LMFDB - Embedded newform 2100.3.bd.e.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,3,Mod(901,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("2100.901");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2100.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$57.2208555157$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2100.901
Dual form			2100.3.bd.e.1501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(6.50000 - 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-6.00000 - 10.3923i) q^{11} +1.73205i q^{13} +(-13.5000 - 7.79423i) q^{19} +(7.50000 - 9.52628i) q^{21} +(12.0000 - 20.7846i) q^{23} -5.19615i q^{27} -6.00000 q^{29} +(-18.0000 + 10.3923i) q^{31} +(-18.0000 - 10.3923i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(1.50000 + 2.59808i) q^{39} -41.5692i q^{41} -50.0000 q^{43} +(-27.0000 - 15.5885i) q^{47} +(35.5000 - 33.7750i) q^{49} +(42.0000 + 72.7461i) q^{53} -27.0000 q^{57} +(27.0000 - 15.5885i) q^{59} +(-52.5000 - 30.3109i) q^{61} +(3.00000 - 20.7846i) q^{63} +(-56.5000 - 97.8609i) q^{67} -41.5692i q^{69} -30.0000 q^{71} +(-10.5000 + 6.06218i) q^{73} +(-66.0000 - 51.9615i) q^{77} +(-47.5000 + 82.2724i) q^{79} +(-4.50000 - 7.79423i) q^{81} +10.3923i q^{83} +(-9.00000 + 5.19615i) q^{87} +(153.000 + 88.3346i) q^{89} +(4.50000 + 11.2583i) q^{91} +(-18.0000 + 31.1769i) q^{93} -112.583i q^{97} -36.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 13 q^{7} + 3 q^{9} - 12 q^{11} - 27 q^{19} + 15 q^{21} + 24 q^{23} - 12 q^{29} - 36 q^{31} - 36 q^{33} - 7 q^{37} + 3 q^{39} - 100 q^{43} - 54 q^{47} + 71 q^{49} + 84 q^{53} - 54 q^{57}+ \cdots - 72 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 13 * q^7 + 3 * q^9 - 12 * q^11 - 27 * q^19 + 15 * q^21 + 24 * q^23 - 12 * q^29 - 36 * q^31 - 36 * q^33 - 7 * q^37 + 3 * q^39 - 100 * q^43 - 54 * q^47 + 71 * q^49 + 84 * q^53 - 54 * q^57 + 54 * q^59 - 105 * q^61 + 6 * q^63 - 113 * q^67 - 60 * q^71 - 21 * q^73 - 132 * q^77 - 95 * q^79 - 9 * q^81 - 18 * q^87 + 306 * q^89 + 9 * q^91 - 36 * q^93 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−6.00000	−	10.3923i	−0.545455	−	0.944755i	−0.998578	−	0.0533073i	$-0.983024\pi$
$11$	−6.00000	−	10.3923i	−0.545455	−	0.944755i	0.453124	−	0.891448i	$-0.350310\pi$
$12$		0			0
$13$			1.73205i			0.133235i	0.997779	+	0.0666173i	$0.0212207\pi$
$13$			1.73205i			0.133235i	−0.997779	+	0.0666173i	$0.978779\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		0			0
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	0.100730	−	0.994914i	$-0.467882\pi$
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	−0.811256	+	0.584691i	$0.801216\pi$
$20$		0			0
$21$	7.50000	−	9.52628i	0.357143	−	0.453632i
$22$		0			0
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	−0.477941	−	0.878392i	$-0.658617\pi$
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	0.999680	−	0.0252868i	$-0.00804990\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−6.00000			−0.206897			−0.103448	−	0.994635i	$-0.532988\pi$
$29$	−6.00000			−0.206897			−0.103448	+	0.994635i	$0.532988\pi$
$30$		0			0
$31$	−18.0000	+	10.3923i	−0.580645	+	0.335236i	−0.761390	−	0.648294i	$-0.775483\pi$
$31$	−18.0000	+	10.3923i	−0.580645	+	0.335236i	0.180745	+	0.983530i	$0.442149\pi$
$32$		0			0
$33$	−18.0000	−	10.3923i	−0.545455	−	0.314918i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.0945946	+	0.163843i	−0.909439	−	0.415837i	$-0.863489\pi$
$37$	−3.50000	+	6.06218i	−0.0945946	+	0.163843i	0.814845	+	0.579679i	$0.196822\pi$
$38$		0			0
$39$	1.50000	+	2.59808i	0.0384615	+	0.0666173i
$40$		0			0
$41$		−	41.5692i		−	1.01388i	−0.861980	−	0.506942i	$-0.830776\pi$
$41$		−	41.5692i		−	1.01388i	0.861980	−	0.506942i	$-0.169224\pi$
$42$		0			0
$43$	−50.0000			−1.16279			−0.581395	−	0.813621i	$-0.697493\pi$
$43$	−50.0000			−1.16279			−0.581395	+	0.813621i	$0.697493\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−27.0000	−	15.5885i	−0.574468	−	0.331669i	0.184464	−	0.982839i	$-0.440945\pi$
$47$	−27.0000	−	15.5885i	−0.574468	−	0.331669i	−0.758932	+	0.651170i	$0.774278\pi$
$48$		0			0
$49$	35.5000	−	33.7750i	0.724490	−	0.689286i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	42.0000	+	72.7461i	0.792453	+	1.37257i	0.924444	+	0.381318i	$0.124530\pi$
$53$	42.0000	+	72.7461i	0.792453	+	1.37257i	−0.131991	+	0.991251i	$0.542137\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−27.0000			−0.473684
$58$		0			0
$59$	27.0000	−	15.5885i	0.457627	−	0.264211i	−0.253419	−	0.967357i	$-0.581555\pi$
$59$	27.0000	−	15.5885i	0.457627	−	0.264211i	0.711046	+	0.703146i	$0.248222\pi$
$60$		0			0
$61$	−52.5000	−	30.3109i	−0.860656	−	0.496900i	0.00357609	−	0.999994i	$-0.498862\pi$
$61$	−52.5000	−	30.3109i	−0.860656	−	0.496900i	−0.864232	+	0.503094i	$0.832195\pi$
$62$		0			0
$63$	3.00000	−	20.7846i	0.0476190	−	0.329914i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−56.5000	−	97.8609i	−0.843284	−	1.46061i	−0.887103	−	0.461571i	$-0.847286\pi$
$67$	−56.5000	−	97.8609i	−0.843284	−	1.46061i	0.0438199	−	0.999039i	$-0.486047\pi$
$68$		0			0
$69$		−	41.5692i		−	0.602452i
$70$		0			0
$71$	−30.0000			−0.422535			−0.211268	−	0.977428i	$-0.567759\pi$
$71$	−30.0000			−0.422535			−0.211268	+	0.977428i	$0.567759\pi$
$72$		0			0
$73$	−10.5000	+	6.06218i	−0.143836	+	0.0830435i	−0.570191	−	0.821512i	$-0.693131\pi$
$73$	−10.5000	+	6.06218i	−0.143836	+	0.0830435i	0.426355	+	0.904556i	$0.359797\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−66.0000	−	51.9615i	−0.857143	−	0.674825i
$78$		0			0
$79$	−47.5000	+	82.2724i	−0.601266	+	1.04142i	0.391364	+	0.920236i	$0.372003\pi$
$79$	−47.5000	+	82.2724i	−0.601266	+	1.04142i	−0.992630	+	0.121187i	$0.961330\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			10.3923i			0.125208i	0.998038	+	0.0626042i	$0.0199406\pi$
$83$			10.3923i			0.125208i	−0.998038	+	0.0626042i	$0.980059\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.00000	+	5.19615i	−0.103448	+	0.0597259i
