+	94.1008i	−0.103473	+	0.123980i
$760$		0			0
$761$			1229.64i			1.61582i	0.589305	+	0.807910i	$0.299401\pi$
$761$			1229.64i			1.61582i	−0.589305	+	0.807910i	$0.700599\pi$
$762$			9.71415i			0.0127482i
$763$			1162.26i			1.52328i
$764$	−912.545			−1.19443
$765$		0			0
$766$		−	141.120i		−	0.184229i
$767$	218.242			0.284540
$768$		−	30.4587i		−	0.0396597i
$769$		−	1225.78i		−	1.59399i	−0.603985	−	0.796996i	$-0.706421\pi$
$769$		−	1225.78i		−	1.59399i	0.603985	−	0.796996i	$-0.293579\pi$
$770$		0			0
$771$	−315.481			−0.409185
$772$	−562.072			−0.728073
$773$		−	86.0374i		−	0.111303i	−0.998450	−	0.0556516i	$-0.982276\pi$
$773$		−	86.0374i		−	0.111303i	0.998450	−	0.0556516i	$-0.0177236\pi$
$774$	−112.858			−0.145812
$775$		0			0
$776$		−	190.512i		−	0.245506i
$777$	−346.335			−0.445734
$778$	−352.991			−0.453715
$779$	407.968			0.523707
$780$		0			0
$781$	−487.537	+	584.162i	−0.624247	+	0.747967i
$782$			94.2563i			0.120532i
$783$	107.923			0.137833
$784$	227.943			0.290744
$785$		0			0
$786$	−214.346			−0.272705
$787$	1109.97			1.41038			0.705188	−	0.709021i	$-0.250863\pi$
$787$	1109.97			1.41038			0.705188	+	0.709021i	$0.250863\pi$
$788$	−722.722			−0.917160
$789$		−	96.5108i		−	0.122320i
$790$		0			0
$791$		−	317.604i		−	0.401523i
$792$	−106.259	+	127.318i	−0.134165	+	0.160755i
$793$		−	1930.01i		−	2.43381i
$794$			410.157i			0.516570i
$795$		0			0
$796$	1019.30			1.28053
$797$		−	532.778i		−	0.668480i	−0.942488	−	0.334240i	$-0.891520\pi$
$797$		−	532.778i		−	0.668480i	0.942488	−	0.334240i	$-0.108480\pi$
$798$	58.8246			0.0737150
$799$		−	793.212i		−	0.992756i
$800$		0			0
$801$	219.213			0.273674
$802$	199.856			0.249197
$803$	549.947	−	658.941i	0.684865	−	0.820599i
$804$	−428.573			−0.533051
$805$		0			0
$806$	560.230			0.695075
$807$		−	80.9702i		−	0.100335i
$808$		−	106.920i		−	0.132326i
$809$			803.028i			0.992619i	0.868146	+	0.496309i	$0.165312\pi$
$809$			803.028i			0.992619i	−0.868146	+	0.496309i	$0.834688\pi$
$810$		0			0
$811$			323.073i			0.398364i	0.979962	+	0.199182i	$0.0638285\pi$
$811$			323.073i			0.398364i	−0.979962	+	0.199182i	$0.936171\pi$
$812$		−	617.963i		−	0.761038i
$813$	140.708			0.173073
$814$	−134.267	−	112.058i	−0.164947	−	0.137664i
$815$		0			0
$816$		−	415.653i		−	0.509378i
$817$		−	345.589i		−	0.422998i
$818$			462.964i			0.565971i
$819$	403.351			0.492492
$820$		0			0
$821$		−	345.071i		−	0.420306i	−0.977668	−	0.210153i	$-0.932604\pi$
$821$		−	345.071i		−	0.420306i	0.977668	−	0.210153i	$-0.0673962\pi$
$822$	−46.7356			−0.0568560
$823$			61.4018i			0.0746073i	0.999304	+	0.0373036i	$0.0118769\pi$
