LMFDB - Embedded newform 1150.3.d.b.551.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(551,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1150.551");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.d (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:	$31.3352304014$
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} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.6
Root			$3.68124i$ of defining polynomial
Character	$\chi$	$=$	1150.551
Dual form			1150.3.d.b.551.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +3.36596 q^{3} +2.00000 q^{4} -4.76019 q^{6} +1.16919i q^{7} -2.82843 q^{8} +2.32968 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +3.36596 q^{3} +2.00000 q^{4} -4.76019 q^{6} +1.16919i q^{7} -2.82843 q^{8} +2.32968 q^{9} -10.6148i q^{11} +6.73192 q^{12} +15.0913 q^{13} -1.65348i q^{14} +4.00000 q^{16} +20.0887i q^{17} -3.29467 q^{18} -22.5221i q^{19} +3.93543i q^{21} +15.0116i q^{22} +(20.9683 + 9.45142i) q^{23} -9.52037 q^{24} -21.3424 q^{26} -22.4520 q^{27} +2.33837i q^{28} +32.5993 q^{29} -27.0975 q^{31} -5.65685 q^{32} -35.7289i q^{33} -28.4097i q^{34} +4.65936 q^{36} -53.0568i q^{37} +31.8510i q^{38} +50.7968 q^{39} +9.43720 q^{41} -5.56554i q^{42} +36.4382i q^{43} -21.2296i q^{44} +(-29.6537 - 13.3663i) q^{46} +49.1365 q^{47} +13.4638 q^{48} +47.6330 q^{49} +67.6176i q^{51} +30.1827 q^{52} -104.253i q^{53} +31.7520 q^{54} -3.30696i q^{56} -75.8083i q^{57} -46.1023 q^{58} +53.5457 q^{59} +23.5166i q^{61} +38.3217 q^{62} +2.72383i q^{63} +8.00000 q^{64} +50.5284i q^{66} +59.4754i q^{67} +40.1773i q^{68} +(70.5785 + 31.8131i) q^{69} +55.2130 q^{71} -6.58933 q^{72} +8.77305 q^{73} +75.0337i q^{74} -45.0441i q^{76} +12.4107 q^{77} -71.8376 q^{78} -57.0848i q^{79} -96.5397 q^{81} -13.3462 q^{82} -55.1788i q^{83} +7.87086i q^{84} -51.5314i q^{86} +109.728 q^{87} +30.0232i q^{88} -139.825i q^{89} +17.6446i q^{91} +(41.9366 + 18.9028i) q^{92} -91.2091 q^{93} -69.4894 q^{94} -19.0407 q^{96} -19.8635i q^{97} -67.3632 q^{98} -24.7291i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$1$

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
$3$	3.36596			1.12199			0.560993	−	0.827820i	$-0.310419\pi$
$3$	3.36596			1.12199			0.560993	+	0.827820i	$0.310419\pi$
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−4.76019			−0.793364
$7$			1.16919i			0.167026i	0.996507	+	0.0835132i	$0.0266141\pi$
$7$			1.16919i			0.167026i	−0.996507	+	0.0835132i	$0.973386\pi$
$8$	−2.82843			−0.353553
$9$	2.32968			0.258853
$10$		0			0
$11$		−	10.6148i		−	0.964981i	−0.875901	−	0.482490i	$-0.839732\pi$
$11$		−	10.6148i		−	0.964981i	0.875901	−	0.482490i	$-0.160268\pi$
$12$	6.73192			0.560993
$13$	15.0913			1.16087			0.580436	−	0.814306i	$-0.302882\pi$
$13$	15.0913			1.16087			0.580436	+	0.814306i	$0.302882\pi$
$14$		−	1.65348i		−	0.118106i
$15$		0			0
$16$	4.00000			0.250000
$17$			20.0887i			1.18169i	0.806787	+	0.590843i	$0.201205\pi$
$17$			20.0887i			1.18169i	−0.806787	+	0.590843i	$0.798795\pi$
$18$	−3.29467			−0.183037
$19$		−	22.5221i		−	1.18537i	−0.805434	−	0.592686i	$-0.798068\pi$
$19$		−	22.5221i		−	1.18537i	0.805434	−	0.592686i	$-0.201932\pi$
$20$		0			0
$21$			3.93543i			0.187401i
$22$			15.0116i			0.682344i
$23$	20.9683	+	9.45142i	0.911666	+	0.410931i
$23$	20.9683	+	9.45142i	0.911666	+	0.410931i
$24$	−9.52037			−0.396682
$25$		0			0
$26$	−21.3424			−0.820860
$27$	−22.4520			−0.831556
$28$			2.33837i			0.0835132i
$29$	32.5993			1.12411			0.562056	−	0.827099i	$-0.310010\pi$
$29$	32.5993			1.12411			0.562056	+	0.827099i	$0.310010\pi$
$30$		0			0
$31$	−27.0975			−0.874113			−0.437056	−	0.899434i	$-0.643979\pi$
$31$	−27.0975			−0.874113			−0.437056	+	0.899434i	$0.643979\pi$
$32$	−5.65685			−0.176777
$33$		−	35.7289i		−	1.08270i
$34$		−	28.4097i		−	0.835578i
$35$		0			0
$36$	4.65936			0.129427
$37$		−	53.0568i		−	1.43397i	−0.697089	−	0.716984i	$-0.745522\pi$
$37$		−	53.0568i		−	1.43397i	0.697089	−	0.716984i	$-0.254478\pi$
$38$			31.8510i			0.838184i
$39$	50.7968			1.30248
$40$		0			0
$41$	9.43720			0.230176			0.115088	−	0.993355i	$-0.463285\pi$
$41$	9.43720			0.230176			0.115088	+	0.993355i	$0.463285\pi$
$42$		−	5.56554i		−	0.132513i
$43$			36.4382i			0.847400i	0.905802	+	0.423700i	$0.139269\pi$
$43$			36.4382i			0.847400i	−0.905802	+	0.423700i	$0.860731\pi$
$44$		−	21.2296i		−	0.482490i
$45$		0			0
$46$	−29.6537	−	13.3663i	−0.644645	−	0.290572i
$47$	49.1365			1.04546			0.522728	−	0.852499i	$-0.324914\pi$
$47$	49.1365			1.04546			0.522728	+	0.852499i	$0.324914\pi$
$48$	13.4638			0.280497
$49$	47.6330			0.972102
$50$		0			0
$51$			67.6176i			1.32584i
$52$	30.1827			0.580436
$53$		−	104.253i		−	1.96703i	−0.180815	−	0.983517i	$-0.557874\pi$
$53$		−	104.253i		−	1.96703i	0.180815	−	0.983517i	$-0.442126\pi$
$54$	31.7520			0.587999
$55$		0			0
$56$		−	3.30696i		−	0.0590528i
$57$		−	75.8083i		−	1.32997i
$58$	−46.1023			−0.794868
$59$	53.5457			0.907554			0.453777	−	0.891115i	$-0.350076\pi$
$59$	53.5457			0.907554			0.453777	+	0.891115i	$0.350076\pi$
$60$		0			0
$61$			23.5166i			0.385518i	0.981246	+	0.192759i	$0.0617435\pi$
$61$			23.5166i			0.385518i	−0.981246	+	0.192759i	$0.938257\pi$
$62$	38.3217			0.618091
$63$			2.72383i			0.0432354i
$64$	8.00000			0.125000
$65$		0			0
$66$			50.5284i			0.765581i
$67$			59.4754i			0.887692i	0.896103	+	0.443846i	$0.146386\pi$
$67$			59.4754i			0.887692i	−0.896103	+	0.443846i	$0.853614\pi$
$68$			40.1773i			0.590843i
$69$	70.5785	+	31.8131i	1.02288	+	0.461060i
$70$		0			0
$71$	55.2130			0.777648			0.388824	−	0.921312i	$-0.372881\pi$
$71$	55.2130			0.777648			0.388824	+	0.921312i	$0.372881\pi$
$72$	−6.58933			−0.0915185
$73$	8.77305			0.120179			0.0600894	−	0.998193i	$-0.480861\pi$
$73$	8.77305			0.120179			0.0600894	+	0.998193i	$0.480861\pi$
$74$			75.0337i			1.01397i
$75$		0			0
$76$		−	45.0441i		−	0.592686i
$77$	12.4107			0.161177
$78$	−71.8376			−0.920994
$79$		−	57.0848i		−	0.722592i	−0.932451	−	0.361296i	$-0.882334\pi$
$79$		−	57.0848i		−	0.722592i	0.932451	−	0.361296i	$-0.117666\pi$
$80$		0			0
$81$	−96.5397			−1.19185