$88$		0			0
$89$	153.000	+	88.3346i	1.71910	+	0.992523i	0.920577	+	0.390560i	$0.127719\pi$
$89$	153.000	+	88.3346i	1.71910	+	0.992523i	0.798524	+	0.601963i	$0.205615\pi$
$90$		0			0
$91$	4.50000	+	11.2583i	0.0494505	+	0.123718i
$92$		0			0
$93$	−18.0000	+	31.1769i	−0.193548	+	0.335236i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	112.583i		−	1.16065i	−0.814384	−	0.580326i	$-0.802925\pi$
$97$		−	112.583i		−	1.16065i	0.814384	−	0.580326i	$-0.197075\pi$
$98$		0			0
$99$	−36.0000			−0.363636
$100$		0			0
$101$	18.0000	−	10.3923i	0.178218	−	0.102894i	−0.408237	−	0.912876i	$-0.633856\pi$
$101$	18.0000	−	10.3923i	0.178218	−	0.102894i	0.586455	+	0.809982i	$0.300523\pi$
$102$		0			0
$103$	−4.50000	−	2.59808i	−0.0436893	−	0.0252240i	0.477996	−	0.878362i	$-0.341363\pi$
$103$	−4.50000	−	2.59808i	−0.0436893	−	0.0252240i	−0.521686	+	0.853138i	$0.674697\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.0560748	+	0.0971243i	−0.892700	−	0.450651i	$-0.851192\pi$
$107$	−6.00000	+	10.3923i	−0.0560748	+	0.0971243i	0.836625	+	0.547775i	$0.184525\pi$
$108$		0			0
$109$	8.50000	+	14.7224i	0.0779817	+	0.135068i	0.902379	−	0.430943i	$-0.141819\pi$
$109$	8.50000	+	14.7224i	0.0779817	+	0.135068i	−0.824397	+	0.566011i	$0.808486\pi$
$110$		0			0
$111$			12.1244i			0.109228i
$112$		0			0
$113$	54.0000			0.477876			0.238938	−	0.971035i	$-0.423201\pi$
$113$	54.0000			0.477876			0.238938	+	0.971035i	$0.423201\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.50000	+	2.59808i	0.0384615	+	0.0222058i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−11.5000	+	19.9186i	−0.0950413	+	0.164616i
$122$		0			0
$123$	−36.0000	−	62.3538i	−0.292683	−	0.506942i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−109.000			−0.858268			−0.429134	−	0.903241i	$-0.641181\pi$
$127$	−109.000			−0.858268			−0.429134	+	0.903241i	$0.641181\pi$
$128$		0			0
$129$	−75.0000	+	43.3013i	−0.581395	+	0.335669i
$130$		0			0
$131$	18.0000	+	10.3923i	0.137405	+	0.0793306i	0.567126	−	0.823631i	$-0.308055\pi$
$131$	18.0000	+	10.3923i	0.137405	+	0.0793306i	−0.429722	+	0.902961i	$0.641388\pi$
$132$		0			0
$133$	−108.000	−	15.5885i	−0.812030	−	0.117206i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−78.0000	−	135.100i	−0.569343	−	0.986131i	−0.996631	−	0.0820155i	$-0.973864\pi$
$137$	−78.0000	−	135.100i	−0.569343	−	0.986131i	0.427288	−	0.904116i	$-0.359469\pi$
$138$		0			0
$139$			15.5885i			0.112147i	0.998427	+	0.0560736i	$0.0178581\pi$
$139$			15.5885i			0.112147i	−0.998427	+	0.0560736i	$0.982142\pi$
$140$		0			0
$141$	−54.0000			−0.382979
$142$		0			0
$143$	18.0000	−	10.3923i	0.125874	−	0.0726735i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	24.0000	−	81.4064i	0.163265	−	0.553785i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	−48.5000	−	84.0045i	−0.321192	−	0.556321i	0.659542	−	0.751668i	$-0.270750\pi$
$151$	−48.5000	−	84.0045i	−0.321192	−	0.556321i	−0.980734	+	0.195347i	$0.937417\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−46.5000	+	26.8468i	−0.296178	+	0.170999i	−0.640725	−	0.767771i	$-0.721366\pi$
$157$	−46.5000	+	26.8468i	−0.296178	+	0.170999i	0.344546	+	0.938769i	$0.388033\pi$
$158$		0			0
$159$	126.000	+	72.7461i	0.792453	+	0.457523i
$160$		0			0
$161$	24.0000	−	166.277i	0.149068	−	1.03278i
$162$		0			0
$163$	111.500	−	193.124i	0.684049	−	1.18481i	−0.289686	−	0.957122i	$-0.593551\pi$
$163$	111.500	−	193.124i	0.684049	−	1.18481i	0.973735	−	0.227686i	$-0.0731159\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	166.277i		−	0.995670i	−0.867272	−	0.497835i	$-0.834129\pi$
$167$		−	166.277i		−	0.995670i	0.867272	−	0.497835i	$-0.165871\pi$
$168$		0			0
$169$	166.000			0.982249
$170$		0			0
$171$	−40.5000	+	23.3827i	−0.236842	+	0.136741i
$172$		0			0
$173$	−117.000	−	67.5500i	−0.676301	−	0.390462i	0.122159	−	0.992511i	$-0.461018\pi$
$173$	−117.000	−	67.5500i	−0.676301	−	0.390462i	−0.798460	+	0.602048i	$0.794351\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	27.0000	−	46.7654i	0.152542	−	0.264211i
$178$		0			0
$179$	81.0000	+	140.296i	0.452514	+	0.783777i	0.998541	−	0.0539901i	$-0.0171939\pi$
$179$	81.0000	+	140.296i	0.452514	+	0.783777i	−0.546028	+	0.837767i	$0.683861\pi$
$180$		0			0
$181$		−	277.128i		−	1.53109i	−0.643380	−	0.765547i	$-0.722468\pi$
$181$		−	277.128i		−	1.53109i	0.643380	−	0.765547i	$-0.277532\pi$
$182$		0			0
$183$	−105.000			−0.573770
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−13.5000	−	33.7750i	−0.0714286	−	0.178704i
$190$		0			0
$191$	−78.0000	+	135.100i	−0.408377	+	0.707330i	−0.994708	−	0.102742i	$-0.967238\pi$
$191$	−78.0000	+	135.100i	−0.408377	+	0.707330i	0.586331	+	0.810072i	$0.300572\pi$
$192$		0			0
$193$	−65.0000	−	112.583i	−0.336788	−	0.583333i	0.647039	−	0.762457i	$-0.276007\pi$
$193$	−65.0000	−	112.583i	−0.336788	−	0.583333i	−0.983827	+	0.179124i	$0.942674\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−150.000			−0.761421			−0.380711	−	0.924694i	$-0.624321\pi$
$197$	−150.000			−0.761421			−0.380711	+	0.924694i	$0.624321\pi$
$198$		0			0
$199$	−4.50000	+	2.59808i	−0.0226131	+	0.0130557i	−0.511264	−	0.859424i	$-0.670823\pi$
$199$	−4.50000	+	2.59808i	−0.0226131	+	0.0130557i	0.488651	+	0.872479i	$0.337489\pi$
$200$		0			0
$201$	−169.500	−	97.8609i	−0.843284	−	0.486870i
$202$		0			0
$203$	−39.0000	+	15.5885i	−0.192118	+	0.0767904i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−36.0000	−	62.3538i	−0.173913	−	0.301226i
$208$		0			0
$209$			187.061i			0.895031i
$210$		0			0
$211$	−305.000			−1.44550			−0.722749	−	0.691111i	$-0.757122\pi$
$211$	−305.000			−1.44550			−0.722749	+	0.691111i	$0.757122\pi$
$212$		0			0
$213$	−45.0000	+	25.9808i	−0.211268	+	0.121975i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−90.0000	+	114.315i	−0.414747	+	0.526799i
$218$		0			0
