LMFDB - Embedded newform 1710.2.d.d.1369.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.1
Root			$1.32001 + 1.32001i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.d.1369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-1.80487 + 1.32001i) q^{5} +4.12489i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.80487 + 1.32001i) q^{5} +4.12489i q^{7} +1.00000i q^{8} +(1.32001 + 1.80487i) q^{10} +2.64002 q^{11} -2.51514i q^{13} +4.12489 q^{14} +1.00000 q^{16} +0.515138i q^{17} -1.00000 q^{19} +(1.80487 - 1.32001i) q^{20} -2.64002i q^{22} +3.09461i q^{23} +(1.51514 - 4.76491i) q^{25} -2.51514 q^{26} -4.12489i q^{28} -7.79518 q^{29} +3.67030 q^{31} -1.00000i q^{32} +0.515138 q^{34} +(-5.44490 - 7.44490i) q^{35} +10.2498i q^{37} +1.00000i q^{38} +(-1.32001 - 1.80487i) q^{40} -8.88979 q^{41} -8.64002i q^{43} -2.64002 q^{44} +3.09461 q^{46} +4.96972i q^{47} -10.0147 q^{49} +(-4.76491 - 1.51514i) q^{50} +2.51514i q^{52} +5.48486i q^{53} +(-4.76491 + 3.48486i) q^{55} -4.12489 q^{56} +7.79518i q^{58} +3.15516 q^{59} -12.6400 q^{61} -3.67030i q^{62} -1.00000 q^{64} +(3.32001 + 4.53951i) q^{65} -7.40493i q^{67} -0.515138i q^{68} +(-7.44490 + 5.44490i) q^{70} -11.1396 q^{71} +2.70436i q^{73} +10.2498 q^{74} +1.00000 q^{76} +10.8898i q^{77} -16.7493 q^{79} +(-1.80487 + 1.32001i) q^{80} +8.88979i q^{82} +3.28005i q^{83} +(-0.679988 - 0.929759i) q^{85} -8.64002 q^{86} +2.64002i q^{88} -7.60975 q^{89} +10.3747 q^{91} -3.09461i q^{92} +4.96972 q^{94} +(1.80487 - 1.32001i) q^{95} +3.93945i q^{97} +10.0147i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^5	$ 6 q - 6 q^{4} - 2 q^{5} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 2 q^{20} + 10 q^{25} - 16 q^{26} - 16 q^{29} + 8 q^{31} + 4 q^{34} - 8 q^{35} - 4 q^{41} + 6 q^{49} + 4 q^{50} + 4 q^{55} - 8 q^{56} + 4 q^{59} - 60 q^{61} - 6 q^{64} + 12 q^{65} - 20 q^{70} + 16 q^{71} + 28 q^{74} + 6 q^{76} - 2 q^{80} - 12 q^{85} - 36 q^{86} - 28 q^{89} + 12 q^{91} + 28 q^{94} + 2 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 2 * q^20 + 10 * q^25 - 16 * q^26 - 16 * q^29 + 8 * q^31 + 4 * q^34 - 8 * q^35 - 4 * q^41 + 6 * q^49 + 4 * q^50 + 4 * q^55 - 8 * q^56 + 4 * q^59 - 60 * q^61 - 6 * q^64 + 12 * q^65 - 20 * q^70 + 16 * q^71 + 28 * q^74 + 6 * q^76 - 2 * q^80 - 12 * q^85 - 36 * q^86 - 28 * q^89 + 12 * q^91 + 28 * q^94 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.80487	+	1.32001i	−0.807164	+	0.590327i
$5$	−1.80487	+	1.32001i	−0.807164	+	0.590327i
$6$		0			0
$7$			4.12489i			1.55906i	0.626365	+	0.779530i	$0.284542\pi$
$7$			4.12489i			1.55906i	−0.626365	+	0.779530i	$0.715458\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.32001	+	1.80487i	0.417424	+	0.570751i
$11$	2.64002			0.795997			0.397999	−	0.917386i	$-0.369705\pi$
$11$	2.64002			0.795997			0.397999	+	0.917386i	$0.369705\pi$
$12$		0			0