$82$	−13.3462			−0.162759
$83$		−	55.1788i		−	0.664805i	−0.943138	−	0.332403i	$-0.892141\pi$
$83$		−	55.1788i		−	0.664805i	0.943138	−	0.332403i	$-0.107859\pi$
$84$			7.87086i			0.0937007i
$85$		0			0
$86$		−	51.5314i		−	0.599203i
$87$	109.728			1.26124
$88$			30.0232i			0.341172i
$89$		−	139.825i		−	1.57107i	−0.618815	−	0.785536i	$-0.712387\pi$
$89$		−	139.825i		−	1.57107i	0.618815	−	0.785536i	$-0.287613\pi$
$90$		0			0
$91$			17.6446i			0.193896i
$92$	41.9366	+	18.9028i	0.455833	+	0.205466i
$93$	−91.2091			−0.980743
$94$	−69.4894			−0.739249
$95$		0			0
$96$	−19.0407			−0.198341
$97$		−	19.8635i		−	0.204778i	−0.994744	−	0.102389i	$-0.967351\pi$
$97$		−	19.8635i		−	0.204778i	0.994744	−	0.102389i	$-0.0326487\pi$
$98$	−67.3632			−0.687380
$99$		−	24.7291i		−	0.249789i
$100$		0			0
$101$	86.5639			0.857068			0.428534	−	0.903526i	$-0.359030\pi$
$101$	86.5639			0.857068			0.428534	+	0.903526i	$0.359030\pi$
$102$		−	95.6258i		−	0.937507i
$103$			144.118i			1.39920i	0.714535	+	0.699600i	$0.246639\pi$
$103$			144.118i			1.39920i	−0.714535	+	0.699600i	$0.753361\pi$
$104$	−42.6847			−0.410430
$105$		0			0
$106$			147.436i			1.39090i
$107$		−	10.4544i		−	0.0977050i	−0.998806	−	0.0488525i	$-0.984444\pi$
$107$		−	10.4544i		−	0.0977050i	0.998806	−	0.0488525i	$-0.0155564\pi$
$108$	−44.9040			−0.415778
$109$			69.1221i			0.634148i	0.948401	+	0.317074i	$0.102700\pi$
$109$			69.1221i			0.634148i	−0.948401	+	0.317074i	$0.897300\pi$
$110$		0			0
$111$		−	178.587i		−	1.60889i
$112$			4.67674i			0.0417566i
$113$			137.264i			1.21473i	0.794423	+	0.607364i	$0.207773\pi$
$113$			137.264i			1.21473i	−0.794423	+	0.607364i	$0.792227\pi$
$114$			107.209i			0.940431i
$115$		0			0
$116$	65.1985			0.562056
$117$	35.1580			0.300496
$118$	−75.7250			−0.641738
$119$	−23.4874			−0.197373
$120$		0			0
$121$	8.32629			0.0688123
$122$		−	33.2575i		−	0.272602i
$123$	31.7652			0.258254
$124$	−54.1950			−0.437056
$125$		0			0
$126$		−	3.85208i		−	0.0305720i
$127$	−57.9697			−0.456455			−0.228227	−	0.973608i	$-0.573293\pi$
$127$	−57.9697			−0.456455			−0.228227	+	0.973608i	$0.573293\pi$
$128$	−11.3137			−0.0883883
$129$			122.650i			0.950772i
$130$		0			0
$131$	−95.0810			−0.725809			−0.362905	−	0.931826i	$-0.618215\pi$
$131$	−95.0810			−0.725809			−0.362905	+	0.931826i	$0.618215\pi$
$132$		−	71.4579i		−	0.541348i
$133$	26.3325			0.197988
$134$		−	84.1109i		−	0.627693i
$135$		0			0
$136$		−	56.8193i		−	0.417789i
$137$		−	198.711i		−	1.45045i	−0.688514	−	0.725223i	$-0.741737\pi$
$137$		−	198.711i		−	1.45045i	0.688514	−	0.725223i	$-0.258263\pi$
$138$	−99.8131	−	44.9905i	−0.723283	−	0.326018i
$139$	−0.129480			−0.000931508			−0.000465754	−	1.00000i	$-0.500148\pi$
$139$	−0.129480			−0.000931508			−0.000465754		1.00000i	$0.500148\pi$
$140$		0			0
$141$	165.391			1.17299
$142$	−78.0830			−0.549880
$143$		−	160.191i		−	1.12022i
$144$	9.31873			0.0647134
$145$		0			0
$146$	−12.4070			−0.0849792
$147$	160.331			1.09069
$148$		−	106.114i		−	0.716984i
$149$			63.8745i			0.428688i	0.976758	+	0.214344i	$0.0687613\pi$
$149$			63.8745i			0.428688i	−0.976758	+	0.214344i	$0.931239\pi$
$150$		0			0
$151$	−35.2673			−0.233558			−0.116779	−	0.993158i	$-0.537257\pi$
$151$	−35.2673			−0.233558			−0.116779	+	0.993158i	$0.537257\pi$
$152$			63.7020i			0.419092i
$153$			46.8002i			0.305884i
$154$	−17.5513			−0.113970
$155$		0			0
$156$	101.594			0.651241
$157$			289.136i			1.84163i	0.390002	+	0.920814i	$0.372474\pi$
$157$			289.136i			1.84163i	−0.390002	+	0.920814i	$0.627526\pi$
$158$			80.7300i			0.510950i
$159$		−	350.911i		−	2.20699i
$160$		0			0
$161$	−11.0505	+	24.5159i	−0.0686364	+	0.152272i
$162$	136.528			0.842764
$163$	46.2536			0.283764			0.141882	−	0.989884i	$-0.454685\pi$
$163$	46.2536			0.283764			0.141882	+	0.989884i	$0.454685\pi$
$164$	18.8744			0.115088
$165$		0			0
$166$			78.0346i			0.470088i
$167$	90.8735			0.544153			0.272076	−	0.962276i	$-0.412290\pi$
$167$	90.8735			0.544153			0.272076	+	0.962276i	$0.412290\pi$
$168$		−	11.1311i		−	0.0662564i
$169$	58.7484			0.347624
$170$		0			0
$171$		−	52.4692i		−	0.306837i
$172$			72.8764i			0.423700i
$173$	90.7893			0.524794			0.262397	−	0.964960i	$-0.415487\pi$
$173$	90.7893			0.524794			0.262397	+	0.964960i	$0.415487\pi$
$174$	−155.179			−0.891831
$175$		0			0
$176$		−	42.4591i		−	0.241245i
$177$	180.233			1.01826
$178$			197.743i			1.11092i
$179$	301.636			1.68511			0.842557	−	0.538607i	$-0.181049\pi$
$179$	301.636			1.68511			0.842557	+	0.538607i	$0.181049\pi$
$180$		0			0
$181$		−	248.547i		−	1.37319i	−0.727040	−	0.686595i	$-0.759105\pi$
$181$		−	248.547i		−	1.37319i	0.727040	−	0.686595i	$-0.240895\pi$
$182$		−	24.9532i		−	0.137105i
$183$			79.1558i			0.432546i
$184$	−59.3074	−	26.7327i	−0.322323	−	0.145286i
$185$		0			0
$186$	128.989			0.693490
$187$	213.237			1.14030
$188$	98.2729			0.522728
$189$		−	26.2506i		−	0.138892i
$190$		0			0
$191$		−	146.382i		−	0.766397i	−0.923666	−	0.383199i	$-0.874822\pi$
$191$		−	146.382i		−	0.766397i	0.923666	−	0.383199i	$-0.125178\pi$
$192$	26.9277			0.140248
$193$	120.648			0.625120			0.312560	−	0.949898i	$-0.398813\pi$
$193$	120.648			0.625120			0.312560	+	0.949898i	$0.398813\pi$
$194$			28.0912i			0.144800i
$195$		0			0
$196$	95.2660			0.486051
$197$	−31.6502			−0.160661			−0.0803305	−	0.996768i	$-0.525598\pi$
$197$	−31.6502			−0.160661			−0.0803305	+	0.996768i	$0.525598\pi$
$198$			34.9722i			0.176627i
$199$		−	37.4496i		−	0.188189i	−0.995563	−	0.0940944i	$-0.970004\pi$
$199$		−	37.4496i		−	0.188189i	0.995563	−	0.0940944i	$-0.0299955\pi$
$200$		0			0
$201$			200.192i			0.995979i
$202$	−122.420			−0.606039
$203$			38.1146i			0.187757i
$204$			135.235i			0.662918i
$205$		0			0
$206$		−	203.813i		−	0.989384i
$207$	48.8495	+	22.0188i	0.235988	+	0.106371i
$208$	60.3653			0.290218
$209$	−239.067			−1.14386
$210$		0			0
$211$	−43.6572			−0.206906			−0.103453	−	0.994634i	$-0.532989\pi$
$211$	−43.6572			−0.206906			−0.103453	+	0.994634i	$0.532989\pi$
$212$		−	208.506i		−	0.983517i
$213$	185.845			0.872510
$214$			14.7848i			0.0690879i
