LMFDB - Embedded newform 2100.2.s.b.1457.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.9
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.b.1793.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27746 + 1.16966i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(0.263792 + 2.98838i) q^{9} +O(q^{10})$	\(q+(1.27746 + 1.16966i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(0.263792 + 2.98838i) q^{9} +2.66926i q^{11} +(-1.79204 + 1.79204i) q^{13} +(-1.27125 + 1.27125i) q^{17} +5.59577i q^{19} +(-0.0762239 - 1.73037i) q^{21} +(-6.30672 - 6.30672i) q^{23} +(-3.15841 + 4.12607i) q^{27} -0.475975 q^{29} -0.444136 q^{31} +(-3.12213 + 3.40987i) q^{33} +(-3.01080 - 3.01080i) q^{37} +(-4.38533 + 0.193177i) q^{39} +4.01600i q^{41} +(6.42331 - 6.42331i) q^{43} +(-0.964802 + 0.964802i) q^{47} +1.00000i q^{49} +(-3.11091 + 0.137037i) q^{51} +(-0.484079 - 0.484079i) q^{53} +(-6.54515 + 7.14835i) q^{57} -8.72277 q^{59} -2.10457 q^{61} +(1.92657 - 2.29963i) q^{63} +(8.71588 + 8.71588i) q^{67} +(-0.679845 - 15.4333i) q^{69} +11.4237i q^{71} +(-8.99671 + 8.99671i) q^{73} +(1.88745 - 1.88745i) q^{77} +10.3740i q^{79} +(-8.86083 + 1.57662i) q^{81} +(-6.12377 - 6.12377i) q^{83} +(-0.608037 - 0.556729i) q^{87} +5.60386 q^{89} +2.53433 q^{91} +(-0.567364 - 0.519488i) q^{93} +(12.6451 + 12.6451i) q^{97} +(-7.97677 + 0.704129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.27746	+	1.16966i	0.737540	+	0.675303i
$3$	1.27746	+	1.16966i	0.737540	+	0.675303i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$	0.263792	+	2.98838i	0.0879306	+	0.996127i
$10$		0			0
$11$			2.66926i			0.804813i	0.915461	+	0.402406i	$0.131826\pi$
$11$			2.66926i			0.804813i	−0.915461	+	0.402406i	$0.868174\pi$
$12$		0			0
$13$	−1.79204	+	1.79204i	−0.497023	+	0.497023i	−0.910510	−	0.413487i	$-0.864311\pi$
$13$	−1.79204	+	1.79204i	−0.497023	+	0.497023i	0.413487	+	0.910510i	$0.364311\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.27125	+	1.27125i	−0.308324	+	0.308324i	−0.844259	−	0.535935i	$-0.819959\pi$
$17$	−1.27125	+	1.27125i	−0.308324	+	0.308324i	0.535935	+	0.844259i	$0.319959\pi$
$18$		0			0
$19$			5.59577i			1.28376i	0.766806	+	0.641879i	$0.221845\pi$
$19$			5.59577i			1.28376i	−0.766806	+	0.641879i	$0.778155\pi$
$20$		0			0
$21$	−0.0762239	−	1.73037i	−0.0166334	−	0.377598i
$22$		0			0
$23$	−6.30672	−	6.30672i	−1.31504	−	1.31504i	−0.917647	−	0.397395i	$-0.869914\pi$
$23$	−6.30672	−	6.30672i	−1.31504	−	1.31504i	−0.397395	−	0.917647i	$-0.630086\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.15841	+	4.12607i	−0.607835	+	0.794063i
$28$		0			0
$29$	−0.475975			−0.0883863			−0.0441932	−	0.999023i	$-0.514072\pi$
$29$	−0.475975			−0.0883863			−0.0441932	+	0.999023i	$0.514072\pi$
$30$		0			0
$31$	−0.444136			−0.0797691			−0.0398846	−	0.999204i	$-0.512699\pi$
$31$	−0.444136			−0.0797691			−0.0398846	+	0.999204i	$0.512699\pi$
$32$		0			0
$33$	−3.12213	+	3.40987i	−0.543493	+	0.593581i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.01080	−	3.01080i	−0.494972	−	0.494972i	0.414897	−	0.909869i	$-0.363818\pi$
$37$	−3.01080	−	3.01080i	−0.494972	−	0.494972i	−0.909869	+	0.414897i	$0.863818\pi$
$38$		0			0
$39$	−4.38533	+	0.193177i	−0.702215	+	0.0309330i
$40$		0			0
$41$			4.01600i			0.627193i	0.949556	+	0.313597i	$0.101534\pi$
$41$			4.01600i			0.627193i	−0.949556	+	0.313597i	$0.898466\pi$
$42$		0			0
$43$	6.42331	−	6.42331i	0.979545	−	0.979545i	−0.0202500	−	0.999795i	$-0.506446\pi$
$43$	6.42331	−	6.42331i	0.979545	−	0.979545i	0.999795	+	0.0202500i	$0.00644620\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.964802	+	0.964802i	−0.140731	+	0.140731i	−0.773962	−	0.633232i	$-0.781728\pi$
$47$	−0.964802	+	0.964802i	−0.140731	+	0.140731i	0.633232	+	0.773962i	$0.281728\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−3.11091	+	0.137037i	−0.435614	+	0.0191890i
$52$		0			0
$53$	−0.484079	−	0.484079i	−0.0664933	−	0.0664933i	0.673078	−	0.739571i	$-0.264972\pi$
$53$	−0.484079	−	0.484079i	−0.0664933	−	0.0664933i	−0.739571	+	0.673078i	$0.764972\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.54515	+	7.14835i	−0.866926	+	0.946823i
$58$		0			0
$59$	−8.72277			−1.13561			−0.567804	−	0.823164i	$-0.692207\pi$
$59$	−8.72277			−1.13561			−0.567804	+	0.823164i	$0.692207\pi$
$60$		0			0
$61$	−2.10457			−0.269463			−0.134731	−	0.990882i	$-0.543017\pi$
$61$	−2.10457			−0.269463			−0.134731	+	0.990882i	$0.543017\pi$
$62$		0			0
$63$	1.92657	−	2.29963i	0.242726	−	0.289726i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.71588	+	8.71588i	1.06481	+	1.06481i	0.997749	+	0.0670663i	$0.0213639\pi$
$67$	8.71588	+	8.71588i	1.06481	+	1.06481i	0.0670663	+	0.997749i	$0.478636\pi$
$68$		0			0
$69$	−0.679845	−	15.4333i	−0.0818438	−	1.85795i
$70$		0			0
$71$			11.4237i			1.35575i	0.735179	+	0.677873i	$0.237098\pi$
$71$			11.4237i			1.35575i	−0.735179	+	0.677873i	$0.762902\pi$
$72$		0			0
$73$	−8.99671	+	8.99671i	−1.05299	+	1.05299i	−0.0544701	+	0.998515i	$0.517347\pi$
$73$	−8.99671	+	8.99671i	−1.05299	+	1.05299i	−0.998515	+	0.0544701i	$0.982653\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.88745	−	1.88745i	0.215095	−	0.215095i
$78$		0			0
$79$			10.3740i			1.16717i	0.812053	+	0.583583i	$0.198350\pi$
$79$			10.3740i			1.16717i	−0.812053	+	0.583583i	$0.801650\pi$
$80$		0			0
$81$	−8.86083	+	1.57662i	−0.984536	+	0.175180i
$82$		0			0
$83$	−6.12377	−	6.12377i	−0.672171	−	0.672171i	0.286045	−	0.958216i	$-0.407659\pi$
$83$	−6.12377	−	6.12377i	−0.672171	−	0.672171i	−0.958216	+	0.286045i	$0.907659\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.608037	−	0.556729i	−0.0651884	−	0.0596876i
$88$		0			0
$89$	5.60386			0.594008			0.297004	−	0.954876i	$-0.404013\pi$
$89$	5.60386			0.594008			0.297004	+	0.954876i	$0.404013\pi$
$90$		0			0
$91$	2.53433			0.265670
$92$		0			0