$823$			61.4018i			0.0746073i	−0.999304	+	0.0373036i	$0.988123\pi$
$824$		−	743.043i		−	0.901751i
$825$		0			0
$826$	75.4751			0.0913742
$827$	−1331.04			−1.60948			−0.804741	−	0.593626i	$-0.797696\pi$
$827$	−1331.04			−1.60948			−0.804741	+	0.593626i	$0.797696\pi$
$828$		−	68.6654i		−	0.0829292i
$829$	−177.243			−0.213803			−0.106902	−	0.994270i	$-0.534093\pi$
$829$	−177.243			−0.213803			−0.106902	+	0.994270i	$0.534093\pi$
$830$		0			0
$831$		−	535.274i		−	0.644133i
$832$	−408.078			−0.490478
$833$	461.229			0.553697
$834$	−101.502			−0.121705
$835$		0			0
$836$	−183.531	−	153.174i	−0.219535	−	0.183222i
$837$		−	272.310i		−	0.325340i
$838$	−217.165			−0.259147
$839$	−477.684			−0.569349			−0.284675	−	0.958624i	$-0.591886\pi$
$839$	−477.684			−0.569349			−0.284675	+	0.958624i	$0.591886\pi$
$840$		0			0
$841$	409.612			0.487054
$842$	−15.6571			−0.0185951
$843$	530.784			0.629637
$844$		−	493.981i		−	0.585286i
$845$		0			0
$846$		−	71.8023i		−	0.0848727i
$847$	180.989	+	995.540i	0.213682	+	1.17537i
$848$			912.393i			1.07594i
$849$		−	858.985i		−	1.01176i
$850$		0			0
$851$	153.824			0.180757
$852$		−	426.263i		−	0.500309i
$853$	−129.866			−0.152247			−0.0761234	−	0.997098i	$-0.524254\pi$
$853$	−129.866			−0.152247			−0.0761234	+	0.997098i	$0.524254\pi$
$854$		−	667.459i		−	0.781568i
$855$		0			0
$856$	−580.917			−0.678641
$857$	419.114			0.489048			0.244524	−	0.969643i	$-0.421368\pi$
$857$	419.114			0.489048			0.244524	+	0.969643i	$0.421368\pi$
$858$	156.371	+	130.506i	0.182251	+	0.152105i
$859$	−254.977			−0.296830			−0.148415	−	0.988925i	$-0.547417\pi$
$859$	−254.977			−0.296830			−0.148415	+	0.988925i	$0.547417\pi$
$860$		0			0
$861$	967.420			1.12360
$862$			148.681i			0.172484i
$863$			59.8124i			0.0693075i	0.999399	+	0.0346538i	$0.0110328\pi$
$863$			59.8124i			0.0693075i	−0.999399	+	0.0346538i	$0.988967\pi$
$864$		−	142.074i		−	0.164437i
$865$		0			0
$866$		−	120.368i		−	0.138994i
$867$		−	340.485i		−	0.392717i
$868$	−1559.23			−1.79635
$869$	64.6790	+	53.9806i	0.0744293	+	0.0621180i
$870$		0			0
$871$			1118.14i			1.28375i
$872$		−	698.439i		−	0.800962i
$873$			113.733i			0.130278i
$874$	−26.1268			−0.0298934
$875$		0			0
$876$			480.830i			0.548892i
$877$	563.009			0.641971			0.320986	−	0.947084i	$-0.395986\pi$
$877$	563.009			0.641971			0.320986	+	0.947084i	$0.395986\pi$
$878$		−	44.1804i		−	0.0503194i
$879$			678.154i			0.771506i
$880$		0			0
$881$	1178.14			1.33728			0.668641	−	0.743586i	$-0.266876\pi$
$881$	1178.14			1.33728			0.668641	+	0.743586i	$0.266876\pi$
$882$	41.7509			0.0473367