$215$		0			0
$216$	63.5039			0.294000
$217$		−	31.6820i		−	0.146000i
$218$		−	97.7535i		−	0.448410i
$219$	29.5297			0.134839
$220$		0			0
$221$			303.165i			1.37179i
$222$			252.560i			1.13766i
$223$	−348.623			−1.56333			−0.781666	−	0.623697i	$-0.785630\pi$
$223$	−348.623			−1.56333			−0.781666	+	0.623697i	$0.785630\pi$
$224$		−	6.61391i		−	0.0295264i
$225$		0			0
$226$		−	194.121i		−	0.858943i
$227$			175.793i			0.774421i	0.921991	+	0.387210i	$0.126561\pi$
$227$			175.793i			0.774421i	−0.921991	+	0.387210i	$0.873439\pi$
$228$		−	151.617i		−	0.664985i
$229$		−	1.44148i		−	0.00629466i	−0.999995	−	0.00314733i	$-0.998998\pi$
$229$		−	1.44148i		−	0.00629466i	0.999995	−	0.00314733i	$-0.00100183\pi$
$230$		0			0
$231$	41.7738			0.180839
$232$	−92.2047			−0.397434
$233$	113.416			0.486763			0.243381	−	0.969931i	$-0.421743\pi$
$233$	113.416			0.486763			0.243381	+	0.969931i	$0.421743\pi$
$234$	−49.7209			−0.212483
$235$		0			0
$236$	107.091			0.453777
$237$		−	192.145i		−	0.810738i
$238$	33.2162			0.139564
$239$	367.260			1.53665			0.768326	−	0.640059i	$-0.221090\pi$
$239$	367.260			1.53665			0.768326	+	0.640059i	$0.221090\pi$
$240$		0			0
$241$		−	220.365i		−	0.914378i	−0.889370	−	0.457189i	$-0.848856\pi$
$241$		−	220.365i		−	0.914378i	0.889370	−	0.457189i	$-0.151144\pi$
$242$	−11.7752			−0.0486577
$243$	−122.881			−0.505681
$244$			47.0332i			0.192759i
$245$		0			0
$246$	−44.9228			−0.182613
$247$		−	339.888i		−	1.37606i
$248$	76.6433			0.309046
$249$		−	185.730i		−	0.745902i
$250$		0			0
$251$			440.210i			1.75382i	0.480650	+	0.876912i	$0.340401\pi$
$251$			440.210i			1.75382i	−0.480650	+	0.876912i	$0.659599\pi$
$252$			5.44766i			0.0216177i
$253$	100.325	−	222.574i	0.396541	−	0.879740i
$254$	81.9816			0.322762
$255$		0			0
$256$	16.0000			0.0625000
$257$	−491.519			−1.91252			−0.956262	−	0.292512i	$-0.905509\pi$
$257$	−491.519			−1.91252			−0.956262	+	0.292512i	$0.905509\pi$
$258$		−	173.453i		−	0.672297i
$259$	62.0333			0.239511
$260$		0			0
$261$	75.9459			0.290980
$262$	134.465			0.513225
$263$		−	267.833i		−	1.01838i	−0.860655	−	0.509189i	$-0.829946\pi$
$263$		−	267.833i		−	1.01838i	0.860655	−	0.509189i	$-0.170054\pi$
$264$			101.057i			0.382791i
$265$		0			0
$266$	−37.2397			−0.139999
$267$		−	470.647i		−	1.76272i
$268$			118.951i			0.443846i
$269$	95.6985			0.355756			0.177878	−	0.984053i	$-0.443077\pi$
$269$	95.6985			0.355756			0.177878	+	0.984053i	$0.443077\pi$
$270$		0			0
$271$	−452.255			−1.66884			−0.834419	−	0.551131i	$-0.814197\pi$
$271$	−452.255			−1.66884			−0.834419	+	0.551131i	$0.814197\pi$
$272$			80.3547i			0.295422i
$273$			59.3909i			0.217549i
$274$			281.020i			1.02562i
$275$		0			0
$276$	141.157	+	63.6262i	0.511439	+	0.230530i
$277$	87.4783			0.315806			0.157903	−	0.987455i	$-0.449527\pi$
$277$	87.4783			0.315806			0.157903	+	0.987455i	$0.449527\pi$
$278$	0.183112			0.000658676
$279$	−63.1285			−0.226267
$280$		0			0
$281$			232.157i			0.826183i	0.910690	+	0.413091i	$0.135551\pi$
$281$			232.157i			0.826183i	−0.910690	+	0.413091i	$0.864449\pi$
$282$	−233.899			−0.829428
$283$			239.367i			0.845820i	0.906172	+	0.422910i	$0.138991\pi$
$283$			239.367i			0.845820i	−0.906172	+	0.422910i	$0.861009\pi$
$284$	110.426			0.388824
$285$		0			0
$286$			226.545i			0.792114i
$287$			11.0338i			0.0384454i
$288$	−13.1787			−0.0457593
$289$	−114.554			−0.396382
$290$		0			0
$291$		−	66.8597i		−	0.229758i
$292$	17.5461			0.0600894
$293$		−	581.830i		−	1.98577i	−0.119092	−	0.992883i	$-0.537998\pi$
$293$		−	581.830i		−	1.98577i	0.119092	−	0.992883i	$-0.462002\pi$
$294$	−226.742			−0.771231
$295$		0			0
$296$			150.067i			0.506984i
$297$			238.323i			0.802436i
$298$		−	90.3322i		−	0.303128i
$299$	316.440	+	142.635i	1.05833	+	0.477039i
$300$		0			0
$301$	−42.6030			−0.141538
$302$	49.8755			0.165151
$303$	291.370			0.961619
$304$		−	90.0882i		−	0.296343i
$305$		0			0
$306$		−	66.1855i		−	0.216292i
$307$	−110.134			−0.358742			−0.179371	−	0.983782i	$-0.557406\pi$
$307$	−110.134			−0.358742			−0.179371	+	0.983782i	$0.557406\pi$
$308$	24.8213			0.0805887
$309$			485.094i			1.56988i
$310$		0			0
$311$	−298.100			−0.958520			−0.479260	−	0.877673i	$-0.659095\pi$
$311$	−298.100			−0.958520			−0.479260	+	0.877673i	$0.659095\pi$
$312$	−143.675			−0.460497
$313$		−	109.474i		−	0.349758i	−0.984590	−	0.174879i	$-0.944047\pi$
$313$		−	109.474i		−	0.349758i	0.984590	−	0.174879i	$-0.0559534\pi$
$314$		−	408.900i		−	1.30223i
$315$		0			0
$316$		−	114.170i		−	0.361296i
$317$	−474.434			−1.49664			−0.748318	−	0.663340i	$-0.769138\pi$
$317$	−474.434			−1.49664			−0.748318	+	0.663340i	$0.769138\pi$
$318$			496.263i			1.56057i
$319$		−	346.034i		−	1.08475i
$320$		0			0
$321$		−	35.1892i		−	0.109624i
$322$	15.6277	−	34.6707i	0.0485333	−	0.107673i
$323$	452.438			1.40074
$324$	−193.079			−0.595924
$325$		0			0
$326$	−65.4124			−0.200652
$327$			232.662i			0.711506i
$328$	−26.6924			−0.0813794
$329$			57.4496i			0.174619i
$330$		0			0
$331$	255.367			0.771503			0.385751	−	0.922603i	$-0.373942\pi$
$331$	255.367			0.771503			0.385751	+	0.922603i	$0.373942\pi$
$332$		−	110.358i		−	0.332403i
$333$		−	123.606i		−	0.371188i
$334$	−128.515			−0.384774
$335$		0			0
$336$			15.7417i			0.0468504i
$337$			458.486i			1.36049i	0.732983	+	0.680247i	$0.238127\pi$
$337$			458.486i			1.36049i	−0.732983	+	0.680247i	$0.761873\pi$
$338$	−83.0828			−0.245807
$339$			462.026i			1.36291i
$340$		0			0
$341$			287.634i			0.843502i
$342$			74.2027i			0.216967i
$343$			112.982i			0.329393i
$344$		−	103.063i		−	0.299601i
$345$		0			0
$346$	−128.395			−0.371085
$347$	−510.676			−1.47169			−0.735845	−	0.677151i	$-0.763215\pi$
$347$	−510.676			−1.47169			−0.735845	+	0.677151i	$0.763215\pi$
$348$	219.456			0.630620
$349$	−591.870			−1.69590			−0.847951	−	0.530075i	$-0.822164\pi$
$349$	−591.870			−1.69590			−0.847951	+	0.530075i	$0.822164\pi$
$350$		0			0
$351$	−338.831			−0.965330
$352$			60.0463i			0.170586i
$353$	−168.334			−0.476866			−0.238433	−	0.971159i	$-0.576634\pi$
$353$	−168.334			−0.476866			−0.238433	+	0.971159i	$0.576634\pi$