$93$	−0.567364	−	0.519488i	−0.0588329	−	0.0538684i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.6451	+	12.6451i	1.28392	+	1.28392i	0.938420	+	0.345495i	$0.112289\pi$
$97$	12.6451	+	12.6451i	1.28392	+	1.28392i	0.345495	+	0.938420i	$0.387711\pi$
$98$		0			0
$99$	−7.97677	+	0.704129i	−0.801695	+	0.0707676i
$100$		0			0
$101$			12.4047i			1.23431i	0.786841	+	0.617156i	$0.211715\pi$
$101$			12.4047i			1.23431i	−0.786841	+	0.617156i	$0.788285\pi$
$102$		0			0
$103$	8.62130	−	8.62130i	0.849482	−	0.849482i	−0.140587	−	0.990068i	$-0.544899\pi$
$103$	8.62130	−	8.62130i	0.849482	−	0.849482i	0.990068	+	0.140587i	$0.0448989\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.2775	+	11.2775i	−1.09023	+	1.09023i	−0.0947294	+	0.995503i	$0.530199\pi$
$107$	−11.2775	+	11.2775i	−1.09023	+	1.09023i	−0.995503	+	0.0947294i	$0.969801\pi$
$108$		0			0
$109$		−	13.3852i		−	1.28207i	−0.767514	−	0.641033i	$-0.778506\pi$
$109$		−	13.3852i		−	1.28207i	0.767514	−	0.641033i	$-0.221494\pi$
$110$		0			0
$111$	−0.324555	−	7.36777i	−0.0308054	−	0.699318i
$112$		0			0
$113$	2.01522	+	2.01522i	0.189576	+	0.189576i	0.795513	−	0.605937i	$-0.207202\pi$
$113$	2.01522	+	2.01522i	0.189576	+	0.189576i	−0.605937	+	0.795513i	$0.707202\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.82802	−	4.88257i	−0.538801	−	0.451394i
$118$		0			0
$119$	1.79782			0.164806
$120$		0			0
$121$	3.87504			0.352277
$122$		0			0
$123$	−4.69735	+	5.13026i	−0.423546	+	0.462580i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.33400	−	8.33400i	−0.739523	−	0.739523i	0.232962	−	0.972486i	$-0.425158\pi$
$127$	−8.33400	−	8.33400i	−0.739523	−	0.739523i	−0.972486	+	0.232962i	$0.925158\pi$
$128$		0			0
$129$	15.7186	−	0.692413i	1.38394	−	0.0609635i
$130$		0			0
$131$		−	1.60764i		−	0.140460i	−0.997531	−	0.0702299i	$-0.977627\pi$
$131$		−	1.60764i		−	0.140460i	0.997531	−	0.0702299i	$-0.0223733\pi$
$132$		0			0
$133$	3.95681	−	3.95681i	0.343099	−	0.343099i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.3887	+	13.3887i	−1.14387	+	1.14387i	−0.156137	+	0.987735i	$0.549904\pi$
$137$	−13.3887	+	13.3887i	−1.14387	+	1.14387i	−0.987735	+	0.156137i	$0.950096\pi$
$138$		0			0
$139$		−	18.5750i		−	1.57551i	−0.615988	−	0.787755i	$-0.711243\pi$
$139$		−	18.5750i		−	1.57551i	0.615988	−	0.787755i	$-0.288757\pi$
$140$		0			0
$141$	−2.36098	+	0.104003i	−0.198831	+	0.00875861i
$142$		0			0
$143$	−4.78343	−	4.78343i	−0.400010	−	0.400010i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.16966	+	1.27746i	−0.0964719	+	0.105363i
$148$		0			0
$149$	−21.1846			−1.73551			−0.867754	−	0.496994i	$-0.834437\pi$
$149$	−21.1846			−1.73551			−0.867754	+	0.496994i	$0.834437\pi$
$150$		0			0
$151$	19.6302			1.59748			0.798742	−	0.601674i	$-0.205499\pi$
$151$	19.6302			1.59748			0.798742	+	0.601674i	$0.205499\pi$
$152$		0			0
$153$	−4.13433	−	3.46364i	−0.334241	−	0.280019i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.67010	−	8.67010i	−0.691949	−	0.691949i	0.270712	−	0.962661i	$-0.412741\pi$
$157$	−8.67010	−	8.67010i	−0.691949	−	0.691949i	−0.962661	+	0.270712i	$0.912741\pi$
$158$		0			0
$159$	−0.0521822	−	1.18460i	−0.00413832	−	0.0939447i
$160$		0			0
$161$			8.91905i			0.702920i
$162$		0			0
$163$	5.49057	−	5.49057i	0.430054	−	0.430054i	−0.458592	−	0.888647i	$-0.651646\pi$
$163$	5.49057	−	5.49057i	0.430054	−	0.430054i	0.888647	+	0.458592i	$0.151646\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.27850	−	2.27850i	0.176316	−	0.176316i	−0.613432	−	0.789748i	$-0.710211\pi$
$167$	2.27850	−	2.27850i	0.176316	−	0.176316i	0.789748	+	0.613432i	$0.210211\pi$
$168$		0			0
$169$			6.57718i			0.505937i
$170$		0			0
$171$	−16.7223	+	1.47612i	−1.27879	+	0.112882i
$172$		0			0
$173$	1.59286	+	1.59286i	0.121103	+	0.121103i	0.765061	−	0.643958i	$-0.222709\pi$
$173$	1.59286	+	1.59286i	0.121103	+	0.121103i	−0.643958	+	0.765061i	$0.722709\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.1430	−	10.2027i	−0.837557	−	0.766880i
$178$		0			0
$179$	20.3198			1.51877			0.759386	−	0.650640i	$-0.225499\pi$
$179$	20.3198			1.51877			0.759386	+	0.650640i	$0.225499\pi$
$180$		0			0
$181$	11.0406			0.820642			0.410321	−	0.911941i	$-0.365417\pi$
$181$	11.0406			0.820642			0.410321	+	0.911941i	$0.365417\pi$
$182$		0			0
$183$	−2.68850	−	2.46163i	−0.198740	−	0.181969i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.39331	−	3.39331i	−0.248143	−	0.248143i
$188$		0			0
$189$	5.15090	−	0.684244i	0.374673	−	0.0497714i
$190$		0			0
$191$		−	17.8623i		−	1.29247i	−0.763138	−	0.646236i	$-0.776342\pi$
$191$		−	17.8623i		−	1.29247i	0.763138	−	0.646236i	$-0.223658\pi$
$192$		0			0
$193$	10.1871	−	10.1871i	0.733281	−	0.733281i	−0.237987	−	0.971268i	$-0.576488\pi$
$193$	10.1871	−	10.1871i	0.733281	−	0.733281i	0.971268	+	0.237987i	$0.0764876\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.883558	−	0.883558i	0.0629509	−	0.0629509i	−0.674930	−	0.737881i	$-0.735826\pi$
$197$	0.883558	−	0.883558i	0.0629509	−	0.0629509i	0.737881	+	0.674930i	$0.235826\pi$
$198$		0			0
$199$			14.8123i			1.05002i	0.851097	+	0.525009i	$0.175938\pi$
$199$			14.8123i			1.05002i	−0.851097	+	0.525009i	$0.824062\pi$
$200$		0			0
$201$	0.939546	+	21.3288i	0.0662704	+	1.50442i
$202$		0			0
$203$	0.336565	+	0.336565i	0.0236222	+	0.0236222i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	17.1832	−	20.5105i	1.19432	−	1.42558i
$208$		0			0
$209$	−14.9366			−1.03318
$210$		0			0
$211$	14.9856			1.03165			0.515825	−	0.856694i	$-0.327486\pi$
$211$	14.9856			1.03165			0.515825	+	0.856694i	$0.327486\pi$
$212$		0			0
$213$	−13.3619	+	14.5933i	−0.915540	+	0.999917i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.314051	+	0.314051i	0.0213192	+	0.0213192i
$218$		0			0
$219$	−22.0160	+	0.969818i	−1.48770	+	0.0655342i
$220$		0			0
$221$		−	4.55628i		−	0.306488i
$222$		0			0