$219$	−10.5000	+	18.1865i	−0.0479452	+	0.0830435i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	22.5167i		−	0.100972i	−0.998725	−	0.0504858i	$-0.983923\pi$
$223$		−	22.5167i		−	0.100972i	0.998725	−	0.0504858i	$-0.0160770\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−333.000	+	192.258i	−1.46696	+	0.846950i	−0.999316	−	0.0369670i	$-0.988230\pi$
$227$	−333.000	+	192.258i	−1.46696	+	0.846950i	−0.467644	+	0.883917i	$0.654897\pi$
$228$		0			0
$229$	205.500	+	118.645i	0.897380	+	0.518103i	0.876349	−	0.481676i	$-0.159972\pi$
$229$	205.500	+	118.645i	0.897380	+	0.518103i	0.0210307	+	0.999779i	$0.493305\pi$
$230$		0			0
$231$	−144.000	−	20.7846i	−0.623377	−	0.0899767i
$232$		0			0
$233$	150.000	−	259.808i	0.643777	−	1.11505i	−0.340806	−	0.940134i	$-0.610700\pi$
$233$	150.000	−	259.808i	0.643777	−	1.11505i	0.984583	−	0.174920i	$-0.0559668\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			164.545i			0.694282i
$238$		0			0
$239$	240.000			1.00418			0.502092	−	0.864814i	$-0.332564\pi$
$239$	240.000			1.00418			0.502092	+	0.864814i	$0.332564\pi$
$240$		0			0
$241$	184.500	−	106.521i	0.765560	−	0.441996i	−0.0657283	−	0.997838i	$-0.520937\pi$
$241$	184.500	−	106.521i	0.765560	−	0.441996i	0.831289	+	0.555841i	$0.187604\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.5000	−	23.3827i	0.0546559	−	0.0946667i
$248$		0			0
$249$	9.00000	+	15.5885i	0.0361446	+	0.0626042i
$250$		0			0
$251$			114.315i			0.455440i	0.973727	+	0.227720i	$0.0731270\pi$
$251$			114.315i			0.455440i	−0.973727	+	0.227720i	$0.926873\pi$
$252$		0			0
$253$	−288.000			−1.13834
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−333.000	−	192.258i	−1.29572	−	0.748084i	−0.316058	−	0.948740i	$-0.602359\pi$
$257$	−333.000	−	192.258i	−1.29572	−	0.748084i	−0.979662	+	0.200656i	$0.935693\pi$
$258$		0			0
$259$	−7.00000	+	48.4974i	−0.0270270	+	0.187249i
$260$		0			0
$261$	−9.00000	+	15.5885i	−0.0344828	+	0.0597259i
$262$		0			0
$263$	−96.0000	−	166.277i	−0.365019	−	0.632231i	0.623760	−	0.781616i	$-0.285604\pi$
$263$	−96.0000	−	166.277i	−0.365019	−	0.632231i	−0.988779	+	0.149384i	$0.952271\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	306.000			1.14607
$268$		0			0
$269$	−63.0000	+	36.3731i	−0.234201	+	0.135216i	−0.612508	−	0.790464i	$-0.709839\pi$
$269$	−63.0000	+	36.3731i	−0.234201	+	0.135216i	0.378308	+	0.925680i	$0.376506\pi$
$270$		0			0
$271$	−210.000	−	121.244i	−0.774908	−	0.447393i	0.0597148	−	0.998215i	$-0.480981\pi$
$271$	−210.000	−	121.244i	−0.774908	−	0.447393i	−0.834623	+	0.550822i	$0.814314\pi$
$272$		0			0
$273$	16.5000	+	12.9904i	0.0604396	+	0.0475838i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	57.5000	+	99.5929i	0.207581	+	0.359541i	0.950952	−	0.309338i	$-0.100108\pi$
$277$	57.5000	+	99.5929i	0.207581	+	0.359541i	−0.743371	+	0.668880i	$0.766774\pi$
$278$		0			0
$279$			62.3538i			0.223490i
$280$		0			0
$281$	528.000			1.87900			0.939502	−	0.342544i	$-0.111289\pi$
$281$	528.000			1.87900			0.939502	+	0.342544i	$0.111289\pi$
$282$		0			0
$283$	−172.500	+	99.5929i	−0.609541	+	0.351918i	−0.772786	−	0.634667i	$-0.781137\pi$
$283$	−172.500	+	99.5929i	−0.609541	+	0.351918i	0.163245	+	0.986586i	$0.447804\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−108.000	−	270.200i	−0.376307	−	0.941463i
$288$		0			0
$289$	−144.500	+	250.281i	−0.500000	+	0.866025i
$290$		0			0
$291$	−97.5000	−	168.875i	−0.335052	−	0.580326i
$292$		0			0
$293$			197.454i			0.673904i	0.941522	+	0.336952i	$0.109396\pi$
$293$			197.454i			0.673904i	−0.941522	+	0.336952i	$0.890604\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−54.0000	+	31.1769i	−0.181818	+	0.104973i
$298$		0			0
$299$	36.0000	+	20.7846i	0.120401	+	0.0695137i
$300$		0			0
$301$	−325.000	+	129.904i	−1.07973	+	0.431574i
$302$		0			0
$303$	18.0000	−	31.1769i	0.0594059	−	0.102894i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	478.046i		−	1.55715i	−0.627550	−	0.778577i	$-0.715942\pi$
$307$		−	478.046i		−	1.55715i	0.627550	−	0.778577i	$-0.284058\pi$
$308$		0			0
$309$	−9.00000			−0.0291262
$310$		0			0
$311$	207.000	−	119.512i	0.665595	−	0.384281i	−0.128811	−	0.991669i	$-0.541116\pi$
$311$	207.000	−	119.512i	0.665595	−	0.384281i	0.794405	+	0.607388i	$0.207783\pi$
$312$		0			0
$313$	276.000	+	159.349i	0.881789	+	0.509101i	0.871248	−	0.490843i	$-0.163311\pi$
$313$	276.000	+	159.349i	0.881789	+	0.509101i	0.0105412	+	0.999944i	$0.496645\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	33.0000	−	57.1577i	0.104101	−	0.180308i	−0.809270	−	0.587437i	$-0.800137\pi$
$317$	33.0000	−	57.1577i	0.104101	−	0.180308i	0.913371	+	0.407129i	$0.133470\pi$
$318$		0			0
$319$	36.0000	+	62.3538i	0.112853	+	0.195467i
$320$		0			0
$321$			20.7846i			0.0647496i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	25.5000	+	14.7224i	0.0779817	+	0.0450227i
$328$		0			0
$329$	−216.000	−	31.1769i	−0.656535	−	0.0947627i
$330$		0			0
$331$	−111.500	+	193.124i	−0.336858	+	0.583455i	−0.983840	−	0.179050i	$-0.942698\pi$
$331$	−111.500	+	193.124i	−0.336858	+	0.583455i	0.646982	+	0.762505i	$0.276031\pi$
$332$		0			0
$333$	10.5000	+	18.1865i	0.0315315	+	0.0546142i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−158.000			−0.468843			−0.234421	−	0.972135i	$-0.575320\pi$
$337$	−158.000			−0.468843			−0.234421	+	0.972135i	$0.575320\pi$
$338$		0			0
$339$	81.0000	−	46.7654i	0.238938	−	0.137951i
$340$		0			0
$341$	216.000	+	124.708i	0.633431	+	0.365712i
$342$		0			0
$343$	143.000	−	311.769i	0.416910	−	0.908948i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−30.0000	−	51.9615i	−0.0864553	−	0.149745i	0.819555	−	0.573000i	$-0.194221\pi$
$347$	−30.0000	−	51.9615i	−0.0864553	−	0.149745i	−0.906010	+	0.423255i	$0.860887\pi$
$348$		0			0
$349$		−	34.6410i		−	0.0992579i	−0.998768	−	0.0496290i	$-0.984196\pi$
$349$		−	34.6410i		−	0.0992579i	0.998768	−	0.0496290i	$-0.0158039\pi$
$350$		0			0
$351$	9.00000			0.0256410
$352$		0			0