$354$	−254.887			−0.720021
$355$		0			0
$356$		−	279.651i		−	0.785536i
$357$	−79.0575			−0.221450
$358$	−426.577			−1.19156
$359$		−	37.5719i		−	0.104657i	−0.998630	−	0.0523285i	$-0.983336\pi$
$359$		−	37.5719i		−	0.104657i	0.998630	−	0.0523285i	$-0.0166643\pi$
$360$		0			0
$361$	−146.243			−0.405105
$362$			351.499i			0.970992i
$363$	28.0260			0.0772065
$364$			35.2891i			0.0969482i
$365$		0			0
$366$		−	111.943i		−	0.305856i
$367$			427.036i			1.16359i	0.813337	+	0.581793i	$0.197649\pi$
$367$			427.036i			1.16359i	−0.813337	+	0.581793i	$0.802351\pi$
$368$	83.8733	+	37.8057i	0.227917	+	0.102733i
$369$	21.9857			0.0595818
$370$		0			0
$371$	121.891			0.328547
$372$	−182.418			−0.490371
$373$			369.980i			0.991904i	0.868350	+	0.495952i	$0.165181\pi$
$373$			369.980i			0.991904i	−0.868350	+	0.495952i	$0.834819\pi$
$374$	−301.563			−0.806317
$375$		0			0
$376$	−138.979			−0.369625
$377$	491.966			1.30495
$378$			37.1239i			0.0982114i
$379$		−	78.8009i		−	0.207918i	−0.994582	−	0.103959i	$-0.966849\pi$
$379$		−	78.8009i		−	0.207918i	0.994582	−	0.103959i	$-0.0331511\pi$
$380$		0			0
$381$	−195.124			−0.512136
$382$			207.015i			0.541925i
$383$			254.083i			0.663403i	0.943384	+	0.331702i	$0.107623\pi$
$383$			254.083i			0.663403i	−0.943384	+	0.331702i	$0.892377\pi$
$384$	−38.0815			−0.0991705
$385$		0			0
$386$	−170.622			−0.442027
$387$			84.8894i			0.219353i
$388$		−	39.7270i		−	0.102389i
$389$			322.363i			0.828698i	0.910118	+	0.414349i	$0.135991\pi$
$389$			322.363i			0.828698i	−0.910118	+	0.414349i	$0.864009\pi$
$390$		0			0
$391$	−189.866	+	421.226i	−0.485592	+	1.07730i
$392$	−134.726			−0.343690
$393$	−320.039			−0.814348
$394$	44.7602			0.113605
$395$		0			0
$396$		−	49.4581i		−	0.124894i
$397$	−715.832			−1.80310			−0.901552	−	0.432671i	$-0.857571\pi$
$397$	−715.832			−1.80310			−0.901552	+	0.432671i	$0.857571\pi$
$398$			52.9617i			0.133070i
$399$	88.6340			0.222140
$400$		0			0
$401$		−	441.435i		−	1.10083i	−0.834890	−	0.550417i	$-0.814469\pi$
$401$		−	441.435i		−	1.10083i	0.834890	−	0.550417i	$-0.185531\pi$
$402$		−	283.114i		−	0.704263i
$403$	−408.937			−1.01473
$404$	173.128			0.428534
$405$		0			0
$406$		−	53.9022i		−	0.132764i
$407$	−563.187			−1.38375
$408$		−	191.252i		−	0.468754i
$409$	−608.727			−1.48833			−0.744164	−	0.667996i	$-0.767152\pi$
$409$	−608.727			−1.48833			−0.744164	+	0.667996i	$0.767152\pi$
$410$		0			0
$411$		−	668.853i		−	1.62738i
$412$			288.235i			0.699600i
$413$			62.6048i			0.151586i
$414$	−69.0836	−	31.1393i	−0.166869	−	0.0752157i
$415$		0			0
$416$	−85.3695			−0.205215
$417$	−0.435823			−0.00104514
$418$	338.091			0.808831
$419$			287.454i			0.686047i	0.939327	+	0.343023i	$0.111451\pi$
$419$			287.454i			0.686047i	−0.939327	+	0.343023i	$0.888549\pi$
$420$		0			0
$421$			130.848i			0.310803i	0.987851	+	0.155402i	$0.0496672\pi$
$421$			130.848i			0.310803i	−0.987851	+	0.155402i	$0.950333\pi$
$422$	61.7406			0.146305
$423$	114.472			0.270620
$424$			294.871i			0.695452i
$425$		0			0
$426$	−262.824			−0.616958
$427$	−27.4952			−0.0643917
$428$		−	20.9089i		−	0.0488525i
$429$		−	539.197i		−	1.25687i
$430$		0			0
$431$			239.816i			0.556417i	0.960521	+	0.278209i	$0.0897406\pi$
$431$			239.816i			0.556417i	−0.960521	+	0.278209i	$0.910259\pi$
$432$	−89.8081			−0.207889
$433$		−	305.542i		−	0.705640i	−0.935691	−	0.352820i	$-0.885223\pi$
$433$		−	305.542i		−	0.705640i	0.935691	−	0.352820i	$-0.114777\pi$
$434$			44.8051i			0.103238i
$435$		0			0
$436$			138.244i			0.317074i
$437$	212.865	−	472.250i	0.487106	−	1.08066i
$438$	−41.7613			−0.0953455
$439$	−579.018			−1.31895			−0.659474	−	0.751727i	$-0.729221\pi$
$439$	−579.018			−1.31895			−0.659474	+	0.751727i	$0.729221\pi$
$440$		0			0
$441$	110.970			0.251632
$442$		−	428.740i		−	0.969999i
$443$	606.274			1.36856			0.684282	−	0.729217i	$-0.260116\pi$
$443$	606.274			1.36856			0.684282	+	0.729217i	$0.260116\pi$
$444$		−	357.174i		−	0.804446i
$445$		0			0
$446$	493.028			1.10544
$447$			214.999i			0.480982i
$448$			9.35348i			0.0208783i
$449$	−202.580			−0.451181			−0.225590	−	0.974222i	$-0.572431\pi$
$449$	−202.580			−0.451181			−0.225590	+	0.974222i	$0.572431\pi$
$450$		0			0
$451$		−	100.174i		−	0.222115i
$452$			274.529i			0.607364i
$453$	−118.708			−0.262049
$454$		−	248.609i		−	0.547598i
$455$		0			0
$456$			214.418i			0.470215i
$457$			373.760i			0.817857i	0.912567	+	0.408928i	$0.134097\pi$
$457$			373.760i			0.817857i	−0.912567	+	0.408928i	$0.865903\pi$
$458$			2.03856i			0.00445100i
$459$		−	451.031i		−	0.982639i
$460$		0			0
$461$	709.377			1.53878			0.769390	−	0.638780i	$-0.220561\pi$
$461$	709.377			1.53878			0.769390	+	0.638780i	$0.220561\pi$
$462$	−59.0770			−0.127872
$463$	−266.488			−0.575569			−0.287785	−	0.957695i	$-0.592919\pi$
$463$	−266.488			−0.575569			−0.287785	+	0.957695i	$0.592919\pi$
$464$	130.397			0.281028
$465$		0			0
$466$	−160.394			−0.344193
$467$			686.135i			1.46924i	0.678479	+	0.734620i	$0.262639\pi$
$467$			686.135i			1.46924i	−0.678479	+	0.734620i	$0.737361\pi$
$468$	70.3160			0.150248
$469$	−69.5378			−0.148268
$470$		0			0
$471$			973.219i			2.06628i
$472$	−151.450			−0.320869
$473$	386.784			0.817725
$474$			271.734i			0.573279i
$475$		0			0
$476$	−46.9747			−0.0986864
$477$		−	242.876i		−	0.509174i
$478$	−519.384			−1.08658
$479$			176.517i			0.368511i	0.982878	+	0.184256i	$0.0589874\pi$
$479$			176.517i			0.368511i	−0.982878	+	0.184256i	$0.941013\pi$
$480$		0			0
$481$		−	800.698i		−	1.66465i
$482$			311.643i			0.646563i
$483$	−37.1954	+	82.5194i	−0.0770091	+	0.170848i
$484$	16.6526			0.0344062
$485$		0			0
$486$	173.779			0.357571
$487$	−524.802			−1.07762			−0.538811	−	0.842427i	$-0.681126\pi$
$487$	−524.802			−1.07762			−0.538811	+	0.842427i	$0.681126\pi$
$488$		−	66.5149i		−	0.136301i
$489$	155.688			0.318380
$490$		0			0
$491$	−551.047			−1.12229			−0.561147	−	0.827716i	$-0.689640\pi$
$491$	−551.047			−1.12229			−0.561147	+	0.827716i	$0.689640\pi$
$492$	63.5304			0.129127
$493$			654.876i			1.32835i
$494$			480.674i			0.973024i