$13$		−	2.51514i		−	0.697574i	−0.937202	−	0.348787i	$-0.886594\pi$
$13$		−	2.51514i		−	0.697574i	0.937202	−	0.348787i	$-0.113406\pi$
$14$	4.12489			1.10242
$15$		0			0
$16$	1.00000			0.250000
$17$			0.515138i			0.124939i	0.998047	+	0.0624697i	$0.0198977\pi$
$17$			0.515138i			0.124939i	−0.998047	+	0.0624697i	$0.980102\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.80487	−	1.32001i	0.403582	−	0.295164i
$21$		0			0
$22$		−	2.64002i		−	0.562855i
$23$			3.09461i			0.645271i	0.946523	+	0.322635i	$0.104569\pi$
$23$			3.09461i			0.645271i	−0.946523	+	0.322635i	$0.895431\pi$
$24$		0			0
$25$	1.51514	−	4.76491i	0.303028	−	0.952982i
$26$	−2.51514			−0.493259
$27$		0			0
$28$		−	4.12489i		−	0.779530i
$29$	−7.79518			−1.44753			−0.723765	−	0.690047i	$-0.757590\pi$
$29$	−7.79518			−1.44753			−0.723765	+	0.690047i	$0.757590\pi$
$30$		0			0
$31$	3.67030			0.659205			0.329603	−	0.944120i	$-0.393085\pi$
$31$	3.67030			0.659205			0.329603	+	0.944120i	$0.393085\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.515138			0.0883454
$35$	−5.44490	−	7.44490i	−0.920356	−	1.25842i
$36$		0			0
$37$			10.2498i			1.68505i	0.538656	+	0.842526i	$0.318932\pi$
$37$			10.2498i			1.68505i	−0.538656	+	0.842526i	$0.681068\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	−1.32001	−	1.80487i	−0.208712	−	0.285376i
$41$	−8.88979			−1.38835			−0.694176	−	0.719805i	$-0.744231\pi$
$41$	−8.88979			−1.38835			−0.694176	+	0.719805i	$0.744231\pi$
$42$		0			0
$43$		−	8.64002i		−	1.31759i	−0.752322	−	0.658796i	$-0.771066\pi$
$43$		−	8.64002i		−	1.31759i	0.752322	−	0.658796i	$-0.228934\pi$
$44$	−2.64002			−0.397999
$45$		0			0
$46$	3.09461			0.456275
$47$			4.96972i			0.724909i	0.932002	+	0.362454i	$0.118061\pi$
$47$			4.96972i			0.724909i	−0.932002	+	0.362454i	$0.881939\pi$
$48$		0			0
$49$	−10.0147			−1.43067
$50$	−4.76491	−	1.51514i	−0.673860	−	0.214273i
$51$		0			0
$52$			2.51514i			0.348787i
$53$			5.48486i			0.753404i	0.926335	+	0.376702i	$0.122942\pi$
$53$			5.48486i			0.753404i	−0.926335	+	0.376702i	$0.877058\pi$
$54$		0			0
$55$	−4.76491	+	3.48486i	−0.642500	+	0.469899i
$56$	−4.12489			−0.551211
$57$		0			0
$58$			7.79518i			1.02356i
$59$	3.15516			0.410767			0.205384	−	0.978682i	$-0.434156\pi$
$59$	3.15516			0.410767			0.205384	+	0.978682i	$0.434156\pi$
$60$		0			0
$61$	−12.6400			−1.61839			−0.809195	−	0.587541i	$-0.800096\pi$
$61$	−12.6400			−1.61839			−0.809195	+	0.587541i	$0.800096\pi$
$62$		−	3.67030i		−	0.466129i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.32001	+	4.53951i	0.411797	+	0.563056i
$66$		0			0
$67$		−	7.40493i		−	0.904656i	−0.891852	−	0.452328i	$-0.850594\pi$
$67$		−	7.40493i		−	0.904656i	0.891852	−	0.452328i	$-0.149406\pi$
$68$		−	0.515138i		−	0.0624697i
$69$		0			0
$70$	−7.44490	+	5.44490i	−0.889835	+	0.650790i
$71$	−11.1396			−1.32202			−0.661012	−	0.750376i	$-0.729873\pi$