$353$	−18.0000	+	10.3923i	−0.0509915	+	0.0294400i	−0.525279	−	0.850930i	$-0.676039\pi$
$353$	−18.0000	+	10.3923i	−0.0509915	+	0.0294400i	0.474288	+	0.880370i	$0.342706\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	135.000	−	233.827i	0.376045	−	0.651328i	−0.614438	−	0.788965i	$-0.710617\pi$
$359$	135.000	−	233.827i	0.376045	−	0.651328i	0.990483	+	0.137637i	$0.0439506\pi$
$360$		0			0
$361$	−59.0000	−	102.191i	−0.163435	−	0.283078i
$362$		0			0
$363$			39.8372i			0.109744i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	462.000	−	266.736i	1.25886	−	0.726801i	0.286004	−	0.958229i	$-0.407673\pi$
$367$	462.000	−	266.736i	1.25886	−	0.726801i	0.972852	+	0.231428i	$0.0743398\pi$
$368$		0			0
$369$	−108.000	−	62.3538i	−0.292683	−	0.168981i
$370$		0			0
$371$	462.000	+	363.731i	1.24528	+	0.980406i
$372$		0			0
$373$	−152.500	+	264.138i	−0.408847	+	0.708144i	−0.994761	−	0.102229i	$-0.967402\pi$
$373$	−152.500	+	264.138i	−0.408847	+	0.708144i	0.585914	+	0.810373i	$0.300736\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	10.3923i		−	0.0275658i
$378$		0			0
$379$	271.000			0.715040			0.357520	−	0.933906i	$-0.383622\pi$
$379$	271.000			0.715040			0.357520	+	0.933906i	$0.383622\pi$
$380$		0			0
$381$	−163.500	+	94.3968i	−0.429134	+	0.247761i
$382$		0			0
$383$	441.000	+	254.611i	1.15144	+	0.664782i	0.949237	−	0.314562i	$-0.101858\pi$
$383$	441.000	+	254.611i	1.15144	+	0.664782i	0.202199	+	0.979344i	$0.435191\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−75.0000	+	129.904i	−0.193798	+	0.335669i
$388$		0			0
$389$	339.000	+	587.165i	0.871465	+	1.50942i	0.860481	+	0.509482i	$0.170163\pi$
$389$	339.000	+	587.165i	0.871465	+	1.50942i	0.0109843	+	0.999940i	$0.496504\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	36.0000			0.0916031
$394$		0			0
$395$		0			0
$396$		0			0
$397$	414.000	+	239.023i	1.04282	+	0.602073i	0.920631	−	0.390434i	$-0.127675\pi$
$397$	414.000	+	239.023i	1.04282	+	0.602073i	0.122190	+	0.992507i	$0.461008\pi$
$398$		0			0
$399$	−175.500	+	70.1481i	−0.439850	+	0.175810i
$400$		0			0
$401$	117.000	−	202.650i	0.291771	−	0.505361i	−0.682458	−	0.730925i	$-0.739089\pi$
$401$	117.000	−	202.650i	0.291771	−	0.505361i	0.974228	+	0.225563i	$0.0724223\pi$
$402$		0			0
$403$	−18.0000	−	31.1769i	−0.0446650	−	0.0773621i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	84.0000			0.206388
$408$		0			0
$409$	−388.500	+	224.301i	−0.949878	+	0.548412i	−0.893043	−	0.449971i	$-0.851434\pi$
$409$	−388.500	+	224.301i	−0.949878	+	0.548412i	−0.0568348	+	0.998384i	$0.518101\pi$
$410$		0			0
$411$	−234.000	−	135.100i	−0.569343	−	0.328710i
$412$		0			0
$413$	135.000	−	171.473i	0.326877	−	0.415189i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.5000	+	23.3827i	0.0323741	+	0.0560736i
$418$		0			0
$419$		−	800.207i		−	1.90980i	−0.296923	−	0.954902i	$-0.595960\pi$
$419$		−	800.207i		−	1.90980i	0.296923	−	0.954902i	$-0.404040\pi$
$420$		0			0
$421$	−151.000			−0.358670			−0.179335	−	0.983788i	$-0.557395\pi$
$421$	−151.000			−0.358670			−0.179335	+	0.983788i	$0.557395\pi$
$422$		0			0
$423$	−81.0000	+	46.7654i	−0.191489	+	0.110556i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−420.000	−	60.6218i	−0.983607	−	0.141971i
$428$		0			0
$429$	18.0000	−	31.1769i	0.0419580	−	0.0726735i
$430$		0			0
$431$	297.000	+	514.419i	0.689095	+	1.19355i	0.972131	+	0.234438i	$0.0753251\pi$
$431$	297.000	+	514.419i	0.689095	+	1.19355i	−0.283036	+	0.959109i	$0.591342\pi$
$432$		0			0
$433$			311.769i			0.720021i	0.932948	+	0.360011i	$0.117227\pi$
$433$			311.769i			0.720021i	−0.932948	+	0.360011i	$0.882773\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−324.000	+	187.061i	−0.741419	+	0.428058i
$438$		0			0
$439$	−484.500	−	279.726i	−1.10364	−	0.637190i	−0.166469	−	0.986047i	$-0.553236\pi$
$439$	−484.500	−	279.726i	−1.10364	−	0.637190i	−0.937176	+	0.348857i	$0.886570\pi$
$440$		0			0
$441$	−34.5000	−	142.894i	−0.0782313	−	0.324023i
$442$		0			0
$443$	207.000	−	358.535i	0.467269	−	0.809333i	−0.532032	−	0.846724i	$-0.678571\pi$
$443$	207.000	−	358.535i	0.467269	−	0.809333i	0.999301	+	0.0373912i	$0.0119048\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	234.000			0.521158			0.260579	−	0.965453i	$-0.416087\pi$
$449$	234.000			0.521158			0.260579	+	0.965453i	$0.416087\pi$
$450$		0			0
$451$	−432.000	+	249.415i	−0.957871	+	0.553027i
$452$		0			0
$453$	−145.500	−	84.0045i	−0.321192	−	0.185440i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	41.5000	−	71.8801i	0.0908096	−	0.157287i	−0.817042	−	0.576578i	$-0.804388\pi$
$457$	41.5000	−	71.8801i	0.0908096	−	0.157287i	0.907852	+	0.419291i	$0.137721\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	457.261i		−	0.991890i	−0.868354	−	0.495945i	$-0.834822\pi$
$461$		−	457.261i		−	0.991890i	0.868354	−	0.495945i	$-0.165178\pi$
$462$		0			0
$463$	−517.000			−1.11663			−0.558315	−	0.829629i	$-0.688552\pi$
$463$	−517.000			−1.11663			−0.558315	+	0.829629i	$0.688552\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−477.000	−	275.396i	−1.02141	−	0.589713i	−0.106900	−	0.994270i	$-0.534093\pi$
$467$	−477.000	−	275.396i	−1.02141	−	0.589713i	−0.914513	+	0.404557i	$0.867426\pi$
$468$		0			0
$469$	−621.500	−	489.304i	−1.32516	−	1.04329i
$470$		0			0
$471$	−46.5000	+	80.5404i	−0.0987261	+	0.170999i
$472$		0			0
$473$	300.000	+	519.615i	0.634249	+	1.09855i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	252.000			0.528302
$478$		0			0
$479$	297.000	−	171.473i	0.620042	−	0.357981i	−0.156844	−	0.987623i	$-0.550132\pi$
$479$	297.000	−	171.473i	0.620042	−	0.357981i	0.776885	+	0.629642i	$0.216798\pi$
$480$		0			0
$481$	−10.5000	−	6.06218i	−0.0218295	−	0.0126033i
$482$		0			0
$483$	−108.000	−	270.200i	−0.223602	−	0.559420i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	355.000	+	614.878i	0.728953	+	1.26258i	0.957326	+	0.289010i	$0.0933260\pi$