$495$		0			0
$496$	−108.390			−0.218528
$497$			64.5542i			0.129888i
$498$			262.661i			0.527433i
$499$	−736.739			−1.47643			−0.738216	−	0.674565i	$-0.764331\pi$
$499$	−736.739			−1.47643			−0.738216	+	0.674565i	$0.764331\pi$
$500$		0			0
$501$	305.876			0.610532
$502$		−	622.551i		−	1.24014i
$503$			699.308i			1.39027i	0.718877	+	0.695137i	$0.244656\pi$
$503$			699.308i			1.39027i	−0.718877	+	0.695137i	$0.755344\pi$
$504$		−	7.70415i		−	0.0152860i
$505$		0			0
$506$	−141.881	+	314.768i	−0.280397	+	0.622070i
$507$	197.745			0.390029
$508$	−115.939			−0.228227
$509$	−316.428			−0.621666			−0.310833	−	0.950464i	$-0.600608\pi$
$509$	−316.428			−0.621666			−0.310833	+	0.950464i	$0.600608\pi$
$510$		0			0
$511$			10.2573i			0.0200730i
$512$	−22.6274			−0.0441942
$513$			505.666i			0.985703i
$514$	695.112			1.35236
$515$		0			0
$516$			245.299i			0.475386i
$517$		−	521.573i		−	1.00885i
$518$	−87.7283			−0.169360
$519$	305.593			0.588811
$520$		0			0
$521$		−	798.875i		−	1.53335i	−0.642035	−	0.766675i	$-0.721910\pi$
$521$		−	798.875i		−	1.53335i	0.642035	−	0.766675i	$-0.278090\pi$
$522$	−107.404			−0.205754
$523$		−	819.091i		−	1.56614i	−0.621934	−	0.783070i	$-0.713653\pi$
$523$		−	819.091i		−	1.56614i	0.621934	−	0.783070i	$-0.286347\pi$
$524$	−190.162			−0.362905
$525$		0			0
$526$			378.773i			0.720101i
$527$		−	544.353i		−	1.03293i
$528$		−	142.916i		−	0.270674i
$529$	350.341	+	396.361i	0.662271	+	0.749265i
$530$		0			0
$531$	124.744			0.234924
$532$	52.6649			0.0989942
$533$	142.420			0.267204
$534$			665.595i			1.24643i
$535$		0			0
$536$		−	168.222i		−	0.313847i
$537$	1015.29			1.89068
$538$	−135.338			−0.251558
$539$		−	505.614i		−	0.938060i
$540$		0			0
$541$	289.616			0.535335			0.267668	−	0.963511i	$-0.413747\pi$
$541$	289.616			0.535335			0.267668	+	0.963511i	$0.413747\pi$
$542$	639.585			1.18005
$543$		−	836.600i		−	1.54070i
$544$		−	113.639i		−	0.208895i
$545$		0			0
$546$		−	83.9914i		−	0.153830i
$547$	−996.117			−1.82106			−0.910528	−	0.413448i	$-0.864324\pi$
$547$	−996.117			−1.82106			−0.910528	+	0.413448i	$0.864324\pi$
$548$		−	397.422i		−	0.725223i
$549$			54.7861i			0.0997926i
$550$		0			0
$551$		−	734.202i		−	1.33249i
$552$	−199.626	−	89.9811i	−0.361642	−	0.163009i
$553$	66.7427			0.120692
$554$	−123.713			−0.223309
$555$		0			0
$556$	−0.258959			−0.000465754
$557$			937.756i			1.68358i	0.539802	+	0.841792i	$0.318499\pi$
$557$			937.756i			1.68358i	−0.539802	+	0.841792i	$0.681501\pi$
$558$	89.2772			0.159995
$559$			549.901i			0.983723i
$560$		0			0
$561$	717.747			1.27941
$562$		−	328.320i		−	0.584200i
$563$		−	785.252i		−	1.39476i	−0.716700	−	0.697382i	$-0.754348\pi$
$563$		−	785.252i		−	1.39476i	0.716700	−	0.697382i	$-0.245652\pi$
$564$	330.783			0.586494
$565$		0			0
$566$		−	338.516i		−	0.598085i
$567$		−	112.873i		−	0.199070i
$568$	−156.166			−0.274940
$569$		−	403.851i		−	0.709755i	−0.934913	−	0.354877i	$-0.884523\pi$
$569$		−	403.851i		−	0.709755i	0.934913	−	0.354877i	$-0.115477\pi$
$570$		0			0
$571$			335.474i			0.587519i	0.955879	+	0.293760i	$0.0949065\pi$
$571$			335.474i			0.587519i	−0.955879	+	0.293760i	$0.905093\pi$
$572$		−	320.383i		−	0.560110i
$573$		−	492.715i		−	0.859887i
$574$		−	15.6042i		−	0.0271850i
$575$		0			0
$576$	18.6375			0.0323567
$577$	152.703			0.264649			0.132325	−	0.991206i	$-0.457756\pi$
$577$	152.703			0.264649			0.132325	+	0.991206i	$0.457756\pi$
$578$	162.004			0.280284
$579$	406.097			0.701376
$580$		0			0
$581$	64.5143			0.111040
$582$			94.5538i			0.162464i
$583$	−1106.62			−1.89815
$584$	−24.8139			−0.0424896
$585$		0			0
$586$			822.831i			1.40415i
$587$	−129.262			−0.220207			−0.110104	−	0.993920i	$-0.535118\pi$
$587$	−129.262			−0.220207			−0.110104	+	0.993920i	$0.535118\pi$
$588$	320.662			0.545343
$589$			610.291i			1.03615i
$590$		0			0
$591$	−106.533			−0.180260
$592$		−	212.227i		−	0.358492i
$593$	879.853			1.48373			0.741866	−	0.670548i	$-0.233941\pi$
$593$	879.853			1.48373			0.741866	+	0.670548i	$0.233941\pi$
$594$		−	337.040i		−	0.567408i
$595$		0			0
$596$			127.749i			0.214344i
$597$		−	126.054i		−	0.211145i
$598$	−447.514	−	201.716i	−0.748351	−	0.337317i
$599$	−709.708			−1.18482			−0.592411	−	0.805636i	$-0.701824\pi$
$599$	−709.708			−1.18482			−0.592411	+	0.805636i	$0.701824\pi$
$600$		0			0
$601$	238.861			0.397439			0.198719	−	0.980056i	$-0.436322\pi$
$601$	238.861			0.397439			0.198719	+	0.980056i	$0.436322\pi$
$602$	60.2498			0.100083
$603$			138.559i			0.229782i
$604$	−70.5346			−0.116779
$605$		0			0
$606$	−412.060			−0.679967
$607$	1082.53			1.78341			0.891703	−	0.452621i	$-0.149511\pi$
$607$	1082.53			1.78341			0.891703	+	0.452621i	$0.149511\pi$
$608$			127.404i			0.209546i
$609$			128.292i			0.210660i
$610$		0			0
$611$	741.535			1.21364
$612$			93.6004i			0.152942i
$613$			54.0902i			0.0882384i	0.999026	+	0.0441192i	$0.0140481\pi$
$613$			54.0902i			0.0882384i	−0.999026	+	0.0441192i	$0.985952\pi$
$614$	155.753			0.253669
$615$		0			0
$616$	−35.1026			−0.0569848
$617$		−	454.342i		−	0.736373i	−0.929752	−	0.368186i	$-0.879979\pi$
$617$		−	454.342i		−	0.736373i	0.929752	−	0.368186i	$-0.120021\pi$
$618$		−	686.027i		−	1.11008i
$619$			153.676i			0.248264i	0.992266	+	0.124132i	$0.0396147\pi$
$619$			153.676i			0.248264i	−0.992266	+	0.124132i	$0.960385\pi$
$620$		0			0
$621$	−470.781	−	212.204i	−0.758102	−	0.341713i
$622$	421.577			0.677776
$623$	163.482			0.262411
$624$	203.187			0.325621
$625$		0			0
$626$			154.820i			0.247316i
$627$	−804.689			−1.28340
$628$			578.271i			0.920814i
$629$	1065.84			1.69450
$630$		0			0
$631$			1241.15i			1.96696i	0.181027	+	0.983478i	$0.442058\pi$
$631$			1241.15i			1.96696i	−0.181027	+	0.983478i	$0.557942\pi$
$632$			161.460i			0.255475i
$633$	−146.948			−0.232146
$634$	670.950			1.05828
$635$		0			0
$636$		−	701.821i		−	1.10349i
$637$	718.846			1.12849
$638$			489.366i			0.767032i
$639$	128.629			0.201297
$640$		0			0
$641$		−	545.978i		−	0.851759i	−0.904780	−	0.425880i	$-0.859965\pi$
$641$		−	545.978i		−	0.851759i	0.904780	−	0.425880i	$-0.140035\pi$