$71$	−11.1396			−1.32202			−0.661012	+	0.750376i	$0.729873\pi$
$72$		0			0
$73$			2.70436i			0.316521i	0.987397	+	0.158261i	$0.0505886\pi$
$73$			2.70436i			0.316521i	−0.987397	+	0.158261i	$0.949411\pi$
$74$	10.2498			1.19151
$75$		0			0
$76$	1.00000			0.114708
$77$			10.8898i			1.24101i
$78$		0			0
$79$	−16.7493			−1.88444			−0.942222	−	0.334988i	$-0.891268\pi$
$79$	−16.7493			−1.88444			−0.942222	+	0.334988i	$0.891268\pi$
$80$	−1.80487	+	1.32001i	−0.201791	+	0.147582i
$81$		0			0
$82$			8.88979i			0.981714i
$83$			3.28005i			0.360032i	0.983664	+	0.180016i	$0.0576149\pi$
$83$			3.28005i			0.360032i	−0.983664	+	0.180016i	$0.942385\pi$
$84$		0			0
$85$	−0.679988	−	0.929759i	−0.0737551	−	0.100847i
$86$	−8.64002			−0.931678
$87$		0			0
$88$			2.64002i			0.281427i
$89$	−7.60975			−0.806632			−0.403316	−	0.915061i	$-0.632142\pi$
$89$	−7.60975			−0.806632			−0.403316	+	0.915061i	$0.632142\pi$
$90$		0			0
$91$	10.3747			1.08756
$92$		−	3.09461i		−	0.322635i
$93$		0			0
$94$	4.96972			0.512588
$95$	1.80487	−	1.32001i	0.185176	−	0.135430i
$96$		0			0
$97$			3.93945i			0.399990i	0.979797	+	0.199995i	$0.0640926\pi$
$97$			3.93945i			0.399990i	−0.979797	+	0.199995i	$0.935907\pi$
$98$			10.0147i			1.01164i
$99$		0			0
$100$	−1.51514	+	4.76491i	−0.151514	+	0.476491i
$101$	13.7990			1.37305			0.686524	−	0.727107i	$-0.259136\pi$
$101$	13.7990			1.37305			0.686524	+	0.727107i	$0.259136\pi$
$102$		0			0
$103$		−	4.57947i		−	0.451229i	−0.974217	−	0.225614i	$-0.927561\pi$
$103$		−	4.57947i		−	0.451229i	0.974217	−	0.225614i	$-0.0724389\pi$
$104$	2.51514			0.246630
$105$		0			0
$106$	5.48486			0.532737
$107$			10.3747i			1.00296i	0.865170	+	0.501478i	$0.167210\pi$
$107$			10.3747i			1.00296i	−0.865170	+	0.501478i	$0.832790\pi$
$108$		0			0
$109$	−3.01468			−0.288754			−0.144377	−	0.989523i	$-0.546118\pi$
$109$	−3.01468			−0.288754			−0.144377	+	0.989523i	$0.546118\pi$
$110$	3.48486	+	4.76491i	0.332269	+	0.454316i
$111$		0			0
$112$			4.12489i			0.389765i
$113$		−	19.2001i		−	1.80620i	−0.429435	−	0.903098i	$-0.641287\pi$
$113$		−	19.2001i		−	1.80620i	0.429435	−	0.903098i	$-0.358713\pi$
$114$		0			0
$115$	−4.08492	−	5.58538i	−0.380921	−	0.520839i
$116$	7.79518			0.723765
$117$		0			0
$118$		−	3.15516i		−	0.290456i
$119$	−2.12489			−0.194788
$120$		0			0
$121$	−4.03028			−0.366389
$122$			12.6400i			1.14437i
$123$		0			0
$124$	−3.67030			−0.329603
$125$	3.55510	+	10.6001i	0.317978	+	0.948098i
$126$		0			0
$127$			14.3103i			1.26984i	0.772580	+	0.634918i	$0.218966\pi$
$127$			14.3103i			1.26984i	−0.772580	+	0.634918i	$0.781034\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.53951	−	3.32001i	0.398141	−	0.291184i
$131$	6.56009			0.573158			0.286579	−	0.958057i	$-0.407482\pi$
$131$	6.56009			0.573158			0.286579	+	0.958057i	$0.407482\pi$
$132$		0			0