$883$			704.399i			0.797733i	0.917009	+	0.398867i	$0.130596\pi$
$883$			704.399i			0.797733i	−0.917009	+	0.398867i	$0.869404\pi$
$884$	−1260.53			−1.42593
$885$		0			0
$886$			286.199i			0.323024i
$887$	1582.21			1.78378			0.891888	−	0.452257i	$-0.149381\pi$
$887$	1582.21			1.78378			0.891888	+	0.452257i	$0.149381\pi$
$888$	208.124			0.234374
$889$	−70.5376			−0.0793448
$890$		0			0
$891$	63.4347	−	76.0069i	0.0711949	−	0.0853051i
$892$		−	889.714i		−	0.997438i
$893$	219.870			0.246214
$894$	104.341			0.116712
$895$		0			0
$896$	−1055.71			−1.17825
$897$	−179.147			−0.199718
$898$	173.980			0.193741
$899$			1088.47i			1.21075i
$900$		0			0
$901$			1846.17i			2.04903i
$902$	375.049	+	313.013i	0.415797	+	0.347021i
$903$		−	819.501i		−	0.907532i
$904$			190.859i			0.211127i
$905$		0			0
$906$	43.8845			0.0484376
$907$		−	436.018i		−	0.480725i	−0.970683	−	0.240363i	$-0.922734\pi$
$907$		−	436.018i		−	0.480725i	0.970683	−	0.240363i	$-0.0772663\pi$
$908$	880.260			0.969449
$909$			63.8292i			0.0702192i
$910$		0			0
$911$	−82.7040			−0.0907838			−0.0453919	−	0.998969i	$-0.514454\pi$
$911$	−82.7040			−0.0907838			−0.0453919	+	0.998969i	$0.514454\pi$
$912$	115.214			0.126332
$913$	−40.1250	+	48.0774i	−0.0439485	+	0.0526587i
$914$	−124.638			−0.136365
$915$		0			0
$916$	1293.84			1.41249
$917$		−	1556.44i		−	1.69731i
$918$		−	76.1325i		−	0.0829330i
$919$		−	1713.21i		−	1.86421i	−0.362193	−	0.932103i	$-0.617972\pi$
$919$		−	1713.21i		−	1.86421i	0.362193	−	0.932103i	$-0.382028\pi$
$920$		0			0
$921$			160.568i			0.174340i
$922$			454.132i			0.492551i
$923$	−1112.12			−1.20489
$924$	−435.211	−	363.223i	−0.471007	−	0.393099i
$925$		0			0
$926$			48.1695i			0.0520189i
$927$			443.584i			0.478515i
$928$			567.891i			0.611952i
$929$	−537.309			−0.578374			−0.289187	−	0.957273i	$-0.593385\pi$
$929$	−537.309			−0.578374			−0.289187	+	0.957273i	$0.593385\pi$
$930$		0			0
$931$			127.848i			0.137323i
$932$	937.034			1.00540
$933$		−	767.041i		−	0.822124i
$934$		−	266.963i		−	0.285828i
$935$		0			0
$936$	−242.386			−0.258960
$937$	321.591			0.343213			0.171607	−	0.985166i	$-0.445104\pi$
$937$	321.591			0.343213			0.171607	+	0.985166i	$0.445104\pi$
$938$			386.690i			0.412249i
$939$	−169.711			−0.180735
$940$		0			0
$941$		−	880.847i		−	0.936076i	−0.883708	−	0.468038i	$-0.844961\pi$
$941$		−	880.847i		−	0.936076i	0.883708	−	0.468038i	$-0.155039\pi$
$942$	312.927			0.332194
$943$	−429.677			−0.455649
$944$	147.826			0.156595
$945$		0			0
$946$	265.153	−	317.704i	0.280289	−	0.335839i
$947$		−	227.350i		−	0.240074i	−0.992769	−	0.120037i	$-0.961699\pi$