$487$	355.000	+	614.878i	0.728953	+	1.26258i	−0.228373	+	0.973574i	$0.573341\pi$
$488$		0			0
$489$		−	386.247i		−	0.789872i
$490$		0			0
$491$	498.000			1.01426			0.507128	−	0.861871i	$-0.330707\pi$
$491$	498.000			1.01426			0.507128	+	0.861871i	$0.330707\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−195.000	+	77.9423i	−0.392354	+	0.156826i
$498$		0			0
$499$	434.500	−	752.576i	0.870741	−	1.50817i	0.00951049	−	0.999955i	$-0.496973\pi$
$499$	434.500	−	752.576i	0.870741	−	1.50817i	0.861231	−	0.508214i	$-0.169694\pi$
$500$		0			0
$501$	−144.000	−	249.415i	−0.287425	−	0.497835i
$502$		0			0
$503$			550.792i			1.09501i	0.836801	+	0.547507i	$0.184423\pi$
$503$			550.792i			1.09501i	−0.836801	+	0.547507i	$0.815577\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	249.000	−	143.760i	0.491124	−	0.283551i
$508$		0			0
$509$	315.000	+	181.865i	0.618861	+	0.357299i	0.776425	−	0.630209i	$-0.217031\pi$
$509$	315.000	+	181.865i	0.618861	+	0.357299i	−0.157565	+	0.987509i	$0.550364\pi$
$510$		0			0
$511$	−52.5000	+	66.6840i	−0.102740	+	0.130497i
$512$		0			0
$513$	−40.5000	+	70.1481i	−0.0789474	+	0.136741i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			374.123i			0.723642i
$518$		0			0
$519$	−234.000			−0.450867
$520$		0			0
$521$	270.000	−	155.885i	0.518234	−	0.299203i	−0.217978	−	0.975954i	$-0.569946\pi$
$521$	270.000	−	155.885i	0.518234	−	0.299203i	0.736212	+	0.676751i	$0.236613\pi$
$522$		0			0
$523$	−300.000	−	173.205i	−0.573614	−	0.331176i	0.184978	−	0.982743i	$-0.440779\pi$
$523$	−300.000	−	173.205i	−0.573614	−	0.331176i	−0.758591	+	0.651567i	$0.774112\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−23.5000	−	40.7032i	−0.0444234	−	0.0769437i
$530$		0			0
$531$		−	93.5307i		−	0.176141i
$532$		0			0
$533$	72.0000			0.135084
$534$		0			0
$535$		0			0
$536$		0			0
$537$	243.000	+	140.296i	0.452514	+	0.261259i
$538$		0			0
$539$	−564.000	−	166.277i	−1.04638	−	0.308491i
$540$		0			0
$541$	−68.5000	+	118.645i	−0.126617	+	0.219308i	−0.922364	−	0.386322i	$-0.873745\pi$
$541$	−68.5000	+	118.645i	−0.126617	+	0.219308i	0.795747	+	0.605630i	$0.207079\pi$
$542$		0			0
$543$	−240.000	−	415.692i	−0.441989	−	0.765547i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	758.000			1.38574			0.692870	−	0.721062i	$-0.256346\pi$
$547$	758.000			1.38574			0.692870	+	0.721062i	$0.256346\pi$
$548$		0			0
$549$	−157.500	+	90.9327i	−0.286885	+	0.165633i
$550$		0			0
$551$	81.0000	+	46.7654i	0.147005	+	0.0848736i
$552$		0			0
$553$	−95.0000	+	658.179i	−0.171790	+	1.19020i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	333.000	+	576.773i	0.597846	+	1.03550i	0.993139	+	0.116944i	$0.0373098\pi$
$557$	333.000	+	576.773i	0.597846	+	1.03550i	−0.395293	+	0.918555i	$0.629357\pi$
$558$		0			0
$559$		−	86.6025i		−	0.154924i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	279.000	−	161.081i	0.495560	−	0.286111i	−0.231318	−	0.972878i	$-0.574304\pi$
$563$	279.000	−	161.081i	0.495560	−	0.286111i	0.726878	+	0.686767i	$0.240971\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−49.5000	−	38.9711i	−0.0873016	−	0.0687322i
$568$		0			0
$569$	−342.000	+	592.361i	−0.601054	+	1.04106i	0.391607	+	0.920132i	$0.371919\pi$
$569$	−342.000	+	592.361i	−0.601054	+	1.04106i	−0.992662	+	0.120924i	$0.961414\pi$
$570$		0			0
$571$	27.5000	+	47.6314i	0.0481611	+	0.0834175i	0.889101	−	0.457711i	$-0.151331\pi$
$571$	27.5000	+	47.6314i	0.0481611	+	0.0834175i	−0.840940	+	0.541129i	$0.817997\pi$
$572$		0			0
$573$			270.200i			0.471553i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−138.000	+	79.6743i	−0.239168	+	0.138084i	−0.614794	−	0.788687i	$-0.710761\pi$
$577$	−138.000	+	79.6743i	−0.239168	+	0.138084i	0.375626	+	0.926771i	$0.377428\pi$
$578$		0			0
$579$	−195.000	−	112.583i	−0.336788	−	0.194444i
$580$		0			0
$581$	27.0000	+	67.5500i	0.0464716	+	0.116265i
$582$		0			0
$583$	504.000	−	872.954i	0.864494	−	1.49735i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			249.415i			0.424898i	0.977172	+	0.212449i	$0.0681440\pi$
$587$			249.415i			0.424898i	−0.977172	+	0.212449i	$0.931856\pi$
$588$		0			0
$589$	324.000			0.550085
$590$		0			0
$591$	−225.000	+	129.904i	−0.380711	+	0.219803i
$592$		0			0
$593$	963.000	+	555.988i	1.62395	+	0.937586i	0.985850	+	0.167629i	$0.0536110\pi$
$593$	963.000	+	555.988i	1.62395	+	0.937586i	0.638096	+	0.769957i	$0.279722\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.50000	+	7.79423i	−0.00753769	+	0.0130557i
$598$		0			0
$599$	−432.000	−	748.246i	−0.721202	−	1.24916i	−0.960518	−	0.278217i	$-0.910257\pi$
$599$	−432.000	−	748.246i	−0.721202	−	1.24916i	0.239316	−	0.970942i	$-0.423077\pi$
$600$		0			0
$601$		−	829.652i		−	1.38045i	−0.723593	−	0.690227i	$-0.757511\pi$
$601$		−	829.652i		−	1.38045i	0.723593	−	0.690227i	$-0.242489\pi$
$602$		0			0
$603$	−339.000			−0.562189
$604$		0			0
$605$		0			0
$606$		0			0
$607$	763.500	+	440.807i	1.25783	+	0.726206i	0.972651	−	0.232270i	$-0.0746153\pi$
$607$	763.500	+	440.807i	1.25783	+	0.726206i	0.285174	+	0.958476i	$0.407949\pi$
$608$		0			0
$609$	−45.0000	+	57.1577i	−0.0738916	+	0.0938550i
$610$		0			0
$611$	27.0000	−	46.7654i	0.0441899	−	0.0765391i
$612$		0			0
$613$	23.0000	+	39.8372i	0.0375204	+	0.0649872i	0.884176	−	0.467154i	$-0.154721\pi$
$613$	23.0000	+	39.8372i	0.0375204	+	0.0649872i	−0.846655	+	0.532142i	$0.821387\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	174.000			0.282010			0.141005	−	0.990009i	$-0.454967\pi$
$617$	174.000			0.282010			0.141005	+	0.990009i	$0.454967\pi$
$618$		0			0
$619$	−762.000	+	439.941i	−1.23102	+	0.710728i	−0.967242	−	0.253856i	$-0.918301\pi$
$619$	−762.000	+	439.941i	−1.23102	+	0.710728i	−0.263776	+	0.964584i	$0.584968\pi$
$620$		0			0
$621$	−108.000	−	62.3538i	−0.173913	−	0.100409i
$622$		0			0
$623$	1224.00	+	176.669i	1.96469	+	0.283578i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	162.000	+	280.592i	0.258373	+	0.447516i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	875.000			1.38669			0.693344	−	0.720607i	$-0.256137\pi$