$133$		−	4.12489i		−	0.357673i
$134$	−7.40493			−0.639689
$135$		0			0
$136$	−0.515138			−0.0441727
$137$			6.45459i			0.551452i	0.961236	+	0.275726i	$0.0889183\pi$
$137$			6.45459i			0.551452i	−0.961236	+	0.275726i	$0.911082\pi$
$138$		0			0
$139$	23.0596			1.95589			0.977946	−	0.208856i	$-0.0669740\pi$
$139$	23.0596			1.95589			0.977946	+	0.208856i	$0.0669740\pi$
$140$	5.44490	+	7.44490i	0.460178	+	0.629209i
$141$		0			0
$142$			11.1396i			0.934812i
$143$		−	6.64002i		−	0.555267i
$144$		0			0
$145$	14.0693	−	10.2897i	1.16839	−	0.854516i
$146$	2.70436			0.223814
$147$		0			0
$148$		−	10.2498i		−	0.842526i
$149$	16.0294			1.31318			0.656588	−	0.754249i	$-0.271999\pi$
$149$	16.0294			1.31318			0.656588	+	0.754249i	$0.271999\pi$
$150$		0			0
$151$	−14.3103			−1.16456			−0.582279	−	0.812989i	$-0.697839\pi$
$151$	−14.3103			−1.16456			−0.582279	+	0.812989i	$0.697839\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	10.8898			0.877525
$155$	−6.62443	+	4.84484i	−0.532087	+	0.389147i
$156$		0			0
$157$		−	18.0294i		−	1.43890i	−0.694544	−	0.719450i	$-0.744394\pi$
$157$		−	18.0294i		−	1.43890i	0.694544	−	0.719450i	$-0.255606\pi$
$158$			16.7493i			1.33250i
$159$		0			0
$160$	1.32001	+	1.80487i	0.104356	+	0.142688i
$161$	−12.7649			−1.00602
$162$		0			0
$163$		−	2.70058i		−	0.211525i	−0.994391	−	0.105763i	$-0.966272\pi$
$163$		−	2.70058i		−	0.211525i	0.994391	−	0.105763i	$-0.0337284\pi$
$164$	8.88979			0.694176
$165$		0			0
$166$	3.28005			0.254581
$167$		−	8.95035i		−	0.692599i	−0.938124	−	0.346299i	$-0.887438\pi$
$167$		−	8.95035i		−	0.692599i	0.938124	−	0.346299i	$-0.112562\pi$
$168$		0			0
$169$	6.67408			0.513391
$170$	−0.929759	+	0.679988i	−0.0713093	+	0.0521527i
$171$		0			0
$172$			8.64002i			0.658796i
$173$			0.310323i			0.0235934i	0.999930	+	0.0117967i	$0.00375510\pi$
$173$			0.310323i			0.0235934i	−0.999930	+	0.0117967i	$0.996245\pi$
$174$		0			0
$175$	19.6547	+	6.24977i	1.48576	+	0.472438i
$176$	2.64002			0.198999
$177$		0			0
$178$			7.60975i			0.570375i
$179$	−1.52982			−0.114344			−0.0571720	−	0.998364i	$-0.518208\pi$
$179$	−1.52982			−0.114344			−0.0571720	+	0.998364i	$0.518208\pi$
$180$		0			0
$181$	−14.7493			−1.09631			−0.548154	−	0.836377i	$-0.684669\pi$
$181$	−14.7493			−1.09631			−0.548154	+	0.836377i	$0.684669\pi$
$182$		−	10.3747i		−	0.769021i
$183$		0			0
$184$	−3.09461			−0.228138
$185$	−13.5298	−	18.4995i	−0.994732	−	1.36011i
$186$		0			0
$187$			1.35998i			0.0994513i
$188$		−	4.96972i		−	0.362454i
$189$		0			0
$190$	−1.32001	−	1.80487i	−0.0957637	−	0.130939i
$191$	−18.1249			−1.31147			−0.655735	−	0.754991i	$-0.727641\pi$
$191$	−18.1249			−1.31147			−0.655735	+	0.754991i	$0.727641\pi$
$192$		0			0
$193$			4.56009i			0.328243i	0.986440	+	0.164121i	$0.0524789\pi$
$193$			4.56009i			0.328243i	−0.986440	+	0.164121i	$0.947521\pi$
$194$	3.93945			0.282836