$642$			49.7651i			0.0775157i
$643$			539.118i			0.838441i	0.907884	+	0.419221i	$0.137697\pi$
$643$			539.118i			0.838441i	−0.907884	+	0.419221i	$0.862303\pi$
$644$	−22.1009	+	49.0317i	−0.0343182	+	0.0761362i
$645$		0			0
$646$	−639.844			−0.990470
$647$	−652.715			−1.00883			−0.504417	−	0.863460i	$-0.668292\pi$
$647$	−652.715			−1.00883			−0.504417	+	0.863460i	$0.668292\pi$
$648$	273.056			0.421382
$649$		−	568.376i		−	0.875772i
$650$		0			0
$651$		−	106.640i		−	0.163810i
$652$	92.5071			0.141882
$653$	−374.815			−0.573989			−0.286995	−	0.957932i	$-0.592656\pi$
$653$	−374.815			−0.573989			−0.286995	+	0.957932i	$0.592656\pi$
$654$		−	329.034i		−	0.503110i
$655$		0			0
$656$	37.7488			0.0575439
$657$	20.4384			0.0311087
$658$		−	81.2460i		−	0.123474i
$659$			440.090i			0.667815i	0.942606	+	0.333907i	$0.108367\pi$
$659$			440.090i			0.667815i	−0.942606	+	0.333907i	$0.891633\pi$
$660$		0			0
$661$			72.6725i			0.109943i	0.998488	+	0.0549716i	$0.0175068\pi$
$661$			72.6725i			0.109943i	−0.998488	+	0.0549716i	$0.982493\pi$
$662$	−361.144			−0.545535
$663$			1020.44i			1.53913i
$664$			156.069i			0.235044i
$665$		0			0
$666$			174.805i			0.262469i
$667$	683.552	+	308.110i	1.02482	+	0.461933i
$668$	181.747			0.272076
$669$	−1173.45			−1.75404
$670$		0			0
$671$	249.623			0.372017
$672$		−	22.2622i		−	0.0331282i
$673$	1052.88			1.56445			0.782227	−	0.622993i	$-0.214084\pi$
$673$	1052.88			1.56445			0.782227	+	0.622993i	$0.214084\pi$
$674$		−	648.398i		−	0.962014i
$675$		0			0
$676$	117.497			0.173812
$677$		−	393.587i		−	0.581369i	−0.956819	−	0.290684i	$-0.906117\pi$
$677$		−	393.587i		−	0.581369i	0.956819	−	0.290684i	$-0.0938830\pi$
$678$		−	653.404i		−	0.963722i
$679$	23.2241			0.0342034
$680$		0			0
$681$			591.714i			0.868889i
$682$		−	406.776i		−	0.596446i
$683$	645.240			0.944714			0.472357	−	0.881407i	$-0.343403\pi$
$683$	645.240			0.944714			0.472357	+	0.881407i	$0.343403\pi$
$684$		−	104.938i		−	0.153419i
$685$		0			0
$686$		−	159.781i		−	0.232916i
$687$		−	4.85195i		−	0.00706252i
$688$			145.753i			0.211850i
$689$		−	1573.31i		−	2.28347i
$690$		0			0
$691$	548.216			0.793366			0.396683	−	0.917956i	$-0.370161\pi$
$691$	548.216			0.793366			0.396683	+	0.917956i	$0.370161\pi$
$692$	181.579			0.262397
$693$	28.9129			0.0417213
$694$	722.205			1.04064
$695$		0			0
$696$	−310.357			−0.445915
$697$			189.581i			0.271995i
$698$	837.030			1.19918
$699$	381.753			0.546141
$700$		0			0
$701$			92.2064i			0.131536i	0.997835	+	0.0657678i	$0.0209496\pi$
$701$			92.2064i			0.131536i	−0.997835	+	0.0657678i	$0.979050\pi$
$702$	479.179			0.682592
$703$	−1194.95			−1.69978
$704$		−	84.9183i		−	0.120623i
$705$		0			0
$706$	238.060			0.337195
$707$			101.209i			0.143153i
$708$	360.465			0.509132
$709$			922.612i			1.30129i	0.759384	+	0.650643i	$0.225501\pi$
$709$			922.612i			1.30129i	−0.759384	+	0.650643i	$0.774499\pi$
$710$		0			0
$711$		−	132.989i		−	0.187045i
$712$			395.486i			0.555458i
$713$	−568.189	−	256.110i	−0.796899	−	0.359201i
$714$	111.804			0.156589
$715$		0			0
$716$	603.271			0.842557
$717$	1236.18			1.72410
$718$			53.1347i			0.0740037i
$719$	606.887			0.844071			0.422035	−	0.906579i	$-0.361316\pi$
$719$	606.887			0.844071			0.422035	+	0.906579i	$0.361316\pi$
$720$		0			0
$721$	−168.500			−0.233704
$722$	206.819			0.286452
$723$		−	741.740i		−	1.02592i
$724$		−	497.095i		−	0.686595i
$725$		0			0
$726$	−39.6347			−0.0545932
$727$		−	787.544i		−	1.08328i	−0.840611	−	0.541640i	$-0.817804\pi$
$727$		−	787.544i		−	1.08328i	0.840611	−	0.541640i	$-0.182196\pi$
$728$		−	49.9064i		−	0.0685527i
$729$	455.246			0.624481
$730$		0			0
$731$	−731.995			−1.00136
$732$			158.312i			0.216273i
$733$			415.085i			0.566282i	0.959078	+	0.283141i	$0.0913765\pi$
$733$			415.085i			0.566282i	−0.959078	+	0.283141i	$0.908624\pi$
$734$		−	603.921i		−	0.822780i
$735$		0			0
$736$	−118.615	−	53.4653i	−0.161161	−	0.0726431i
$737$	631.319			0.856606
$738$	−31.0924			−0.0421307
$739$	639.964			0.865987			0.432993	−	0.901397i	$-0.357457\pi$
$739$	639.964			0.865987			0.432993	+	0.901397i	$0.357457\pi$
$740$		0			0
$741$		−	1144.05i		−	1.54393i
$742$	−172.380			−0.232318
$743$		−	743.739i		−	1.00099i	−0.865738	−	0.500497i	$-0.833151\pi$
$743$		−	743.739i		−	1.00099i	0.865738	−	0.500497i	$-0.166849\pi$
$744$	257.978			0.346745
$745$		0			0
$746$		−	523.231i		−	0.701382i
$747$		−	128.549i		−	0.172087i
$748$	426.474			0.570152
$749$	12.2232			0.0163193
$750$		0			0
$751$			517.047i			0.688478i	0.938882	+	0.344239i	$0.111863\pi$
$751$			517.047i			0.688478i	−0.938882	+	0.344239i	$0.888137\pi$
$752$	196.546			0.261364
$753$			1481.73i			1.96777i
$754$	−695.746			−0.922740
$755$		0			0
$756$		−	52.5011i		−	0.0694460i
$757$		−	911.823i		−	1.20452i	−0.798299	−	0.602261i	$-0.794267\pi$
$757$		−	911.823i		−	1.20452i	0.798299	−	0.602261i	$-0.205733\pi$
$758$			111.441i			0.147020i
$759$	337.689	−	749.176i	0.444914	−	0.987057i
$760$		0			0
$761$	954.073			1.25371			0.626855	−	0.779136i	$-0.284342\pi$
$761$	954.073			1.25371			0.626855	+	0.779136i	$0.284342\pi$
$762$	275.947			0.362135
$763$	−80.8166			−0.105920
$764$		−	292.764i		−	0.383199i
$765$		0			0
$766$		−	359.328i		−	0.469097i
$767$	808.076			1.05355
$768$	53.8553			0.0701242
$769$			276.277i			0.359268i	0.983734	+	0.179634i	$0.0574913\pi$
$769$			276.277i			0.359268i	−0.983734	+	0.179634i	$0.942509\pi$
$770$		0			0
$771$	−1654.43			−2.14583
$772$	241.296			0.312560
$773$		−	40.8440i		−	0.0528383i	−0.999651	−	0.0264192i	$-0.991590\pi$
$773$		−	40.8440i		−	0.0528383i	0.999651	−	0.0264192i	$-0.00841046\pi$
$774$		−	120.052i		−	0.155106i
$775$		0			0
$776$			56.1824i			0.0724000i
$777$	208.801			0.268728
$778$		−	455.891i		−	0.585978i
$779$		−	212.545i		−	0.272843i
$780$		0			0
$781$		−	586.074i		−	0.750415i
$782$	268.512	−	595.703i	0.343365	−	0.761768i
$783$	−731.919			−0.934763
$784$	190.532			0.243026
$785$		0			0
$786$	452.603			0.575831
$787$		−	1364.69i		−	1.73404i	−0.498274	−	0.867019i	$-0.666033\pi$
$787$		−	1364.69i		−	1.73404i	0.498274	−	0.867019i	$-0.333967\pi$