$223$	−5.47628	+	5.47628i	−0.366719	+	0.366719i	−0.866279	−	0.499560i	$-0.833495\pi$
$223$	−5.47628	+	5.47628i	−0.366719	+	0.366719i	0.499560	+	0.866279i	$0.333495\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.0160	−	10.0160i	0.664784	−	0.664784i	−0.291720	−	0.956504i	$-0.594228\pi$
$227$	10.0160	−	10.0160i	0.664784	−	0.664784i	0.956504	+	0.291720i	$0.0942275\pi$
$228$		0			0
$229$			12.7390i			0.841817i	0.907103	+	0.420908i	$0.138289\pi$
$229$			12.7390i			0.841817i	−0.907103	+	0.420908i	$0.861711\pi$
$230$		0			0
$231$	4.61882	−	0.203462i	0.303896	−	0.0133868i
$232$		0			0
$233$	6.64712	+	6.64712i	0.435467	+	0.435467i	0.890483	−	0.455016i	$-0.150366\pi$
$233$	6.64712	+	6.64712i	0.435467	+	0.435467i	−0.455016	+	0.890483i	$0.650366\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−12.1341	+	13.2523i	−0.788191	+	0.860832i
$238$		0			0
$239$	−15.9148			−1.02944			−0.514720	−	0.857358i	$-0.672104\pi$
$239$	−15.9148			−1.02944			−0.514720	+	0.857358i	$0.672104\pi$
$240$		0			0
$241$	3.83380			0.246957			0.123478	−	0.992347i	$-0.460595\pi$
$241$	3.83380			0.246957			0.123478	+	0.992347i	$0.460595\pi$
$242$		0			0
$243$	−13.1634	−	8.35009i	−0.844435	−	0.535659i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−10.0278	−	10.0278i	−0.638057	−	0.638057i
$248$		0			0
$249$	−0.660123	−	14.9856i	−0.0418336	−	0.949672i
$250$		0			0
$251$		−	13.9866i		−	0.882829i	−0.897303	−	0.441415i	$-0.854477\pi$
$251$		−	13.9866i		−	0.882829i	0.897303	−	0.441415i	$-0.145523\pi$
$252$		0			0
$253$	16.8343	−	16.8343i	1.05836	−	1.05836i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.37271	−	6.37271i	0.397519	−	0.397519i	−0.479838	−	0.877357i	$-0.659305\pi$
$257$	6.37271	−	6.37271i	0.397519	−	0.397519i	0.877357	+	0.479838i	$0.159305\pi$
$258$		0			0
$259$			4.25791i			0.264574i
$260$		0			0
$261$	−0.125558	−	1.42239i	−0.00777186	−	0.0880440i
$262$		0			0
$263$	2.37801	+	2.37801i	0.146634	+	0.146634i	0.776613	−	0.629978i	$-0.216936\pi$
$263$	2.37801	+	2.37801i	0.146634	+	0.146634i	−0.629978	+	0.776613i	$0.716936\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.15868	+	6.55461i	0.438104	+	0.401135i
$268$		0			0
$269$	25.5152			1.55569			0.777843	−	0.628459i	$-0.216314\pi$
$269$	25.5152			1.55569			0.777843	+	0.628459i	$0.216314\pi$
$270$		0			0
$271$	7.39006			0.448914			0.224457	−	0.974484i	$-0.427939\pi$
$271$	7.39006			0.448914			0.224457	+	0.974484i	$0.427939\pi$
$272$		0			0
$273$	3.23750	+	2.96430i	0.195942	+	0.179408i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.79932	+	3.79932i	0.228279	+	0.228279i	0.811973	−	0.583694i	$-0.198393\pi$
$277$	3.79932	+	3.79932i	0.228279	+	0.228279i	−0.583694	+	0.811973i	$0.698393\pi$
$278$		0			0
$279$	−0.117159	−	1.32725i	−0.00701414	−	0.0794602i
$280$		0			0
$281$		−	29.5840i		−	1.76484i	−0.470466	−	0.882418i	$-0.655914\pi$
$281$		−	29.5840i		−	1.76484i	0.470466	−	0.882418i	$-0.344086\pi$
$282$		0			0
$283$	−2.07493	+	2.07493i	−0.123342	+	0.123342i	−0.766083	−	0.642741i	$-0.777797\pi$
$283$	−2.07493	+	2.07493i	−0.123342	+	0.123342i	0.642741	+	0.766083i	$0.277797\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.83974	−	2.83974i	0.167624	−	0.167624i
$288$		0			0
$289$			13.7678i			0.809872i
$290$		0			0
$291$	1.36310	+	30.9440i	0.0799065	+	1.81397i
$292$		0			0
$293$	13.4481	+	13.4481i	0.785644	+	0.785644i	0.980777	−	0.195133i	$-0.0625138\pi$
$293$	13.4481	+	13.4481i	0.785644	+	0.785644i	−0.195133	+	0.980777i	$0.562514\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−11.0136	−	8.43061i	−0.639072	−	0.489194i
$298$		0			0
$299$	22.6038			1.30721
$300$		0			0
$301$	−9.08393			−0.523589
$302$		0			0
$303$	−14.5093	+	15.8465i	−0.833535	+	0.910355i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.7929	+	11.7929i	0.673055	+	0.673055i	0.958419	−	0.285364i	$-0.0921147\pi$
$307$	11.7929	+	11.7929i	0.673055	+	0.673055i	−0.285364	+	0.958419i	$0.592115\pi$
$308$		0			0
$309$	21.0973	−	0.929349i	1.20018	−	0.0528688i
$310$		0			0
$311$			6.97298i			0.395402i	0.980262	+	0.197701i	$0.0633474\pi$
$311$			6.97298i			0.395402i	−0.980262	+	0.197701i	$0.936653\pi$
$312$		0			0
$313$	−13.3101	+	13.3101i	−0.752330	+	0.752330i	−0.974914	−	0.222584i	$-0.928551\pi$
$313$	−13.3101	+	13.3101i	−0.752330	+	0.752330i	0.222584	+	0.974914i	$0.428551\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.5663	+	15.5663i	−0.874288	+	0.874288i	−0.992936	−	0.118648i	$-0.962144\pi$
$317$	−15.5663	+	15.5663i	−0.874288	+	0.874288i	0.118648	+	0.992936i	$0.462144\pi$
$318$		0			0
$319$		−	1.27050i		−	0.0711344i
$320$		0			0
$321$	−27.5972	+	1.21567i	−1.54033	+	0.0678523i
$322$		0			0
$323$	−7.11364	−	7.11364i	−0.395814	−	0.395814i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	15.6561	−	17.0990i	0.865783	−	0.945574i
$328$		0			0
$329$	1.36444			0.0752238
$330$		0			0
$331$	−11.1958			−0.615379			−0.307690	−	0.951487i	$-0.599556\pi$
$331$	−11.1958			−0.615379			−0.307690	+	0.951487i	$0.599556\pi$
$332$		0			0
$333$	8.20318	−	9.79163i	0.449532	−	0.536578i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	21.1259	+	21.1259i	1.15080	+	1.15080i	0.986392	+	0.164411i	$0.0525723\pi$
$337$	21.1259	+	21.1259i	1.15080	+	1.15080i	0.164411	+	0.986392i	$0.447428\pi$
$338$		0			0
$339$	0.217235	+	4.93148i	0.0117986	+	0.267841i
$340$		0			0
$341$		−	1.18551i		−	0.0641992i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.85696	+	2.85696i	−0.153370	+	0.153370i	−0.779621	−	0.626251i	$-0.784588\pi$
$347$	−2.85696	+	2.85696i	−0.153370	+	0.153370i	0.626251	+	0.779621i	$0.284588\pi$
$348$		0			0
$349$			28.9735i			1.55091i	0.631400	+	0.775457i	$0.282481\pi$
$349$			28.9735i			1.55091i	−0.631400	+	0.775457i	$0.717519\pi$
$350$		0			0
$351$	−1.73410	−	13.0541i	−0.0925594	−	0.696775i
$352$		0			0
$353$	15.9357	+	15.9357i	0.848171	+	0.848171i	0.989905	−	0.141733i	$-0.0452676\pi$