$631$	875.000			1.38669			0.693344	+	0.720607i	$0.256137\pi$
$632$		0			0
$633$	−457.500	+	264.138i	−0.722749	+	0.417279i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	58.5000	+	61.4878i	0.0918367	+	0.0965272i
$638$		0			0
$639$	−45.0000	+	77.9423i	−0.0704225	+	0.121975i
$640$		0			0
$641$	486.000	+	841.777i	0.758190	+	1.31322i	0.943773	+	0.330595i	$0.107250\pi$
$641$	486.000	+	841.777i	0.758190	+	1.31322i	−0.185582	+	0.982629i	$0.559417\pi$
$642$		0			0
$643$		−	195.722i		−	0.304388i	−0.988351	−	0.152194i	$-0.951366\pi$
$643$		−	195.722i		−	0.304388i	0.988351	−	0.152194i	$-0.0486339\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	189.000	−	109.119i	0.292117	−	0.168654i	−0.346779	−	0.937947i	$-0.612725\pi$
$647$	189.000	−	109.119i	0.292117	−	0.168654i	0.638896	+	0.769293i	$0.279391\pi$
$648$		0			0
$649$	−324.000	−	187.061i	−0.499230	−	0.288230i
$650$		0			0
$651$	−36.0000	+	249.415i	−0.0552995	+	0.383126i
$652$		0			0
$653$	−150.000	+	259.808i	−0.229709	+	0.397868i	−0.957722	−	0.287696i	$-0.907111\pi$
$653$	−150.000	+	259.808i	−0.229709	+	0.397868i	0.728013	+	0.685564i	$0.240444\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			36.3731i			0.0553624i
$658$		0			0
$659$	678.000			1.02883			0.514416	−	0.857541i	$-0.328009\pi$
$659$	678.000			1.02883			0.514416	+	0.857541i	$0.328009\pi$
$660$		0			0
$661$	109.500	−	63.2199i	0.165658	−	0.0956427i	−0.414879	−	0.909877i	$-0.636176\pi$
$661$	109.500	−	63.2199i	0.165658	−	0.0956427i	0.580537	+	0.814234i	$0.302843\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−72.0000	+	124.708i	−0.107946	+	0.186968i
$668$		0			0
$669$	−19.5000	−	33.7750i	−0.0291480	−	0.0504858i
$670$		0			0
$671$			727.461i			1.08415i
$672$		0			0
$673$	−407.000			−0.604755			−0.302377	−	0.953188i	$-0.597780\pi$
$673$	−407.000			−0.604755			−0.302377	+	0.953188i	$0.597780\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	954.000	+	550.792i	1.40916	+	0.813578i	0.995307	−	0.0967669i	$-0.0308501\pi$
$677$	954.000	+	550.792i	1.40916	+	0.813578i	0.413851	+	0.910345i	$0.364183\pi$
$678$		0			0
$679$	−292.500	−	731.791i	−0.430781	−	1.07775i
$680$		0			0
$681$	−333.000	+	576.773i	−0.488987	+	0.846950i
$682$		0			0
$683$	−21.0000	−	36.3731i	−0.0307467	−	0.0532549i	0.850243	−	0.526391i	$-0.176455\pi$
$683$	−21.0000	−	36.3731i	−0.0307467	−	0.0532549i	−0.880989	+	0.473136i	$0.843122\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	411.000			0.598253
$688$		0			0
$689$	−126.000	+	72.7461i	−0.182874	+	0.105582i
$690$		0			0
$691$	295.500	+	170.607i	0.427641	+	0.246899i	0.698341	−	0.715765i	$-0.253922\pi$
$691$	295.500	+	170.607i	0.427641	+	0.246899i	−0.270700	+	0.962664i	$0.587255\pi$
$692$		0			0
$693$	−234.000	+	93.5307i	−0.337662	+	0.134965i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	519.615i		−	0.743369i
$700$		0			0
$701$	1182.00			1.68616			0.843081	−	0.537786i	$-0.180739\pi$
$701$	1182.00			1.68616			0.843081	+	0.537786i	$0.180739\pi$
$702$		0			0
$703$	94.5000	−	54.5596i	0.134424	−	0.0776097i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	90.0000	−	114.315i	0.127298	−	0.161691i
$708$		0			0
$709$	−291.500	+	504.893i	−0.411142	+	0.712120i	−0.995015	−	0.0997257i	$-0.968203\pi$
$709$	−291.500	+	504.893i	−0.411142	+	0.712120i	0.583873	+	0.811845i	$0.301537\pi$
$710$		0			0
$711$	142.500	+	246.817i	0.200422	+	0.347141i
$712$		0			0
$713$			498.831i			0.699622i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	360.000	−	207.846i	0.502092	−	0.289883i
$718$		0			0
$719$	522.000	+	301.377i	0.726008	+	0.419161i	0.816960	−	0.576694i	$-0.195658\pi$
$719$	522.000	+	301.377i	0.726008	+	0.419161i	−0.0909518	+	0.995855i	$0.528991\pi$
$720$		0			0
$721$	−36.0000	−	5.19615i	−0.0499307	−	0.00720687i
$722$		0			0
$723$	184.500	−	319.563i	0.255187	−	0.441996i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	84.8705i		−	0.116741i	−0.998295	−	0.0583704i	$-0.981410\pi$
$727$		−	84.8705i		−	0.116741i	0.998295	−	0.0583704i	$-0.0185904\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	187.500	+	108.253i	0.255798	+	0.147685i	0.622416	−	0.782686i	$-0.286151\pi$
$733$	187.500	+	108.253i	0.255798	+	0.147685i	−0.366618	+	0.930371i	$0.619484\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−678.000	+	1174.33i	−0.919946	+	1.59339i
$738$		0			0
$739$	243.500	+	421.754i	0.329499	+	0.570710i	0.982413	−	0.186723i	$-0.0597867\pi$
$739$	243.500	+	421.754i	0.329499	+	0.570710i	−0.652913	+	0.757433i	$0.726453\pi$
$740$		0			0
$741$		−	46.7654i		−	0.0631112i
$742$		0			0
$743$	480.000			0.646030			0.323015	−	0.946394i	$-0.395304\pi$
$743$	480.000			0.646030			0.323015	+	0.946394i	$0.395304\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	27.0000	+	15.5885i	0.0361446	+	0.0208681i
$748$		0			0
$749$	−12.0000	+	83.1384i	−0.0160214	+	0.110999i
$750$		0			0
$751$	−150.500	+	260.674i	−0.200399	+	0.347102i	−0.948657	−	0.316306i	$-0.897557\pi$
$751$	−150.500	+	260.674i	−0.200399	+	0.347102i	0.748258	+	0.663408i	$0.230891\pi$
$752$		0			0
$753$	99.0000	+	171.473i	0.131474	+	0.227720i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	811.000			1.07133			0.535667	−	0.844429i	$-0.320060\pi$
$757$	811.000			1.07133			0.535667	+	0.844429i	$0.320060\pi$
$758$		0			0
$759$	−432.000	+	249.415i	−0.569170	+	0.328610i
$760$		0			0
$761$	828.000	+	478.046i	1.08804	+	0.628181i	0.933054	−	0.359735i	$-0.117133\pi$
$761$	828.000	+	478.046i	1.08804	+	0.628181i	0.154988	+	0.987916i	$0.450466\pi$
$762$		0			0
$763$	93.5000	+	73.6122i	0.122543	+	0.0964773i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.0000	+	46.7654i	0.0352021	+	0.0609718i
$768$		0			0
$769$		−	1344.07i		−	1.74782i	−0.486090	−	0.873909i	$-0.661577\pi$
$769$		−	1344.07i		−	1.74782i	0.486090	−	0.873909i	$-0.338423\pi$