$947$		−	227.350i		−	0.240074i	0.992769	−	0.120037i	$-0.0383013\pi$
$948$	−47.1963			−0.0497851
$949$	1254.48			1.32190
$950$		0			0
$951$	−751.356			−0.790070
$952$	−926.028			−0.972718
$953$	−46.3722			−0.0486592			−0.0243296	−	0.999704i	$-0.507745\pi$
$953$	−46.3722			−0.0486592			−0.0243296	+	0.999704i	$0.507745\pi$
$954$			167.117i			0.175175i
$955$		0			0
$956$			1297.82i			1.35755i
$957$	−253.559	+	303.812i	−0.264952	+	0.317463i
$958$			412.644i			0.430735i
$959$		−	339.362i		−	0.353871i
$960$		0			0
$961$	1785.39			1.85785
$962$		−	255.615i		−	0.265712i
$963$	346.797			0.360122
$964$			532.404i			0.552286i
$965$		0			0
$966$	−61.9549			−0.0641355
$967$	−264.144			−0.273158			−0.136579	−	0.990629i	$-0.543611\pi$
$967$	−264.144			−0.273158			−0.136579	+	0.990629i	$0.543611\pi$
$968$	−108.762	−	598.252i	−0.112357	−	0.618029i
$969$	233.129			0.240587
$970$		0			0
$971$	666.134			0.686029			0.343015	−	0.939330i	$-0.388552\pi$
$971$	666.134			0.686029			0.343015	+	0.939330i	$0.388552\pi$
$972$			55.4622i			0.0570599i
$973$		−	737.037i		−	0.757489i
$974$			358.447i			0.368015i
$975$		0			0
$976$		−	1307.29i		−	1.33944i
$977$			1339.01i			1.37053i	0.728293	+	0.685266i	$0.240314\pi$
$977$			1339.01i			1.37053i	−0.728293	+	0.685266i	$0.759686\pi$
$978$	147.877			0.151203
$979$	−515.026	+	617.100i	−0.526074	+	0.630337i
$980$		0			0
$981$			416.956i			0.425032i
$982$		−	319.664i		−	0.325523i
$983$		−	1241.99i		−	1.26347i	−0.775185	−	0.631735i	$-0.782343\pi$
$983$		−	1241.99i		−	1.26347i	0.775185	−	0.631735i	$-0.217657\pi$
$984$	−581.353			−0.590806
$985$		0			0
$986$			304.314i			0.308635i
$987$	521.380			0.528247
$988$		−	349.404i		−	0.353647i
$989$			363.979i			0.368028i
$990$		0			0
$991$	886.745			0.894798			0.447399	−	0.894334i	$-0.352350\pi$
$991$	886.745			0.894798			0.447399	+	0.894334i	$0.352350\pi$
$992$	1432.89			1.44444
$993$			468.528i			0.471831i
$994$	−384.605			−0.386927
$995$		0			0
$996$		−	35.0821i		−	0.0352230i
$997$	20.1579			0.0202185			0.0101093	−	0.999949i	$-0.496782\pi$
$997$	20.1579			0.0202185			0.0101093	+	0.999949i	$0.496782\pi$
$998$	376.525			0.377280
$999$	−124.246			−0.124371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.3.h.b.274.13		32
5.2	odd	4		825.3.b.d.76.7		16
5.3	odd	4		165.3.b.a.76.10	yes	16
5.4	even	2	inner	825.3.h.b.274.19		32
11.10	odd	2	inner	825.3.h.b.274.20		32
15.8	even	4		495.3.b.c.406.7		16
20.3	even	4		2640.3.c.c.241.2		16
55.32	even	4		825.3.b.d.76.10		16
55.43	even	4		165.3.b.a.76.7	✓	16
55.54	odd	2	inner	825.3.h.b.274.14		32
165.98	odd	4		495.3.b.c.406.10		16