$353$	15.9357	+	15.9357i	0.848171	+	0.848171i	−0.141733	+	0.989905i	$0.545268\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.29664	+	2.10284i	0.121551	+	0.111294i
$358$		0			0
$359$	−11.3154			−0.597205			−0.298603	−	0.954378i	$-0.596520\pi$
$359$	−11.3154			−0.597205			−0.298603	+	0.954378i	$0.596520\pi$
$360$		0			0
$361$	−12.3126			−0.648034
$362$		0			0
$363$	4.95020	+	4.53248i	0.259818	+	0.237894i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	19.6706	+	19.6706i	1.02679	+	1.02679i	0.999631	+	0.0271636i	$0.00864749\pi$
$367$	19.6706	+	19.6706i	1.02679	+	1.02679i	0.0271636	+	0.999631i	$0.491353\pi$
$368$		0			0
$369$	−12.0013	+	1.05939i	−0.624764	+	0.0551495i
$370$		0			0
$371$			0.684591i			0.0355422i
$372$		0			0
$373$	−2.02204	+	2.02204i	−0.104697	+	0.104697i	−0.757515	−	0.652818i	$-0.773587\pi$
$373$	−2.02204	+	2.02204i	−0.104697	+	0.104697i	0.652818	+	0.757515i	$0.273587\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.852966	−	0.852966i	0.0439300	−	0.0439300i
$378$		0			0
$379$		−	24.9963i		−	1.28397i	−0.766716	−	0.641986i	$-0.778111\pi$
$379$		−	24.9963i		−	1.28397i	0.766716	−	0.641986i	$-0.221889\pi$
$380$		0			0
$381$	−0.898380	−	20.3943i	−0.0460254	−	1.04483i
$382$		0			0
$383$	15.9362	+	15.9362i	0.814300	+	0.814300i	0.985275	−	0.170975i	$-0.0546917\pi$
$383$	15.9362	+	15.9362i	0.814300	+	0.814300i	−0.170975	+	0.985275i	$0.554692\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	20.8897	+	17.5009i	1.06188	+	0.889619i
$388$		0			0
$389$	16.8000			0.851792			0.425896	−	0.904772i	$-0.359959\pi$
$389$	16.8000			0.851792			0.425896	+	0.904772i	$0.359959\pi$
$390$		0			0
$391$	16.0349			0.810919
$392$		0			0
$393$	1.88039	−	2.05369i	0.0948530	−	0.103595i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.55276	+	2.55276i	0.128119	+	0.128119i	0.768259	−	0.640139i	$-0.221123\pi$
$397$	2.55276	+	2.55276i	0.128119	+	0.128119i	−0.640139	+	0.768259i	$0.721123\pi$
$398$		0			0
$399$	9.68277	−	0.426532i	0.484745	−	0.0213533i
$400$		0			0
$401$		−	19.8000i		−	0.988764i	−0.869245	−	0.494382i	$-0.835394\pi$
$401$		−	19.8000i		−	0.988764i	0.869245	−	0.494382i	$-0.164606\pi$
$402$		0			0
$403$	0.795909	−	0.795909i	0.0396471	−	0.0396471i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.03660	−	8.03660i	0.398360	−	0.398360i
$408$		0			0
$409$			19.5780i			0.968071i	0.875048	+	0.484036i	$0.160829\pi$
$409$			19.5780i			0.968071i	−0.875048	+	0.484036i	$0.839171\pi$
$410$		0			0
$411$	−32.7637	+	1.44326i	−1.61611	+	0.0711907i
$412$		0			0
$413$	6.16793	+	6.16793i	0.303504	+	0.303504i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	21.7264	−	23.7288i	1.06395	−	1.16200i
$418$		0			0
$419$	−37.3282			−1.82360			−0.911800	−	0.410635i	$-0.865307\pi$
$419$	−37.3282			−1.82360			−0.911800	+	0.410635i	$0.865307\pi$
$420$		0			0
$421$	−5.98929			−0.291900			−0.145950	−	0.989292i	$-0.546624\pi$
$421$	−5.98929			−0.291900			−0.145950	+	0.989292i	$0.546624\pi$
$422$		0			0
$423$	−3.13770	−	2.62869i	−0.152560	−	0.127811i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.48816	+	1.48816i	0.0720170	+	0.0720170i
$428$		0			0
$429$	−0.515639	−	11.7056i	−0.0248953	−	0.565152i
$430$		0			0
$431$		−	33.2463i		−	1.60142i	−0.599054	−	0.800708i	$-0.704457\pi$
$431$		−	33.2463i		−	1.60142i	0.599054	−	0.800708i	$-0.295543\pi$
$432$		0			0
$433$	10.5209	−	10.5209i	0.505605	−	0.505605i	−0.407570	−	0.913174i	$-0.633624\pi$
$433$	10.5209	−	10.5209i	0.505605	−	0.505605i	0.913174	+	0.407570i	$0.133624\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	35.2910	−	35.2910i	1.68820	−	1.68820i
$438$		0			0
$439$		−	15.4243i		−	0.736160i	−0.929794	−	0.368080i	$-0.880015\pi$
$439$		−	15.4243i		−	0.736160i	0.929794	−	0.368080i	$-0.119985\pi$
$440$		0			0
$441$	−2.98838	+	0.263792i	−0.142304	+	0.0125615i
$442$		0			0
$443$	−24.4400	−	24.4400i	−1.16118	−	1.16118i	−0.984218	−	0.176961i	$-0.943373\pi$
$443$	−24.4400	−	24.4400i	−1.16118	−	1.16118i	−0.176961	−	0.984218i	$-0.556627\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−27.0624	−	24.7787i	−1.28001	−	1.17199i
$448$		0			0
$449$	9.04423			0.426824			0.213412	−	0.976962i	$-0.431542\pi$
$449$	9.04423			0.426824			0.213412	+	0.976962i	$0.431542\pi$
$450$		0			0
$451$	−10.7197			−0.504773
$452$		0			0
$453$	25.0767	+	22.9607i	1.17821	+	1.07879i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.45007	+	5.45007i	0.254944	+	0.254944i	0.822994	−	0.568050i	$-0.192302\pi$
$457$	5.45007	+	5.45007i	0.254944	+	0.254944i	−0.568050	+	0.822994i	$0.692302\pi$
$458$		0			0
$459$	−1.23015	−	9.26042i	−0.0574185	−	0.432239i
$460$		0			0
$461$			24.1279i			1.12375i	0.827223	+	0.561873i	$0.189919\pi$
$461$			24.1279i			1.12375i	−0.827223	+	0.561873i	$0.810081\pi$
$462$		0			0
$463$	−6.28613	+	6.28613i	−0.292141	+	0.292141i	−0.837926	−	0.545784i	$-0.816232\pi$
$463$	−6.28613	+	6.28613i	−0.292141	+	0.292141i	0.545784	+	0.837926i	$0.316232\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.26765	−	6.26765i	0.290032	−	0.290032i	−0.547061	−	0.837093i	$-0.684253\pi$
$467$	6.26765	−	6.26765i	0.290032	−	0.290032i	0.837093	+	0.547061i	$0.184253\pi$
$468$		0			0
$469$		−	12.3261i		−	0.569167i
$470$		0			0
$471$	−0.934610	−	21.2167i	−0.0430645	−	0.977616i
$472$		0			0
$473$	17.1455	+	17.1455i	0.788350	+	0.788350i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.31892	−	1.57431i	0.0603890	−	0.0720826i
$478$		0			0
$479$	20.3706			0.930754			0.465377	−	0.885112i	$-0.345919\pi$
$479$	20.3706			0.930754			0.465377	+	0.885112i	$0.345919\pi$
$480$		0			0
$481$	10.7909			0.492025
$482$		0			0
$483$	−10.4323	+	11.3937i	−0.474684	+	0.518432i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.973120	−	0.973120i	−0.0440963	−	0.0440963i	0.684715	−	0.728811i	$-0.259927\pi$