$195$		0			0
$196$	10.0147			0.715334
$197$			2.14048i			0.152503i	0.997089	+	0.0762515i	$0.0242952\pi$
$197$			2.14048i			0.152503i	−0.997089	+	0.0762515i	$0.975705\pi$
$198$		0			0
$199$	−16.5639			−1.17418			−0.587091	−	0.809521i	$-0.699727\pi$
$199$	−16.5639			−1.17418			−0.587091	+	0.809521i	$0.699727\pi$
$200$	4.76491	+	1.51514i	0.336930	+	0.107136i
$201$		0			0
$202$		−	13.7990i		−	0.970892i
$203$		−	32.1542i		−	2.25679i
$204$		0			0
$205$	16.0450	−	11.7346i	1.12063	−	0.819582i
$206$	−4.57947			−0.319067
$207$		0			0
$208$		−	2.51514i		−	0.174393i
$209$	−2.64002			−0.182614
$210$		0			0
$211$	−15.2838			−1.05218			−0.526091	−	0.850428i	$-0.676343\pi$
$211$	−15.2838			−1.05218			−0.526091	+	0.850428i	$0.676343\pi$
$212$		−	5.48486i		−	0.376702i
$213$		0			0
$214$	10.3747			0.709197
$215$	11.4049	+	15.5942i	0.777810	+	1.06351i
$216$		0			0
$217$			15.1396i			1.02774i
$218$			3.01468i			0.204180i
$219$		0			0
$220$	4.76491	−	3.48486i	0.321250	−	0.234949i
$221$	1.29564			0.0871544
$222$		0			0
$223$			3.75023i			0.251134i	0.992085	+	0.125567i	$0.0400750\pi$
$223$			3.75023i			0.251134i	−0.992085	+	0.125567i	$0.959925\pi$
$224$	4.12489			0.275606
$225$		0			0
$226$	−19.2001			−1.27717
$227$			24.1542i			1.60317i	0.597878	+	0.801587i	$0.296011\pi$
$227$			24.1542i			1.60317i	−0.597878	+	0.801587i	$0.703989\pi$
$228$		0			0
$229$	13.0596			0.863005			0.431503	−	0.902112i	$-0.357984\pi$
$229$	13.0596			0.863005			0.431503	+	0.902112i	$0.357984\pi$
$230$	−5.58538	+	4.08492i	−0.368289	+	0.269352i
$231$		0			0
$232$		−	7.79518i		−	0.511779i
$233$		−	6.43899i		−	0.421832i	−0.977504	−	0.210916i	$-0.932355\pi$
$233$		−	6.43899i		−	0.421832i	0.977504	−	0.210916i	$-0.0676447\pi$
$234$		0			0
$235$	−6.56009	−	8.96972i	−0.427933	−	0.585120i
$236$	−3.15516			−0.205384
$237$		0			0
$238$			2.12489i			0.137736i
$239$	22.8742			1.47961			0.739804	−	0.672822i	$-0.234918\pi$
$239$	22.8742			1.47961			0.739804	+	0.672822i	$0.234918\pi$
$240$		0			0
$241$	4.96972			0.320128			0.160064	−	0.987107i	$-0.448830\pi$
$241$	4.96972			0.320128			0.160064	+	0.987107i	$0.448830\pi$
$242$			4.03028i			0.259076i
$243$		0			0
$244$	12.6400			0.809195
$245$	18.0752	−	13.2195i	1.15478	−	0.844563i
$246$		0			0
$247$			2.51514i			0.160034i
$248$			3.67030i			0.233064i
$249$		0			0
$250$	10.6001	−	3.55510i	0.670407	−	0.224844i
$251$	−15.9201			−1.00487			−0.502433	−	0.864616i	$-0.667562\pi$
$251$	−15.9201			−1.00487			−0.502433	+	0.864616i	$0.667562\pi$
$252$		0			0
$253$			8.16984i			0.513634i
$254$	14.3103			0.897910
$255$		0			0
$256$	1.00000			0.0625000
$257$			1.04965i			0.0654756i	0.999464	+	0.0327378i	$0.0104226\pi$
$257$			1.04965i			0.0654756i	−0.999464	+	0.0327378i	$0.989577\pi$
$258$		0			0
$259$	−42.2791			−2.62710
$260$	−3.32001	−	4.53951i	−0.205898	−	0.281528i
$261$		0			0