$770$		0			0
$771$	−666.000			−0.863813
$772$		0			0
$773$	−630.000	+	363.731i	−0.815006	+	0.470544i	−0.848691	−	0.528888i	$-0.822609\pi$
$773$	−630.000	+	363.731i	−0.815006	+	0.470544i	0.0336850	+	0.999433i	$0.489276\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	31.5000	+	78.8083i	0.0405405	+	0.101426i
$778$		0			0
$779$	−324.000	+	561.184i	−0.415918	+	0.720391i
$780$		0			0
$781$	180.000	+	311.769i	0.230474	+	0.399192i
$782$		0			0
$783$			31.1769i			0.0398173i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−772.500	+	446.003i	−0.981576	+	0.566713i	−0.902745	−	0.430175i	$-0.858452\pi$
$787$	−772.500	+	446.003i	−0.981576	+	0.566713i	−0.0788301	+	0.996888i	$0.525118\pi$
$788$		0			0
$789$	−288.000	−	166.277i	−0.365019	−	0.210744i
$790$		0			0
$791$	351.000	−	140.296i	0.443742	−	0.177366i
$792$		0			0
$793$	52.5000	−	90.9327i	0.0662043	−	0.114669i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	1351.00i		−	1.69511i	−0.530711	−	0.847553i	$-0.678075\pi$
$797$		−	1351.00i		−	1.69511i	0.530711	−	0.847553i	$-0.321925\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	459.000	−	265.004i	0.573034	−	0.330841i
$802$		0			0
$803$	126.000	+	72.7461i	0.156912	+	0.0905929i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−63.0000	+	109.119i	−0.0780669	+	0.135216i
$808$		0			0
$809$	96.0000	+	166.277i	0.118665	+	0.205534i	0.919239	−	0.393700i	$-0.128805\pi$
$809$	96.0000	+	166.277i	0.118665	+	0.205534i	−0.800574	+	0.599234i	$0.795472\pi$
$810$		0			0
$811$			1234.95i			1.52275i	0.648310	+	0.761376i	$0.275476\pi$
$811$			1234.95i			1.52275i	−0.648310	+	0.761376i	$0.724524\pi$
$812$		0			0
$813$	−420.000			−0.516605
$814$		0			0
$815$		0			0
$816$		0			0
$817$	675.000	+	389.711i	0.826193	+	0.477003i
$818$		0			0
$819$	36.0000	+	5.19615i	0.0439560	+	0.00634451i
$820$		0			0
$821$	−498.000	+	862.561i	−0.606577	+	1.05062i	0.385223	+	0.922824i	$0.374125\pi$
$821$	−498.000	+	862.561i	−0.606577	+	1.05062i	−0.991800	+	0.127799i	$0.959209\pi$
$822$		0			0
$823$	−467.500	−	809.734i	−0.568044	−	0.983881i	−0.996759	−	0.0804411i	$-0.974367\pi$
$823$	−467.500	−	809.734i	−0.568044	−	0.983881i	0.428716	−	0.903439i	$-0.358966\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	228.000			0.275695			0.137848	−	0.990453i	$-0.455982\pi$
$827$	228.000			0.275695			0.137848	+	0.990453i	$0.455982\pi$
$828$		0			0
$829$	−304.500	+	175.803i	−0.367310	+	0.212067i	−0.672283	−	0.740295i	$-0.734686\pi$
$829$	−304.500	+	175.803i	−0.367310	+	0.212067i	0.304973	+	0.952361i	$0.401353\pi$
$830$		0			0
$831$	172.500	+	99.5929i	0.207581	+	0.119847i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	54.0000	+	93.5307i	0.0645161	+	0.111745i
$838$		0			0
$839$		−	852.169i		−	1.01570i	−0.861447	−	0.507848i	$-0.830441\pi$
$839$		−	852.169i		−	1.01570i	0.861447	−	0.507848i	$-0.169559\pi$
$840$		0			0
$841$	−805.000			−0.957194
$842$		0			0
$843$	792.000	−	457.261i	0.939502	−	0.542422i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−23.0000	+	159.349i	−0.0271547	+	0.188133i
$848$		0			0
$849$	−172.500	+	298.779i	−0.203180	+	0.351918i
$850$		0			0
$851$	84.0000	+	145.492i	0.0987074	+	0.170966i
$852$		0			0
$853$			1344.07i			1.57570i	0.615868	+	0.787850i	$0.288806\pi$
$853$			1344.07i			1.57570i	−0.615868	+	0.787850i	$0.711194\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−855.000	+	493.634i	−0.997666	+	0.576003i	−0.907557	−	0.419929i	$-0.862055\pi$
$857$	−855.000	+	493.634i	−0.997666	+	0.576003i	−0.0901093	+	0.995932i	$0.528722\pi$
$858$		0			0
$859$	1194.00	+	689.356i	1.38999	+	0.802510i	0.993313	−	0.115449i	$-0.0368307\pi$
$859$	1194.00	+	689.356i	1.38999	+	0.802510i	0.396675	+	0.917959i	$0.370164\pi$
$860$		0			0
$861$	−396.000	−	311.769i	−0.459930	−	0.362101i
$862$		0			0
$863$	750.000	−	1299.04i	0.869061	−	1.50526i	0.00610429	−	0.999981i	$-0.498057\pi$
$863$	750.000	−	1299.04i	0.869061	−	1.50526i	0.862957	−	0.505277i	$-0.168610\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			500.563i			0.577350i
$868$		0			0
$869$	1140.00			1.31185
$870$		0			0
$871$	169.500	−	97.8609i	0.194604	−	0.112355i
$872$		0			0
$873$	−292.500	−	168.875i	−0.335052	−	0.193442i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−362.500	+	627.868i	−0.413341	+	0.715928i	−0.995253	−	0.0973244i	$-0.968972\pi$
$877$	−362.500	+	627.868i	−0.413341	+	0.715928i	0.581912	+	0.813252i	$0.302305\pi$
$878$		0			0
$879$	171.000	+	296.181i	0.194539	+	0.336952i
$880$		0			0
$881$		−	280.592i		−	0.318493i	−0.987239	−	0.159246i	$-0.949094\pi$
$881$		−	280.592i		−	0.318493i	0.987239	−	0.159246i	$-0.0509064\pi$
$882$		0			0
$883$	691.000			0.782559			0.391280	−	0.920272i	$-0.372032\pi$
$883$	691.000			0.782559			0.391280	+	0.920272i	$0.372032\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−279.000	−	161.081i	−0.314543	−	0.181602i	0.334414	−	0.942426i	$-0.391461\pi$
$887$	−279.000	−	161.081i	−0.314543	−	0.181602i	−0.648958	+	0.760824i	$0.724795\pi$
$888$		0			0
$889$	−708.500	+	283.190i	−0.796963	+	0.318549i
$890$		0			0
$891$	−54.0000	+	93.5307i	−0.0606061	+	0.104973i
$892$		0			0
$893$	243.000	+	420.888i	0.272116	+	0.471320i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	72.0000			0.0802676
$898$		0			0
$899$	108.000	−	62.3538i	0.120133	−	0.0693591i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−375.000	+	476.314i	−0.415282	+	0.527479i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	470.500	+	814.930i	0.518743	+	0.898489i	0.999763	+	0.0217796i	$0.00693322\pi$
$907$	470.500	+	814.930i	0.518743	+	0.898489i	−0.481020	+	0.876710i	$0.659733\pi$
$908$		0			0
$909$		−	62.3538i		−	0.0685961i
$910$		0			0
$911$	780.000			0.856202			0.428101	−	0.903731i	$-0.359183\pi$
$911$	780.000			0.856202			0.428101	+	0.903731i	$0.359183\pi$
$912$		0			0
$913$	108.000	−	62.3538i	0.118291	−	0.0682955i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	144.000	+	20.7846i	0.157034	+	0.0226659i