$487$	−0.973120	−	0.973120i	−0.0440963	−	0.0440963i	−0.728811	+	0.684715i	$0.759927\pi$
$488$		0			0
$489$	13.4361	−	0.591866i	0.607600	−	0.0267651i
$490$		0			0
$491$		−	1.61037i		−	0.0726748i	−0.999340	−	0.0363374i	$-0.988431\pi$
$491$		−	1.61037i		−	0.0726748i	0.999340	−	0.0363374i	$-0.0115691\pi$
$492$		0			0
$493$	0.605085	−	0.605085i	0.0272516	−	0.0272516i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.07779	−	8.07779i	0.362338	−	0.362338i
$498$		0			0
$499$		−	25.2071i		−	1.12842i	−0.825630	−	0.564212i	$-0.809180\pi$
$499$		−	25.2071i		−	1.12842i	0.825630	−	0.564212i	$-0.190820\pi$
$500$		0			0
$501$	5.57576	−	0.245616i	0.249107	−	0.0109733i
$502$		0			0
$503$	−21.1786	−	21.1786i	−0.944306	−	0.944306i	0.0542227	−	0.998529i	$-0.482732\pi$
$503$	−21.1786	−	21.1786i	−0.944306	−	0.944306i	−0.998529	+	0.0542227i	$0.982732\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.69306	+	8.40206i	−0.341661	+	0.373149i
$508$		0			0
$509$	28.4419			1.26066			0.630332	−	0.776326i	$-0.282919\pi$
$509$	28.4419			1.26066			0.630332	+	0.776326i	$0.282919\pi$
$510$		0			0
$511$	12.7233			0.562844
$512$		0			0
$513$	−23.0886	−	17.6737i	−1.01938	−	0.780313i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.57531	−	2.57531i	−0.113262	−	0.113262i
$518$		0			0
$519$	0.171705	+	3.89791i	0.00753702	+	0.171099i
$520$		0			0
$521$			18.3688i			0.804753i	0.915474	+	0.402377i	$0.131816\pi$
$521$			18.3688i			0.804753i	−0.915474	+	0.402377i	$0.868184\pi$
$522$		0			0
$523$	1.13799	−	1.13799i	0.0497609	−	0.0497609i	−0.681788	−	0.731549i	$-0.738798\pi$
$523$	1.13799	−	1.13799i	0.0497609	−	0.0497609i	0.731549	+	0.681788i	$0.238798\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.564609	−	0.564609i	0.0245948	−	0.0245948i
$528$		0			0
$529$			56.5495i			2.45868i
$530$		0			0
$531$	−2.30099	−	26.0670i	−0.0998547	−	1.13121i
$532$		0			0
$533$	−7.19683	−	7.19683i	−0.311729	−	0.311729i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	25.9577	+	23.7672i	1.12016	+	1.02563i
$538$		0			0
$539$	−2.66926			−0.114973
$540$		0			0
$541$	7.24013			0.311277			0.155639	−	0.987814i	$-0.450256\pi$
$541$	7.24013			0.311277			0.155639	+	0.987814i	$0.450256\pi$
$542$		0			0
$543$	14.1039	+	12.9138i	0.605256	+	0.554182i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−19.3360	−	19.3360i	−0.826748	−	0.826748i	0.160317	−	0.987066i	$-0.448748\pi$
$547$	−19.3360	−	19.3360i	−0.826748	−	0.826748i	−0.987066	+	0.160317i	$0.948748\pi$
$548$		0			0
$549$	−0.555168	−	6.28926i	−0.0236940	−	0.268419i
$550$		0			0
$551$		−	2.66345i		−	0.113467i
$552$		0			0
$553$	7.33553	−	7.33553i	0.311938	−	0.311938i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.47041	+	1.47041i	−0.0623034	+	0.0623034i	−0.737572	−	0.675269i	$-0.764028\pi$
$557$	−1.47041	+	1.47041i	−0.0623034	+	0.0623034i	0.675269	+	0.737572i	$0.264028\pi$
$558$		0			0
$559$			23.0217i			0.973712i
$560$		0			0
$561$	−0.365788	−	8.30382i	−0.0154436	−	0.350588i
$562$		0			0
$563$	15.3206	+	15.3206i	0.645685	+	0.645685i	0.951947	−	0.306262i	$-0.0990784\pi$
$563$	15.3206	+	15.3206i	0.645685	+	0.645685i	−0.306262	+	0.951947i	$0.599078\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7.38039	+	5.15071i	0.309947	+	0.216310i
$568$		0			0
$569$	−21.1530			−0.886779			−0.443390	−	0.896329i	$-0.646224\pi$
$569$	−21.1530			−0.886779			−0.443390	+	0.896329i	$0.646224\pi$
$570$		0			0
$571$	24.8161			1.03852			0.519260	−	0.854616i	$-0.326208\pi$
$571$	24.8161			1.03852			0.519260	+	0.854616i	$0.326208\pi$
$572$		0			0
$573$	20.8928	−	22.8183i	0.872811	−	0.953250i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−17.5100	−	17.5100i	−0.728952	−	0.728952i	0.241459	−	0.970411i	$-0.422374\pi$
$577$	−17.5100	−	17.5100i	−0.728952	−	0.728952i	−0.970411	+	0.241459i	$0.922374\pi$
$578$		0			0
$579$	24.9289	−	1.09813i	1.03601	−	0.0456369i
$580$		0			0
$581$			8.66031i			0.359290i
$582$		0			0
$583$	1.29213	−	1.29213i	0.0535147	−	0.0535147i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.76500	−	5.76500i	0.237947	−	0.237947i	−0.578053	−	0.816000i	$-0.696187\pi$
$587$	5.76500	−	5.76500i	0.237947	−	0.237947i	0.816000	+	0.578053i	$0.196187\pi$
$588$		0			0
$589$		−	2.48528i		−	0.102404i
$590$		0			0
$591$	2.16217	−	0.0952449i	0.0889398	−	0.00391785i
$592$		0			0
$593$	12.9961	+	12.9961i	0.533687	+	0.533687i	0.921667	−	0.387981i	$-0.126827\pi$
$593$	12.9961	+	12.9961i	0.533687	+	0.533687i	−0.387981	+	0.921667i	$0.626827\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−17.3254	+	18.9221i	−0.709080	+	0.774430i
$598$		0			0
$599$	10.2770			0.419907			0.209954	−	0.977711i	$-0.432669\pi$
$599$	10.2770			0.419907			0.209954	+	0.977711i	$0.432669\pi$
$600$		0			0
$601$	18.0122			0.734734			0.367367	−	0.930076i	$-0.380259\pi$
$601$	18.0122			0.734734			0.367367	+	0.930076i	$0.380259\pi$
$602$		0			0
$603$	−23.7472	+	28.3456i	−0.967061	+	1.15432i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.7602	−	18.7602i	−0.761452	−	0.761452i	0.215133	−	0.976585i	$-0.430981\pi$
$607$	−18.7602	−	18.7602i	−0.761452	−	0.761452i	−0.976585	+	0.215133i	$0.930981\pi$
$608$		0			0
$609$	0.0362807	+	0.823614i	0.00147017	+	0.0333745i
$610$		0			0
$611$		−	3.45793i		−	0.139893i
$612$		0			0
$613$	−8.21630	+	8.21630i	−0.331853	+	0.331853i	−0.853290	−	0.521437i	$-0.825396\pi$
$613$	−8.21630	+	8.21630i	−0.331853	+	0.331853i	0.521437	+	0.853290i	$0.325396\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.81959	−	8.81959i	0.355063	−	0.355063i	−0.506926	−	0.861989i	$-0.669218\pi$
$617$	8.81959	−	8.81959i	0.355063	−	0.355063i	0.861989	+	0.506926i	$0.169218\pi$
$618$		0			0
$619$		−	7.40002i		−	0.297432i	−0.988880	−	0.148716i	$-0.952486\pi$
$619$		−	7.40002i		−	0.297432i	0.988880	−	0.148716i	$-0.0475140\pi$
$620$		0			0
$621$	45.9412	−	6.10281i	1.84356	−	0.244897i
$622$		0			0