$262$		−	6.56009i		−	0.405284i
$263$		−	11.9394i		−	0.736218i	−0.929783	−	0.368109i	$-0.880005\pi$
$263$		−	11.9394i		−	0.736218i	0.929783	−	0.368109i	$-0.119995\pi$
$264$		0			0
$265$	−7.24008	−	9.89948i	−0.444755	−	0.608120i
$266$	−4.12489			−0.252913
$267$		0			0
$268$			7.40493i			0.452328i
$269$	−15.9394			−0.971845			−0.485923	−	0.874002i	$-0.661516\pi$
$269$	−15.9394			−0.971845			−0.485923	+	0.874002i	$0.661516\pi$
$270$		0			0
$271$	1.46548			0.0890218			0.0445109	−	0.999009i	$-0.485827\pi$
$271$	1.46548			0.0890218			0.0445109	+	0.999009i	$0.485827\pi$
$272$			0.515138i			0.0312348i
$273$		0			0
$274$	6.45459			0.389936
$275$	4.00000	−	12.5795i	0.241209	−	0.758571i
$276$		0			0
$277$			32.4995i			1.95271i	0.216177	+	0.976354i	$0.430641\pi$
$277$			32.4995i			1.95271i	−0.216177	+	0.976354i	$0.569359\pi$
$278$		−	23.0596i		−	1.38303i
$279$		0			0
$280$	7.44490	−	5.44490i	0.444918	−	0.325395i
$281$	−1.04965			−0.0626171			−0.0313085	−	0.999510i	$-0.509967\pi$
$281$	−1.04965			−0.0626171			−0.0313085	+	0.999510i	$0.509967\pi$
$282$		0			0
$283$			9.34060i			0.555241i	0.960691	+	0.277620i	$0.0895458\pi$
$283$			9.34060i			0.555241i	−0.960691	+	0.277620i	$0.910454\pi$
$284$	11.1396			0.661012
$285$		0			0
$286$	−6.64002			−0.392633
$287$		−	36.6694i		−	2.16453i
$288$		0			0
$289$	16.7346			0.984390
$290$	−10.2897	−	14.0693i	−0.604234	−	0.826179i
$291$		0			0
$292$		−	2.70436i		−	0.158261i
$293$			25.5748i			1.49409i	0.664771	+	0.747047i	$0.268529\pi$
$293$			25.5748i			1.49409i	−0.664771	+	0.747047i	$0.731471\pi$
$294$		0			0
$295$	−5.69467	+	4.16485i	−0.331556	+	0.242487i
$296$	−10.2498			−0.595756
$297$		0			0
$298$		−	16.0294i		−	0.928556i
$299$	7.78337			0.450124
$300$		0			0
$301$	35.6391			2.05420
$302$			14.3103i			0.823467i
$303$		0			0
$304$	−1.00000			−0.0573539
$305$	22.8136	−	16.6850i	1.30631	−	0.955379i
$306$		0			0
$307$			9.43991i			0.538764i	0.963033	+	0.269382i	$0.0868194\pi$
$307$			9.43991i			0.538764i	−0.963033	+	0.269382i	$0.913181\pi$
$308$		−	10.8898i		−	0.620504i
$309$		0			0
$310$	4.84484	+	6.62443i	0.275168	+	0.376242i
$311$	17.4655			0.990377			0.495188	−	0.868786i	$-0.335099\pi$
$311$	17.4655			0.990377			0.495188	+	0.868786i	$0.335099\pi$
$312$		0			0
$313$			10.4546i			0.590928i	0.955354	+	0.295464i	$0.0954743\pi$
$313$			10.4546i			0.590928i	−0.955354	+	0.295464i	$0.904526\pi$
$314$	−18.0294			−1.01746
$315$		0			0
$316$	16.7493			0.942222
$317$		−	4.33348i		−	0.243393i	−0.992567	−	0.121696i	$-0.961167\pi$
$317$		−	4.33348i		−	0.243393i	0.992567	−	0.121696i	$-0.0388334\pi$
$318$		0			0
$319$	−20.5795			−1.15223
$320$	1.80487	−	1.32001i	0.100896	−	0.0737909i
$321$		0			0
$322$			12.7649i			0.711361i
$323$		−	0.515138i		−	0.0286630i
$324$		0			0
$325$	−11.9844	−	3.81078i	−0.664775	−	0.211384i
$326$	−2.70058			−0.149571
$327$		0			0