$788$	−63.3005			−0.0803305
$789$		−	901.515i		−	1.14261i
$790$		0			0
$791$	−160.487			−0.202892
$792$			69.9444i			0.0883136i
$793$			354.897i			0.447537i
$794$	1012.34			1.27499
$795$		0			0
$796$		−	74.8991i		−	0.0940944i
$797$			20.2192i			0.0253692i	0.999920	+	0.0126846i	$0.00403774\pi$
$797$			20.2192i			0.0253692i	−0.999920	+	0.0126846i	$0.995962\pi$
$798$	−125.347			−0.157077
$799$			987.086i			1.23540i
$800$		0			0
$801$		−	325.749i		−	0.406678i
$802$			624.283i			0.778407i
$803$		−	93.1240i		−	0.115970i
$804$			400.384i			0.497989i
$805$		0			0
$806$	578.325			0.717525
$807$	322.117			0.399154
$808$	−244.840			−0.303019
$809$	−1032.11			−1.27579			−0.637894	−	0.770124i	$-0.720194\pi$
$809$	−1032.11			−1.27579			−0.637894	+	0.770124i	$0.720194\pi$
$810$		0			0
$811$	−70.2781			−0.0866561			−0.0433281	−	0.999061i	$-0.513796\pi$
$811$	−70.2781			−0.0866561			−0.0433281	+	0.999061i	$0.513796\pi$
$812$			76.2292i			0.0938783i
$813$	−1522.27			−1.87241
$814$	796.467			0.978460
$815$		0			0
$816$			270.470i			0.331459i
$817$	820.663			1.00448
$818$	860.869			1.05241
$819$			41.1062i			0.0501907i
$820$		0			0
$821$	84.7400			0.103216			0.0516078	−	0.998667i	$-0.483565\pi$
$821$	84.7400			0.103216			0.0516078	+	0.998667i	$0.483565\pi$
$822$			945.901i			1.15073i
$823$	−46.0292			−0.0559286			−0.0279643	−	0.999609i	$-0.508902\pi$
$823$	−46.0292			−0.0559286			−0.0279643	+	0.999609i	$0.508902\pi$
$824$		−	407.626i		−	0.494692i
$825$		0			0
$826$		−	88.5366i		−	0.107187i
$827$			1283.77i			1.55232i	0.630536	+	0.776160i	$0.282835\pi$
$827$			1283.77i			1.55232i	−0.630536	+	0.776160i	$0.717165\pi$
$828$	97.6990	+	44.0376i	0.117994	+	0.0531855i
$829$	−483.453			−0.583177			−0.291588	−	0.956544i	$-0.594184\pi$
$829$	−483.453			−0.583177			−0.291588	+	0.956544i	$0.594184\pi$
$830$		0			0
$831$	294.449			0.354330
$832$	120.731			0.145109
$833$			956.883i			1.14872i
$834$	0.616347			0.000739025
$835$		0			0
$836$	−478.134			−0.571930
$837$	608.394			0.726874
$838$		−	406.521i		−	0.485108i
$839$			1060.74i			1.26429i	0.774852	+	0.632143i	$0.217824\pi$
$839$			1060.74i			1.26429i	−0.774852	+	0.632143i	$0.782176\pi$
$840$		0			0
$841$	221.712			0.263629
$842$		−	185.047i		−	0.219771i
$843$			781.432i			0.926966i
$844$	−87.3144			−0.103453
$845$		0			0
$846$	−161.888			−0.191357
$847$			9.73498i			0.0114935i
$848$		−	417.011i		−	0.491759i
$849$			805.700i			0.948999i
$850$		0			0
$851$	501.463	−	1112.51i	0.589263	−	1.30730i
$852$	371.689			0.436255
$853$	−1653.13			−1.93802			−0.969010	−	0.247023i	$-0.920548\pi$
$853$	−1653.13			−1.93802			−0.969010	+	0.247023i	$0.920548\pi$
$854$	38.8841			0.0455318
$855$		0			0
$856$			29.5696i			0.0345439i
$857$	−1453.42			−1.69593			−0.847967	−	0.530048i	$-0.822174\pi$
$857$	−1453.42			−1.69593			−0.847967	+	0.530048i	$0.822174\pi$
$858$			762.540i			0.888742i
$859$	936.399			1.09010			0.545052	−	0.838402i	$-0.316510\pi$
$859$	936.399			1.09010			0.545052	+	0.838402i	$0.316510\pi$
$860$		0			0
$861$			37.1394i			0.0431352i
$862$		−	339.151i		−	0.393446i
$863$	−961.830			−1.11452			−0.557259	−	0.830339i	$-0.688147\pi$
$863$	−961.830			−1.11452			−0.557259	+	0.830339i	$0.688147\pi$
$864$	127.008			0.147000
$865$		0			0
$866$			432.102i			0.498963i
$867$	−385.585			−0.444735
$868$		−	63.3640i		−	0.0730000i
$869$	−605.943			−0.697287
$870$		0			0
$871$			897.563i			1.03050i
$872$		−	195.507i		−	0.224205i
$873$		−	46.2756i		−	0.0530075i
$874$	−301.037	+	667.862i	−0.344436	+	0.764144i
$875$		0			0
$876$	59.0594			0.0674194
$877$	1244.55			1.41910			0.709549	−	0.704657i	$-0.248899\pi$
$877$	1244.55			1.41910			0.709549	+	0.704657i	$0.248899\pi$
$878$	818.855			0.932637
$879$		−	1958.41i		−	2.22800i
$880$		0			0
$881$			961.719i			1.09162i	0.837908	+	0.545811i	$0.183778\pi$
$881$			961.719i			1.09162i	−0.837908	+	0.545811i	$0.816222\pi$
$882$	−156.935			−0.177931
$883$	−42.4945			−0.0481251			−0.0240626	−	0.999710i	$-0.507660\pi$
$883$	−42.4945			−0.0481251			−0.0240626	+	0.999710i	$0.507660\pi$
$884$			606.330i			0.685893i
$885$		0			0
$886$	−857.401			−0.967722
$887$	551.962			0.622279			0.311140	−	0.950364i	$-0.399289\pi$
$887$	551.962			0.622279			0.311140	+	0.950364i	$0.399289\pi$
$888$			505.121i			0.568830i
$889$		−	67.7774i		−	0.0762400i
$890$		0			0
$891$			1024.75i			1.15011i
$892$	−697.246			−0.781666
$893$		−	1106.65i		−	1.23925i
$894$		−	304.054i		−	0.340106i
$895$		0			0
$896$		−	13.2278i		−	0.0147632i
$897$	1065.12	+	480.102i	1.18743	+	0.535231i
$898$	286.492			0.319033
$899$	−883.359			−0.982601
$900$		0			0
$901$	2094.30			2.32442
$902$			141.667i			0.157059i
$903$	−143.400			−0.158804
$904$		−	388.242i		−	0.429472i
$905$		0			0
$906$	167.879			0.185297
$907$			237.524i			0.261878i	0.991390	+	0.130939i	$0.0417993\pi$
$907$			237.524i			0.261878i	−0.991390	+	0.130939i	$0.958201\pi$
$908$			351.587i			0.387210i
$909$	201.666			0.221855
$910$		0			0
$911$			402.885i			0.442245i	0.975246	+	0.221122i	$0.0709720\pi$
$911$			402.885i			0.442245i	−0.975246	+	0.221122i	$0.929028\pi$
$912$		−	303.233i		−	0.332493i
$913$	−585.712			−0.641524
$914$		−	528.577i		−	0.578312i
$915$		0			0
$916$		−	2.88295i		−	0.00314733i
$917$		−	111.167i		−	0.121229i
$918$			637.854i			0.694830i
$919$			1338.53i			1.45650i	0.685310	+	0.728251i	$0.259667\pi$
$919$			1338.53i			1.45650i	−0.685310	+	0.728251i	$0.740333\pi$
$920$		0			0
$921$	−370.706			−0.402503
$922$	−1003.21			−1.08808
$923$	833.238			0.902750
$924$	83.5475			0.0904194
$925$		0			0
$926$	376.872			0.406989
$927$			335.748i			0.362188i
$928$	−184.409			−0.198717
$929$	621.771			0.669291			0.334646	−	0.942344i	$-0.391383\pi$
$929$	621.771			0.669291			0.334646	+	0.942344i	$0.391383\pi$
$930$		0			0
$931$		−	1072.79i		−	1.15230i
$932$	226.831			0.243381
$933$	−1003.39			−1.07545
$934$		−	970.341i		−	1.03891i
$935$		0			0
$936$	−99.4419			−0.106241
$937$		−	915.580i		−	0.977140i	−0.872525	−	0.488570i	$-0.837519\pi$
$937$		−	915.580i		−	0.977140i	0.872525	−	0.488570i	$-0.162481\pi$
$938$	98.3412			0.104841