$623$	−3.96252	−	3.96252i	−0.158755	−	0.158755i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−19.0808	−	17.4707i	−0.762015	−	0.697713i
$628$		0			0
$629$	7.65497			0.305224
$630$		0			0
$631$	−4.48623			−0.178594			−0.0892970	−	0.996005i	$-0.528462\pi$
$631$	−4.48623			−0.178594			−0.0892970	+	0.996005i	$0.528462\pi$
$632$		0			0
$633$	19.1434	+	17.5280i	0.760883	+	0.696676i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.79204	−	1.79204i	−0.0710032	−	0.0710032i
$638$		0			0
$639$	−34.1384	+	3.01348i	−1.35049	+	0.119212i
$640$		0			0
$641$		−	2.11120i		−	0.0833872i	−0.999130	−	0.0416936i	$-0.986725\pi$
$641$		−	2.11120i		−	0.0833872i	0.999130	−	0.0416936i	$-0.0132753\pi$
$642$		0			0
$643$	18.3898	−	18.3898i	0.725221	−	0.725221i	−0.244442	−	0.969664i	$-0.578605\pi$
$643$	18.3898	−	18.3898i	0.725221	−	0.725221i	0.969664	+	0.244442i	$0.0786049\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	27.2831	−	27.2831i	1.07261	−	1.07261i	0.0754588	−	0.997149i	$-0.475958\pi$
$647$	27.2831	−	27.2831i	1.07261	−	1.07261i	0.997149	−	0.0754588i	$-0.0240421\pi$
$648$		0			0
$649$		−	23.2834i		−	0.913952i
$650$		0			0
$651$	0.0338538	+	0.768520i	0.00132683	+	0.0301207i
$652$		0			0
$653$	2.55556	+	2.55556i	0.100007	+	0.100007i	0.755340	−	0.655333i	$-0.227472\pi$
$653$	2.55556	+	2.55556i	0.100007	+	0.100007i	−0.655333	+	0.755340i	$0.727472\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−29.2589	−	24.5123i	−1.14150	−	0.956317i
$658$		0			0
$659$	−24.4933			−0.954124			−0.477062	−	0.878870i	$-0.658298\pi$
$659$	−24.4933			−0.954124			−0.477062	+	0.878870i	$0.658298\pi$
$660$		0			0
$661$	43.7051			1.69993			0.849965	−	0.526838i	$-0.176623\pi$
$661$	43.7051			1.69993			0.849965	+	0.526838i	$0.176623\pi$
$662$		0			0
$663$	5.32929	−	5.82045i	0.206973	−	0.226047i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.00184	+	3.00184i	0.116232	+	0.116232i
$668$		0			0
$669$	−13.4011	+	0.590327i	−0.518117	+	0.0228233i
$670$		0			0
$671$		−	5.61765i		−	0.216867i
$672$		0			0
$673$	−14.5974	+	14.5974i	−0.562689	+	0.562689i	−0.930071	−	0.367381i	$-0.880254\pi$
$673$	−14.5974	+	14.5974i	−0.562689	+	0.562689i	0.367381	+	0.930071i	$0.380254\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.68440	+	5.68440i	−0.218469	+	0.218469i	−0.807853	−	0.589384i	$-0.799371\pi$
$677$	−5.68440	+	5.68440i	−0.218469	+	0.218469i	0.589384	+	0.807853i	$0.299371\pi$
$678$		0			0
$679$		−	17.8829i		−	0.686282i
$680$		0			0
$681$	24.5103	−	1.07969i	0.939235	−	0.0413739i
$682$		0			0
$683$	−13.3035	−	13.3035i	−0.509045	−	0.509045i	0.405189	−	0.914233i	$-0.367206\pi$
$683$	−13.3035	−	13.3035i	−0.509045	−	0.509045i	−0.914233	+	0.405189i	$0.867206\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−14.9003	+	16.2735i	−0.568482	+	0.620874i
$688$		0			0
$689$	1.73498			0.0660974
$690$		0			0
$691$	−32.1289			−1.22224			−0.611121	−	0.791537i	$-0.709281\pi$
$691$	−32.1289			−1.22224			−0.611121	+	0.791537i	$0.709281\pi$
$692$		0			0
$693$	6.13832	+	5.14253i	0.233176	+	0.195349i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.10535	−	5.10535i	−0.193379	−	0.193379i
$698$		0			0
$699$	0.716539	+	16.2663i	0.0271020	+	0.615247i
$700$		0			0
$701$			33.5725i			1.26802i	0.773327	+	0.634008i	$0.218591\pi$
$701$			33.5725i			1.26802i	−0.773327	+	0.634008i	$0.781409\pi$
$702$		0			0
$703$	16.8477	−	16.8477i	0.635424	−	0.635424i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.77144	−	8.77144i	0.329884	−	0.329884i
$708$		0			0
$709$		−	43.1199i		−	1.61940i	−0.586844	−	0.809700i	$-0.699630\pi$
$709$		−	43.1199i		−	1.61940i	0.586844	−	0.809700i	$-0.300370\pi$
$710$		0			0
$711$	−31.0014	+	2.73657i	−1.16265	+	0.102630i
$712$		0			0
$713$	2.80104	+	2.80104i	0.104900	+	0.104900i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.3304	−	18.6149i	−0.759253	−	0.695184i
$718$		0			0
$719$	0.620453			0.0231390			0.0115695	−	0.999933i	$-0.496317\pi$
$719$	0.620453			0.0231390			0.0115695	+	0.999933i	$0.496317\pi$
$720$		0			0
$721$	−12.1924			−0.454067
$722$		0			0
$723$	4.89752	+	4.48424i	0.182141	+	0.166771i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−18.8301	−	18.8301i	−0.698371	−	0.698371i	0.265688	−	0.964059i	$-0.414401\pi$
$727$	−18.8301	−	18.8301i	−0.698371	−	0.698371i	−0.964059	+	0.265688i	$0.914401\pi$
$728$		0			0
$729$	−7.04895	−	26.0636i	−0.261072	−	0.965319i
$730$		0			0
$731$			16.3313i			0.604035i
$732$		0			0
$733$	2.51249	−	2.51249i	0.0928008	−	0.0928008i	−0.659182	−	0.751983i	$-0.729097\pi$
$733$	2.51249	−	2.51249i	0.0928008	−	0.0928008i	0.751983	+	0.659182i	$0.229097\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.2650	+	23.2650i	−0.856976	+	0.856976i
$738$		0			0
$739$			21.5679i			0.793387i	0.917951	+	0.396694i	$0.129842\pi$
$739$			21.5679i			0.793387i	−0.917951	+	0.396694i	$0.870158\pi$
$740$		0			0
$741$	−1.08097	−	24.5393i	−0.0397105	−	0.901474i
$742$		0			0
$743$	22.1908	+	22.1908i	0.814102	+	0.814102i	0.985246	−	0.171144i	$-0.0547463\pi$
$743$	22.1908	+	22.1908i	0.814102	+	0.814102i	−0.171144	+	0.985246i	$0.554746\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	16.6847	−	19.9155i	0.610463	−	0.728672i
$748$		0			0
$749$	15.9487			0.582754
$750$		0			0
$751$	−9.09442			−0.331860			−0.165930	−	0.986138i	$-0.553063\pi$
$751$	−9.09442			−0.331860			−0.165930	+	0.986138i	$0.553063\pi$
$752$		0			0
$753$	16.3596	−	17.8673i	0.596178	−	0.651122i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.23834	+	3.23834i	0.117699	+	0.117699i	0.763503	−	0.645804i	$-0.223478\pi$
$757$	3.23834	+	3.23834i	0.117699	+	0.117699i	−0.645804	+	0.763503i	$0.723478\pi$
$758$		0			0
$759$	41.1955	−	1.81469i	1.49530	−	0.0658689i
$760$		0			0
$761$			38.1713i			1.38371i	0.722037	+	0.691854i	$0.243206\pi$
$761$			38.1713i			1.38371i	−0.722037	+	0.691854i	$0.756794\pi$
$762$		0			0