$328$		−	8.88979i		−	0.490857i
$329$	−20.4995			−1.13018
$330$		0			0
$331$	−4.56387			−0.250853			−0.125427	−	0.992103i	$-0.540030\pi$
$331$	−4.56387			−0.250853			−0.125427	+	0.992103i	$0.540030\pi$
$332$		−	3.28005i		−	0.180016i
$333$		0			0
$334$	−8.95035			−0.489741
$335$	9.77460	+	13.3650i	0.534043	+	0.730206i
$336$		0			0
$337$			13.0109i			0.708749i	0.935104	+	0.354374i	$0.115306\pi$
$337$			13.0109i			0.708749i	−0.935104	+	0.354374i	$0.884694\pi$
$338$		−	6.67408i		−	0.363022i
$339$		0			0
$340$	0.679988	+	0.929759i	0.0368775	+	0.0504233i
$341$	9.68968			0.524725
$342$		0			0
$343$		−	12.4352i		−	0.671438i
$344$	8.64002			0.465839
$345$		0			0
$346$	0.310323			0.0166831
$347$		−	13.2195i		−	0.709660i	−0.934931	−	0.354830i	$-0.884539\pi$
$347$		−	13.2195i		−	0.709660i	0.934931	−	0.354830i	$-0.115461\pi$
$348$		0			0
$349$	20.4390			1.09407			0.547037	−	0.837108i	$-0.315756\pi$
$349$	20.4390			1.09407			0.547037	+	0.837108i	$0.315756\pi$
$350$	6.24977	−	19.6547i	0.334064	−	1.05059i
$351$		0			0
$352$		−	2.64002i		−	0.140714i
$353$			10.7044i			0.569735i	0.958567	+	0.284868i	$0.0919497\pi$
$353$			10.7044i			0.569735i	−0.958567	+	0.284868i	$0.908050\pi$
$354$		0			0
$355$	20.1055	−	14.7044i	1.06709	−	0.780426i
$356$	7.60975			0.403316
$357$		0			0
$358$			1.52982i			0.0808534i
$359$	−4.31410			−0.227690			−0.113845	−	0.993499i	$-0.536317\pi$
$359$	−4.31410			−0.227690			−0.113845	+	0.993499i	$0.536317\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			14.7493i			0.775207i
$363$		0			0
$364$	−10.3747			−0.543780
$365$	−3.56978	−	4.88102i	−0.186851	−	0.255484i
$366$		0			0
$367$		−	12.8099i		−	0.668669i	−0.942454	−	0.334335i	$-0.891488\pi$
$367$		−	12.8099i		−	0.668669i	0.942454	−	0.334335i	$-0.108512\pi$
$368$			3.09461i			0.161318i
$369$		0			0
$370$	−18.4995	+	13.5298i	−0.961745	+	0.703382i
$371$	−22.6244			−1.17460
$372$		0			0
$373$		−	0.704357i		−	0.0364702i	−0.999834	−	0.0182351i	$-0.994195\pi$
$373$		−	0.704357i		−	0.0364702i	0.999834	−	0.0182351i	$-0.00580474\pi$
$374$	1.35998			0.0703227
$375$		0			0
$376$	−4.96972			−0.256294
$377$			19.6060i			1.00976i
$378$		0			0
$379$	−6.12489			−0.314614			−0.157307	−	0.987550i	$-0.550281\pi$
$379$	−6.12489			−0.314614			−0.157307	+	0.987550i	$0.550281\pi$
$380$	−1.80487	+	1.32001i	−0.0925881	+	0.0677152i
$381$		0			0
$382$			18.1249i			0.927350i
$383$			18.6400i			0.952461i	0.879321	+	0.476230i	$0.157997\pi$
$383$			18.6400i			0.952461i	−0.879321	+	0.476230i	$0.842003\pi$
$384$		0			0
$385$	−14.3747	−	19.6547i	−0.732600	−	1.00170i
$386$	4.56009			0.232103
$387$		0			0
$388$		−	3.93945i		−	0.199995i
$389$	13.9201			0.705776			0.352888	−	0.935666i	$-0.385200\pi$
$389$	13.9201			0.705776			0.352888	+	0.935666i	$0.385200\pi$
$390$		0			0
$391$	−1.59415			−0.0806197
$392$		−	10.0147i		−	0.505818i
$393$		0			0