$939$		−	368.486i		−	0.392424i
$940$		0			0
$941$			834.255i			0.886563i	0.896383	+	0.443281i	$0.146186\pi$
$941$			834.255i			0.886563i	−0.896383	+	0.443281i	$0.853814\pi$
$942$		−	1376.34i		−	1.46108i
$943$	197.882	+	89.1950i	0.209843	+	0.0945864i
$944$	214.183			0.226889
$945$		0			0
$946$	−546.995			−0.578219
$947$	−918.683			−0.970099			−0.485049	−	0.874487i	$-0.661198\pi$
$947$	−918.683			−0.970099			−0.485049	+	0.874487i	$0.661198\pi$
$948$		−	384.290i		−	0.405369i
$949$	132.397			0.139512
$950$		0			0
$951$	−1596.92			−1.67921
$952$	66.4323			0.0697818
$953$		−	789.341i		−	0.828270i	−0.910215	−	0.414135i	$-0.864084\pi$
$953$		−	789.341i		−	0.828270i	0.910215	−	0.414135i	$-0.135916\pi$
$954$			343.478i			0.360040i
$955$		0			0
$956$	734.519			0.768326
$957$		−	1164.74i		−	1.21707i
$958$		−	249.632i		−	0.260577i
$959$	232.330			0.242263
$960$		0			0
$961$	−226.725			−0.235927
$962$			1132.36i			1.17709i
$963$		−	24.3555i		−	0.0252913i
$964$		−	440.730i		−	0.457189i
$965$		0			0
$966$	52.6023	−	116.700i	0.0544537	−	0.120807i
$967$	−875.476			−0.905353			−0.452677	−	0.891675i	$-0.649531\pi$
$967$	−875.476			−0.905353			−0.452677	+	0.891675i	$0.649531\pi$
$968$	−23.5503			−0.0243288
$969$	1522.89			1.57161
$970$		0			0
$971$		−	1232.49i		−	1.26930i	−0.772801	−	0.634648i	$-0.781145\pi$
$971$		−	1232.49i		−	1.26930i	0.772801	−	0.634648i	$-0.218855\pi$
$972$	−245.761			−0.252841
$973$		−	0.151386i		−	0.000155587i
$974$	742.182			0.761994
$975$		0			0
$976$			94.0663i			0.0963794i
$977$			879.183i			0.899880i	0.893059	+	0.449940i	$0.148555\pi$
$977$			879.183i			0.899880i	−0.893059	+	0.449940i	$0.851445\pi$
$978$	−220.176			−0.225128
$979$	−1484.22			−1.51606
$980$		0			0
$981$			161.033i			0.164151i
$982$	779.298			0.793582
$983$			247.090i			0.251363i	0.992071	+	0.125682i	$0.0401118\pi$
$983$			247.090i			0.251363i	−0.992071	+	0.125682i	$0.959888\pi$
$984$	−89.8456			−0.0913065
$985$		0			0
$986$		−	926.134i		−	0.939284i
$987$			193.373i			0.195920i
$988$		−	679.776i		−	0.688032i
$989$	−344.393	+	764.048i	−0.348223	+	0.772546i
$990$		0			0
$991$	−1750.79			−1.76669			−0.883347	−	0.468721i	$-0.844715\pi$
$991$	−1750.79			−1.76669			−0.883347	+	0.468721i	$0.844715\pi$
$992$	153.287			0.154523
$993$	859.556			0.865615
$994$		−	91.2935i		−	0.0918445i
$995$		0			0
$996$		−	371.459i		−	0.372951i
$997$	456.156			0.457529			0.228765	−	0.973482i	$-0.426531\pi$
$997$	456.156			0.457529			0.228765	+	0.973482i	$0.426531\pi$
$998$	1041.91			1.04399
$999$			1191.23i			1.19243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.d.b.551.6		16
5.2	odd	4		1150.3.c.c.1149.17		32
5.3	odd	4		1150.3.c.c.1149.16		32
5.4	even	2		230.3.d.a.91.11	✓	16
15.14	odd	2		2070.3.c.a.91.6		16
20.19	odd	2		1840.3.k.d.321.11		16
23.22	odd	2	inner	1150.3.d.b.551.5		16
115.22	even	4		1150.3.c.c.1149.15		32
115.68	even	4		1150.3.c.c.1149.18		32
115.114	odd	2		230.3.d.a.91.12	yes	16
345.344	even	2		2070.3.c.a.91.3		16
460.459	even	2		1840.3.k.d.321.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.11	✓	16	5.4	even	2
230.3.d.a.91.12	yes	16	115.114	odd	2
1150.3.c.c.1149.15		32	115.22	even	4
1150.3.c.c.1149.16		32	5.3	odd	4
1150.3.c.c.1149.17		32	5.2	odd	4
1150.3.c.c.1149.18		32	115.68	even	4
1150.3.d.b.551.5		16	23.22	odd	2	inner
1150.3.d.b.551.6		16	1.1	even	1	trivial
1840.3.k.d.321.11		16	20.19	odd	2
1840.3.k.d.321.12		16	460.459	even	2
2070.3.c.a.91.3		16	345.344	even	2
2070.3.c.a.91.6		16	15.14	odd	2

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +3.36596 q^{3} +2.00000 q^{4} -4.76019 q^{6} +1.16919i q^{7} -2.82843 q^{8} +2.32968 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +3.36596 q^{3} +2.00000 q^{4} -4.76019 q^{6} +1.16919i q^{7} -2.82843 q^{8} +2.32968 q^{9} -10.6148i q^{11} +6.73192 q^{12} +15.0913 q^{13} -1.65348i q^{14} +4.00000 q^{16} +20.0887i q^{17} -3.29467 q^{18} -22.5221i q^{19} +3.93543i q^{21} +15.0116i q^{22} +(20.9683 + 9.45142i) q^{23} -9.52037 q^{24} -21.3424 q^{26} -22.4520 q^{27} +2.33837i q^{28} +32.5993 q^{29} -27.0975 q^{31} -5.65685 q^{32} -35.7289i q^{33} -28.4097i q^{34} +4.65936 q^{36} -53.0568i q^{37} +31.8510i q^{38} +50.7968 q^{39} +9.43720 q^{41} -5.56554i q^{42} +36.4382i q^{43} -21.2296i q^{44} +(-29.6537 - 13.3663i) q^{46} +49.1365 q^{47} +13.4638 q^{48} +47.6330 q^{49} +67.6176i q^{51} +30.1827 q^{52} -104.253i q^{53} +31.7520 q^{54} -3.30696i q^{56} -75.8083i q^{57} -46.1023 q^{58} +53.5457 q^{59} +23.5166i q^{61} +38.3217 q^{62} +2.72383i q^{63} +8.00000 q^{64} +50.5284i q^{66} +59.4754i q^{67} +40.1773i q^{68} +(70.5785 + 31.8131i) q^{69} +55.2130 q^{71} -6.58933 q^{72} +8.77305 q^{73} +75.0337i q^{74} -45.0441i q^{76} +12.4107 q^{77} -71.8376 q^{78} -57.0848i q^{79} -96.5397 q^{81} -13.3462 q^{82} -55.1788i q^{83} +7.87086i q^{84} -51.5314i q^{86} +109.728 q^{87} +30.0232i q^{88} -139.825i q^{89} +17.6446i q^{91} +(41.9366 + 18.9028i) q^{92} -91.2091 q^{93} -69.4894 q^{94} -19.0407 q^{96} -19.8635i q^{97} -67.3632 q^{98} -24.7291i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} - 24 q^{13} + 64 q^{16} + 32 q^{18} - 4 q^{23} - 16 q^{24} + 96 q^{26} + 96 q^{27} - 108 q^{29} - 116 q^{31} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} + 128 q^{47} - 28 q^{49} - 48 q^{52} + 224 q^{54} - 160 q^{58} + 204 q^{59} - 64 q^{62} + 128 q^{64} - 268 q^{69} + 236 q^{71} + 64 q^{72} + 112 q^{73} + 936 q^{77} + 432 q^{78} - 136 q^{81} + 64 q^{82} + 152 q^{87} - 8 q^{92} - 856 q^{93} - 216 q^{94} - 32 q^{96} - 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 - 24 * q^13 + 64 * q^16 + 32 * q^18 - 4 * q^23 - 16 * q^24 + 96 * q^26 + 96 * q^27 - 108 * q^29 - 116 * q^31 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 + 128 * q^47 - 28 * q^49 - 48 * q^52 + 224 * q^54 - 160 * q^58 + 204 * q^59 - 64 * q^62 + 128 * q^64 - 268 * q^69 + 236 * q^71 + 64 * q^72 + 112 * q^73 + 936 * q^77 + 432 * q^78 - 136 * q^81 + 64 * q^82 + 152 * q^87 - 8 * q^92 - 856 * q^93 - 216 * q^94 - 32 * q^96 - 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more