$763$	−9.46473	+	9.46473i	−0.342646	+	0.342646i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.6316	−	15.6316i	0.564423	−	0.564423i
$768$		0			0
$769$			20.4661i			0.738026i	0.929424	+	0.369013i	$0.120304\pi$
$769$			20.4661i			0.738026i	−0.929424	+	0.369013i	$0.879696\pi$
$770$		0			0
$771$	15.5948	−	0.686959i	0.561632	−	0.0247402i
$772$		0			0
$773$	−28.6069	−	28.6069i	−1.02892	−	1.02892i	−0.999569	−	0.0293513i	$-0.990656\pi$
$773$	−28.6069	−	28.6069i	−1.02892	−	1.02892i	−0.0293513	−	0.999569i	$-0.509344\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.98031	+	5.43930i	−0.178668	+	0.195134i
$778$		0			0
$779$	−22.4726			−0.805164
$780$		0			0
$781$	−30.4929			−1.09112
$782$		0			0
$783$	1.50332	−	1.96391i	0.0537243	−	0.0701843i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	8.92169	+	8.92169i	0.318024	+	0.318024i	0.848008	−	0.529984i	$-0.177802\pi$
$787$	8.92169	+	8.92169i	0.318024	+	0.318024i	−0.529984	+	0.848008i	$0.677802\pi$
$788$		0			0
$789$	0.256342	+	5.81926i	0.00912601	+	0.207171i
$790$		0			0
$791$		−	2.84995i		−	0.101333i
$792$		0			0
$793$	3.77148	−	3.77148i	0.133929	−	0.133929i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.52194	+	8.52194i	−0.301863	+	0.301863i	−0.841742	−	0.539880i	$-0.818470\pi$
$797$	−8.52194	+	8.52194i	−0.301863	+	0.301863i	0.539880	+	0.841742i	$0.318470\pi$
$798$		0			0
$799$		−	2.45302i		−	0.0867815i
$800$		0			0
$801$	1.47825	+	16.7465i	0.0522314	+	0.591707i
$802$		0			0
$803$	−24.0146	−	24.0146i	−0.847456	−	0.847456i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	32.5945	+	29.8440i	1.14738	+	1.05056i
$808$		0			0
$809$	45.3222			1.59344			0.796722	−	0.604346i	$-0.206565\pi$
$809$	45.3222			1.59344			0.796722	+	0.604346i	$0.206565\pi$
$810$		0			0
$811$	24.6399			0.865225			0.432612	−	0.901580i	$-0.357592\pi$
$811$	24.6399			0.865225			0.432612	+	0.901580i	$0.357592\pi$
$812$		0			0
$813$	9.44049	+	8.64386i	0.331092	+	0.303153i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	35.9433	+	35.9433i	1.25750	+	1.25750i
$818$		0			0
$819$	0.668535	+	7.57354i	0.0233605	+	0.264641i
$820$		0			0
$821$		−	30.0676i		−	1.04937i	−0.851297	−	0.524684i	$-0.824184\pi$
$821$		−	30.0676i		−	1.04937i	0.851297	−	0.524684i	$-0.175816\pi$
$822$		0			0
$823$	−22.8560	+	22.8560i	−0.796711	+	0.796711i	−0.982575	−	0.185864i	$-0.940491\pi$
$823$	−22.8560	+	22.8560i	−0.796711	+	0.796711i	0.185864	+	0.982575i	$0.440491\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.5172	+	38.5172i	−1.33937	+	1.33937i	−0.442706	+	0.896667i	$0.645982\pi$
$827$	−38.5172	+	38.5172i	−1.33937	+	1.33937i	−0.896667	+	0.442706i	$0.854018\pi$
$828$		0			0
$829$		−	31.3544i		−	1.08898i	−0.838766	−	0.544491i	$-0.816723\pi$
$829$		−	31.3544i		−	1.08898i	0.838766	−	0.544491i	$-0.183277\pi$
$830$		0			0
$831$	0.409555	+	9.29738i	0.0142073	+	0.322522i
$832$		0			0
$833$	−1.27125	−	1.27125i	−0.0440463	−	0.0440463i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.40276	−	1.83254i	0.0484865	−	0.0633417i
$838$		0			0
$839$	−7.18461			−0.248040			−0.124020	−	0.992280i	$-0.539579\pi$
$839$	−7.18461			−0.248040			−0.124020	+	0.992280i	$0.539579\pi$
$840$		0			0
$841$	−28.7734			−0.992188
$842$		0			0
$843$	34.6033	−	37.7923i	1.19180	−	1.30164i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.74007	−	2.74007i	−0.0941499	−	0.0941499i
$848$		0			0
$849$	−5.07760	+	0.223671i	−0.174263	+	0.00767637i
$850$		0			0
$851$			37.9765i			1.30182i
$852$		0			0
$853$	−20.0919	+	20.0919i	−0.687934	+	0.687934i	−0.961775	−	0.273841i	$-0.911706\pi$
$853$	−20.0919	+	20.0919i	−0.687934	+	0.687934i	0.273841	+	0.961775i	$0.411706\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.4295	+	26.4295i	−0.902813	+	0.902813i	−0.995679	−	0.0928657i	$-0.970397\pi$
$857$	−26.4295	+	26.4295i	−0.902813	+	0.902813i	0.0928657	+	0.995679i	$0.470397\pi$
$858$		0			0
$859$		−	9.40855i		−	0.321016i	−0.987035	−	0.160508i	$-0.948687\pi$
$859$		−	9.40855i		−	0.321016i	0.987035	−	0.160508i	$-0.0513132\pi$
$860$		0			0
$861$	6.94917	−	0.306115i	0.236827	−	0.0104324i
$862$		0			0
$863$	−3.90611	−	3.90611i	−0.132965	−	0.132965i	0.637492	−	0.770457i	$-0.279972\pi$
$863$	−3.90611	−	3.90611i	−0.132965	−	0.132965i	−0.770457	+	0.637492i	$0.779972\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−16.1037	+	17.5878i	−0.546910	+	0.597313i
$868$		0			0
$869$	−27.6909			−0.939350
$870$		0			0
$871$	−31.2384			−1.05847
$872$		0			0
$873$	−34.4527	+	41.1240i	−1.16605	+	1.39184i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.9724	−	18.9724i	−0.640651	−	0.640651i	0.310065	−	0.950715i	$-0.399649\pi$
$877$	−18.9724	−	18.9724i	−0.640651	−	0.640651i	−0.950715	+	0.310065i	$0.899649\pi$
$878$		0			0
$879$	1.44966	+	32.9090i	0.0488958	+	1.10999i
$880$		0			0
$881$		−	55.8433i		−	1.88141i	−0.339225	−	0.940705i	$-0.610165\pi$
$881$		−	55.8433i		−	1.88141i	0.339225	−	0.940705i	$-0.389835\pi$
$882$		0			0
$883$	6.13111	−	6.13111i	0.206328	−	0.206328i	−0.596376	−	0.802705i	$-0.703393\pi$
$883$	6.13111	−	6.13111i	0.206328	−	0.206328i	0.802705	+	0.596376i	$0.203393\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.2424	−	13.2424i	0.444638	−	0.444638i	−0.448930	−	0.893567i	$-0.648195\pi$
$887$	13.2424	−	13.2424i	0.444638	−	0.444638i	0.893567	+	0.448930i	$0.148195\pi$
$888$		0			0
$889$			11.7861i			0.395292i
$890$		0			0
$891$	−4.20841	−	23.6519i	−0.140987	−	0.792367i
$892$		0			0
$893$	−5.39881	−	5.39881i	−0.180664	−	0.180664i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	28.8754	+	26.4388i	0.964121	+	0.882765i
$898$		0			0
$899$	0.211397			0.00705050
$900$		0			0
$901$	1.23077			0.0410030
$902$		0			0
$903$	−11.6043	−	10.6251i	−0.386168	−	0.353581i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.62949	+	6.62949i	0.220129	+	0.220129i	0.808553	−	0.588424i	$-0.200251\pi$