220.43	odd	4		2640.3.c.c.241.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.3.b.a.76.7	✓	16	55.43	even	4
165.3.b.a.76.10	yes	16	5.3	odd	4
495.3.b.c.406.7		16	15.8	even	4
495.3.b.c.406.10		16	165.98	odd	4
825.3.b.d.76.7		16	5.2	odd	4
825.3.b.d.76.10		16	55.32	even	4
825.3.h.b.274.13		32	1.1	even	1	trivial
825.3.h.b.274.14		32	55.54	odd	2	inner
825.3.h.b.274.19		32	5.4	even	2	inner
825.3.h.b.274.20		32	11.10	odd	2	inner
2640.3.c.c.241.2		16	20.3	even	4
2640.3.c.c.241.3		16	220.43	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	825.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.664903 q^{2} -1.73205i q^{3} -3.55790 q^{4} +1.15165i q^{6} -8.36247 q^{7} +5.02527 q^{8} -3.00000 q^{9} +(7.04830 - 8.44521i) q^{11} +6.16247i q^{12} +16.0778 q^{13} +5.56023 q^{14} +10.8903 q^{16} +22.0359 q^{17} +1.99471 q^{18} +6.10810i q^{19} +14.4842i q^{21} +(-4.68643 + 5.61524i) q^{22} -6.43313i q^{23} -8.70402i q^{24} -10.6902 q^{26} +5.19615i q^{27} +29.7529 q^{28} -20.7699i q^{29} -52.4060 q^{31} -27.3421 q^{32} +(-14.6275 - 12.2080i) q^{33} -14.6517 q^{34} +10.6737 q^{36} +23.9112i q^{37} -4.06129i q^{38} -27.8476i q^{39} -66.7913i q^{41} -9.63059i q^{42} -56.5789 q^{43} +(-25.0772 + 30.0472i) q^{44} +4.27741i q^{46} -35.9964i q^{47} -18.8626i q^{48} +20.9309 q^{49} -38.1672i q^{51} -57.2034 q^{52} +83.7803i q^{53} -3.45494i q^{54} -42.0237 q^{56} +10.5795 q^{57} +13.8099i q^{58} +13.5741 q^{59} -120.042i q^{61} +34.8449 q^{62} +25.0874 q^{63} -25.3814 q^{64} +(9.72588 + 8.11714i) q^{66} +69.5457i q^{67} -78.4015 q^{68} -11.1425 q^{69} -69.1708 q^{71} -15.0758 q^{72} +78.0255 q^{73} -15.8986i q^{74} -21.7320i q^{76} +(-58.9412 + 70.6228i) q^{77} +18.5159i q^{78} +7.65867i q^{79} +9.00000 q^{81} +44.4097i q^{82} -5.69286 q^{83} -51.5335i q^{84} +37.6195 q^{86} -35.9745 q^{87} +(35.4196 - 42.4394i) q^{88} -73.0710 q^{89} -134.450 q^{91} +22.8885i q^{92} +90.7699i q^{93} +23.9341i q^{94} +47.3579i q^{96} -37.9109i q^{97} -13.9170 q^{98} +(-21.1449 + 25.3356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 96 q^{9} - 56 q^{11} - 32 q^{16} - 176 q^{26} - 192 q^{31} + 400 q^{34} - 48 q^{36} - 600 q^{44} + 992 q^{49} - 64 q^{56} + 272 q^{59} - 912 q^{64} - 360 q^{66} - 336 q^{69} + 432 q^{71}+ \cdots + 168 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 96 * q^9 - 56 * q^11 - 32 * q^16 - 176 * q^26 - 192 * q^31 + 400 * q^34 - 48 * q^36 - 600 * q^44 + 992 * q^49 - 64 * q^56 + 272 * q^59 - 912 * q^64 - 360 * q^66 - 336 * q^69 + 432 * q^71 + 288 * q^81 + 384 * q^86 + 672 * q^89 + 512 * q^91 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more