$918$		0			0
$919$	−809.000	+	1401.23i	−0.880305	+	1.52473i	−0.0293023	+	0.999571i	$0.509329\pi$
$919$	−809.000	+	1401.23i	−0.880305	+	1.52473i	−0.851002	+	0.525162i	$0.824005\pi$
$920$		0			0
$921$	−414.000	−	717.069i	−0.449511	−	0.778577i
$922$		0			0
$923$		−	51.9615i		−	0.0562963i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.5000	+	7.79423i	−0.0145631	+	0.00840801i
$928$		0			0
$929$	225.000	+	129.904i	0.242196	+	0.139832i	0.616186	−	0.787601i	$-0.288677\pi$
$929$	225.000	+	129.904i	0.242196	+	0.139832i	−0.373990	+	0.927433i	$0.622010\pi$
$930$		0			0
$931$	−742.500	+	179.267i	−0.797530	+	0.192553i
$932$		0			0
$933$	207.000	−	358.535i	0.221865	−	0.384281i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			6.92820i			0.00739403i	0.999993	+	0.00369701i	$0.00117680\pi$
$937$			6.92820i			0.00739403i	−0.999993	+	0.00369701i	$0.998823\pi$
$938$		0			0
$939$	552.000			0.587859
$940$		0			0
$941$	621.000	−	358.535i	0.659936	−	0.381014i	−0.132316	−	0.991208i	$-0.542242\pi$
$941$	621.000	−	358.535i	0.659936	−	0.381014i	0.792253	+	0.610193i	$0.208908\pi$
$942$		0			0
$943$	−864.000	−	498.831i	−0.916225	−	0.528983i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−135.000	+	233.827i	−0.142555	+	0.246913i	−0.928458	−	0.371437i	$-0.878865\pi$
$947$	−135.000	+	233.827i	−0.142555	+	0.246913i	0.785903	+	0.618350i	$0.212199\pi$
$948$		0			0
$949$	−10.5000	−	18.1865i	−0.0110643	−	0.0191639i
$950$		0			0
$951$		−	114.315i		−	0.120205i
$952$		0			0
$953$	−1266.00			−1.32844			−0.664218	−	0.747539i	$-0.731235\pi$
$953$	−1266.00			−1.32844			−0.664218	+	0.747539i	$0.731235\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	108.000	+	62.3538i	0.112853	+	0.0651555i
$958$		0			0
$959$	−858.000	−	675.500i	−0.894682	−	0.704379i
$960$		0			0
$961$	−264.500	+	458.127i	−0.275234	+	0.476719i
$962$		0			0
$963$	18.0000	+	31.1769i	0.0186916	+	0.0323748i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1151.00			1.19028			0.595140	−	0.803622i	$-0.297097\pi$
$967$	1151.00			1.19028			0.595140	+	0.803622i	$0.297097\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	441.000	+	254.611i	0.454171	+	0.262216i	0.709590	−	0.704615i	$-0.248880\pi$
$971$	441.000	+	254.611i	0.454171	+	0.262216i	−0.255419	+	0.966830i	$0.582213\pi$
$972$		0			0
$973$	40.5000	+	101.325i	0.0416238	+	0.104137i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	681.000	+	1179.53i	0.697032	+	1.20729i	0.969491	+	0.245127i	$0.0788297\pi$
$977$	681.000	+	1179.53i	0.697032	+	1.20729i	−0.272459	+	0.962167i	$0.587837\pi$
$978$		0			0
$979$		−	2120.03i		−	2.16551i
$980$		0			0
$981$	51.0000			0.0519878
$982$		0			0
$983$	864.000	−	498.831i	0.878942	−	0.507457i	0.00863259	−	0.999963i	$-0.497252\pi$
$983$	864.000	−	498.831i	0.878942	−	0.507457i	0.870309	+	0.492505i	$0.163919\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−351.000	+	140.296i	−0.355623	+	0.142144i
$988$		0			0
$989$	−600.000	+	1039.23i	−0.606673	+	1.05079i
$990$		0			0
$991$	−581.000	−	1006.32i	−0.586276	−	1.01546i	−0.994715	−	0.102675i	$-0.967260\pi$
$991$	−581.000	−	1006.32i	−0.586276	−	1.01546i	0.408438	−	0.912786i	$-0.366073\pi$
$992$		0			0
$993$			386.247i			0.388970i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1306.50	−	754.308i	1.31043	−	0.756578i	0.328264	−	0.944586i	$-0.393536\pi$
$997$	1306.50	−	754.308i	1.31043	−	0.756578i	0.982167	+	0.188008i	$0.0602032\pi$
$998$		0			0
$999$	31.5000	+	18.1865i	0.0315315	+	0.0182047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.3.bd.e.901.1	yes	2
5.2	odd	4		2100.3.be.b.649.1		4
5.3	odd	4		2100.3.be.b.649.2		4
5.4	even	2		2100.3.bd.a.901.1	✓	2
7.3	odd	6	inner	2100.3.bd.e.1501.1	yes	2
35.3	even	12		2100.3.be.b.1249.1		4
35.17	even	12		2100.3.be.b.1249.2		4
35.24	odd	6		2100.3.bd.a.1501.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.3.bd.a.901.1	✓	2	5.4	even	2
2100.3.bd.a.1501.1	yes	2	35.24	odd	6
2100.3.bd.e.901.1	yes	2	1.1	even	1	trivial
2100.3.bd.e.1501.1	yes	2	7.3	odd	6	inner
2100.3.be.b.649.1		4	5.2	odd	4
2100.3.be.b.649.2		4	5.3	odd	4
2100.3.be.b.1249.1		4	35.3	even	12
2100.3.be.b.1249.2		4	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(6.50000 - 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-6.00000 - 10.3923i) q^{11} +1.73205i q^{13} +(-13.5000 - 7.79423i) q^{19} +(7.50000 - 9.52628i) q^{21} +(12.0000 - 20.7846i) q^{23} -5.19615i q^{27} -6.00000 q^{29} +(-18.0000 + 10.3923i) q^{31} +(-18.0000 - 10.3923i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(1.50000 + 2.59808i) q^{39} -41.5692i q^{41} -50.0000 q^{43} +(-27.0000 - 15.5885i) q^{47} +(35.5000 - 33.7750i) q^{49} +(42.0000 + 72.7461i) q^{53} -27.0000 q^{57} +(27.0000 - 15.5885i) q^{59} +(-52.5000 - 30.3109i) q^{61} +(3.00000 - 20.7846i) q^{63} +(-56.5000 - 97.8609i) q^{67} -41.5692i q^{69} -30.0000 q^{71} +(-10.5000 + 6.06218i) q^{73} +(-66.0000 - 51.9615i) q^{77} +(-47.5000 + 82.2724i) q^{79} +(-4.50000 - 7.79423i) q^{81} +10.3923i q^{83} +(-9.00000 + 5.19615i) q^{87} +(153.000 + 88.3346i) q^{89} +(4.50000 + 11.2583i) q^{91} +(-18.0000 + 31.1769i) q^{93} -112.583i q^{97} -36.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 13 q^{7} + 3 q^{9} - 12 q^{11} - 27 q^{19} + 15 q^{21} + 24 q^{23} - 12 q^{29} - 36 q^{31} - 36 q^{33} - 7 q^{37} + 3 q^{39} - 100 q^{43} - 54 q^{47} + 71 q^{49} + 84 q^{53} - 54 q^{57}+ \cdots - 72 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 13 * q^7 + 3 * q^9 - 12 * q^11 - 27 * q^19 + 15 * q^21 + 24 * q^23 - 12 * q^29 - 36 * q^31 - 36 * q^33 - 7 * q^37 + 3 * q^39 - 100 * q^43 - 54 * q^47 + 71 * q^49 + 84 * q^53 - 54 * q^57 + 54 * q^59 - 105 * q^61 + 6 * q^63 - 113 * q^67 - 60 * q^71 - 21 * q^73 - 132 * q^77 - 95 * q^79 - 9 * q^81 - 18 * q^87 + 306 * q^89 + 9 * q^91 - 36 * q^93 - 72 * q^99

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