$907$	6.62949	+	6.62949i	0.220129	+	0.220129i	−0.588424	+	0.808553i	$0.700251\pi$
$908$		0			0
$909$	−37.0699	+	3.27225i	−1.22953	+	0.108534i
$910$		0			0
$911$			25.4696i			0.843844i	0.906632	+	0.421922i	$0.138644\pi$
$911$			25.4696i			0.843844i	−0.906632	+	0.421922i	$0.861356\pi$
$912$		0			0
$913$	16.3459	−	16.3459i	0.540971	−	0.540971i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.13677	+	1.13677i	−0.0375395	+	0.0375395i
$918$		0			0
$919$		−	22.2535i		−	0.734076i	−0.930206	−	0.367038i	$-0.880372\pi$
$919$		−	22.2535i		−	0.734076i	0.930206	−	0.367038i	$-0.119628\pi$
$920$		0			0
$921$	1.27124	+	28.8585i	0.0418886	+	0.950921i
$922$		0			0
$923$	−20.4718	−	20.4718i	−0.673837	−	0.673837i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	28.0379	+	23.4895i	0.920887	+	0.771496i
$928$		0			0
$929$	31.9864			1.04944			0.524720	−	0.851275i	$-0.324170\pi$
$929$	31.9864			1.04944			0.524720	+	0.851275i	$0.324170\pi$
$930$		0			0
$931$	−5.59577			−0.183394
$932$		0			0
$933$	−8.15602	+	8.90768i	−0.267016	+	0.291624i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.4191	+	23.4191i	0.765068	+	0.765068i	0.977234	−	0.212166i	$-0.0680517\pi$
$937$	23.4191	+	23.4191i	0.765068	+	0.765068i	−0.212166	+	0.977234i	$0.568052\pi$
$938$		0			0
$939$	−32.5713	+	1.43478i	−1.06292	+	0.0468224i
$940$		0			0
$941$			1.26007i			0.0410770i	0.999789	+	0.0205385i	$0.00653807\pi$
$941$			1.26007i			0.0410770i	−0.999789	+	0.0205385i	$0.993462\pi$
$942$		0			0
$943$	25.3278	−	25.3278i	0.824786	−	0.824786i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.8361	+	18.8361i	−0.612092	+	0.612092i	−0.943491	−	0.331399i	$-0.892479\pi$
$947$	−18.8361	+	18.8361i	−0.612092	+	0.612092i	0.331399	+	0.943491i	$0.392479\pi$
$948$		0			0
$949$		−	32.2450i		−	1.04672i
$950$		0			0
$951$	−38.0924	+	1.67799i	−1.23523	+	0.0544127i
$952$		0			0
$953$	−27.2821	−	27.2821i	−0.883753	−	0.883753i	0.110161	−	0.993914i	$-0.464863\pi$
$953$	−27.2821	−	27.2821i	−0.883753	−	0.883753i	−0.993914	+	0.110161i	$0.964863\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.48605	−	1.62301i	0.0480373	−	0.0524645i
$958$		0			0
$959$	18.9345			0.611425
$960$		0			0
$961$	−30.8027			−0.993637
$962$		0			0
$963$	−36.6762	−	30.7264i	−1.18187	−	0.990145i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−4.31919	−	4.31919i	−0.138896	−	0.138896i	0.634240	−	0.773136i	$-0.281313\pi$
$967$	−4.31919	−	4.31919i	−0.138896	−	0.138896i	−0.773136	+	0.634240i	$0.781313\pi$
$968$		0			0
$969$	−0.766829	−	17.4079i	−0.0246341	−	0.559223i
$970$		0			0
$971$		−	8.97863i		−	0.288138i	−0.989568	−	0.144069i	$-0.953981\pi$
$971$		−	8.97863i		−	0.288138i	0.989568	−	0.144069i	$-0.0460187\pi$
$972$		0			0
$973$	−13.1345	+	13.1345i	−0.421073	+	0.421073i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.7172	−	13.7172i	0.438853	−	0.438853i	−0.452773	−	0.891626i	$-0.649565\pi$
$977$	13.7172	−	13.7172i	0.438853	−	0.438853i	0.891626	+	0.452773i	$0.149565\pi$
$978$		0			0
$979$			14.9582i			0.478065i
$980$		0			0
$981$	39.9999	−	3.53089i	1.27710	−	0.112733i
$982$		0			0
$983$	33.1638	+	33.1638i	1.05776	+	1.05776i	0.998226	+	0.0595334i	$0.0189613\pi$
$983$	33.1638	+	33.1638i	1.05776	+	1.05776i	0.0595334	+	0.998226i	$0.481039\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.74301	+	1.59593i	0.0554806	+	0.0507989i
$988$		0			0
$989$	−81.0200			−2.57629
$990$		0			0
$991$	25.4841			0.809529			0.404764	−	0.914421i	$-0.367354\pi$
$991$	25.4841			0.809529			0.404764	+	0.914421i	$0.367354\pi$
$992$		0			0
$993$	−14.3022	−	13.0953i	−0.453867	−	0.415568i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	41.6367	+	41.6367i	1.31865	+	1.31865i	0.914847	+	0.403801i	$0.132311\pi$
$997$	41.6367	+	41.6367i	1.31865	+	1.31865i	0.403801	+	0.914847i	$0.367689\pi$
$998$		0			0
$999$	21.9321	−	2.91345i	0.693900	−	0.0921775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.b.1457.9		24
3.2	odd	2	inner	2100.2.s.b.1457.3		24
5.2	odd	4		420.2.s.a.113.10	yes	24
5.3	odd	4	inner	2100.2.s.b.1793.3		24
5.4	even	2		420.2.s.a.197.4	yes	24
15.2	even	4		420.2.s.a.113.4	✓	24
15.8	even	4	inner	2100.2.s.b.1793.9		24
15.14	odd	2		420.2.s.a.197.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.s.a.113.4	✓	24	15.2	even	4
420.2.s.a.113.10	yes	24	5.2	odd	4
420.2.s.a.197.4	yes	24	5.4	even	2
420.2.s.a.197.10	yes	24	15.14	odd	2
2100.2.s.b.1457.3		24	3.2	odd	2	inner
2100.2.s.b.1457.9		24	1.1	even	1	trivial
2100.2.s.b.1793.3		24	5.3	odd	4	inner
2100.2.s.b.1793.9		24	15.8	even	4	inner

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27746 + 1.16966i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(0.263792 + 2.98838i) q^{9} +O(q^{10})\)	\(q+(1.27746 + 1.16966i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(0.263792 + 2.98838i) q^{9} +2.66926i q^{11} +(-1.79204 + 1.79204i) q^{13} +(-1.27125 + 1.27125i) q^{17} +5.59577i q^{19} +(-0.0762239 - 1.73037i) q^{21} +(-6.30672 - 6.30672i) q^{23} +(-3.15841 + 4.12607i) q^{27} -0.475975 q^{29} -0.444136 q^{31} +(-3.12213 + 3.40987i) q^{33} +(-3.01080 - 3.01080i) q^{37} +(-4.38533 + 0.193177i) q^{39} +4.01600i q^{41} +(6.42331 - 6.42331i) q^{43} +(-0.964802 + 0.964802i) q^{47} +1.00000i q^{49} +(-3.11091 + 0.137037i) q^{51} +(-0.484079 - 0.484079i) q^{53} +(-6.54515 + 7.14835i) q^{57} -8.72277 q^{59} -2.10457 q^{61} +(1.92657 - 2.29963i) q^{63} +(8.71588 + 8.71588i) q^{67} +(-0.679845 - 15.4333i) q^{69} +11.4237i q^{71} +(-8.99671 + 8.99671i) q^{73} +(1.88745 - 1.88745i) q^{77} +10.3740i q^{79} +(-8.86083 + 1.57662i) q^{81} +(-6.12377 - 6.12377i) q^{83} +(-0.608037 - 0.556729i) q^{87} +5.60386 q^{89} +2.53433 q^{91} +(-0.567364 - 0.519488i) q^{93} +(12.6451 + 12.6451i) q^{97} +(-7.97677 + 0.704129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

Introduction

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