$394$	2.14048			0.107836
$395$	30.2304	−	22.1093i	1.52106	−	1.11244i
$396$		0			0
$397$		−	28.3784i		−	1.42427i	−0.702041	−	0.712136i	$-0.747728\pi$
$397$		−	28.3784i		−	1.42427i	0.702041	−	0.712136i	$-0.252272\pi$
$398$			16.5639i			0.830272i
$399$		0			0
$400$	1.51514	−	4.76491i	0.0757569	−	0.238245i
$401$	−5.54920			−0.277114			−0.138557	−	0.990354i	$-0.544246\pi$
$401$	−5.54920			−0.277114			−0.138557	+	0.990354i	$0.544246\pi$
$402$		0			0
$403$		−	9.23131i		−	0.459844i
$404$	−13.7990			−0.686524
$405$		0			0
$406$	−32.1542			−1.59579
$407$			27.0596i			1.34130i
$408$		0			0
$409$	5.01090			0.247773			0.123886	−	0.992296i	$-0.460464\pi$
$409$	5.01090			0.247773			0.123886	+	0.992296i	$0.460464\pi$
$410$	−11.7346	−	16.0450i	−0.579532	−	0.792404i
$411$		0			0
$412$			4.57947i			0.225614i
$413$			13.0147i			0.640411i
$414$		0			0
$415$	−4.32970	−	5.92007i	−0.212537	−	0.290605i
$416$	−2.51514			−0.123315
$417$		0			0
$418$			2.64002i			0.129128i
$419$	−15.8889			−0.776222			−0.388111	−	0.921613i	$-0.626872\pi$
$419$	−15.8889			−0.776222			−0.388111	+	0.921613i	$0.626872\pi$
$420$		0			0
$421$	−2.38647			−0.116310			−0.0581548	−	0.998308i	$-0.518522\pi$
$421$	−2.38647			−0.116310			−0.0581548	+	0.998308i	$0.518522\pi$
$422$			15.2838i			0.744005i
$423$		0			0
$424$	−5.48486			−0.266368
$425$	2.45459	+	0.780505i	0.119065	+	0.0378601i
$426$		0			0
$427$		−	52.1386i		−	2.52317i
$428$		−	10.3747i		−	0.501478i
$429$		0			0
$430$	15.5942	−	11.4049i	0.752017	−	0.549995i
$431$	2.35906			0.113632			0.0568160	−	0.998385i	$-0.481905\pi$
$431$	2.35906			0.113632			0.0568160	+	0.998385i	$0.481905\pi$
$432$		0			0
$433$			0.640023i			0.0307576i	0.999882	+	0.0153788i	$0.00489541\pi$
$433$			0.640023i			0.0307576i	−0.999882	+	0.0153788i	$0.995105\pi$
$434$	15.1396			0.726722
$435$		0			0
$436$	3.01468			0.144377
$437$		−	3.09461i		−	0.148035i
$438$		0			0
$439$	25.4499			1.21466			0.607328	−	0.794451i	$-0.292241\pi$
$439$	25.4499			1.21466			0.607328	+	0.794451i	$0.292241\pi$
$440$	−3.48486	−	4.76491i	−0.166134	−	0.227158i
$441$		0			0
$442$		−	1.29564i		−	0.0616275i
$443$		−	35.6685i		−	1.69466i	−0.531067	−	0.847330i	$-0.678209\pi$
$443$		−	35.6685i		−	1.69466i	0.531067	−	0.847330i	$-0.321791\pi$
$444$		0			0
$445$	13.7346	−	10.0450i	0.651084	−	0.476177i
$446$	3.75023			0.177578
$447$		0			0
$448$		−	4.12489i		−	0.194883i
$449$	−11.4399			−0.539883			−0.269941	−	0.962877i	$-0.587004\pi$
$449$	−11.4399			−0.539883			−0.269941	+	0.962877i	$0.587004\pi$
$450$		0			0
$451$	−23.4693			−1.10512
$452$			19.2001i			0.903098i
$453$		0			0
$454$	24.1542			1.13361
$455$	−18.7249	+	13.6947i	−0.877839	+	0.642016i
$456$		0			0
$457$			19.4849i			0.911463i	0.890117	+	0.455732i	$0.150622\pi$
$457$			19.4849i			0.911463i	−0.890117	+	0.455732i	$0.849378\pi$
$458$		−	13.0596i		−	0.610237i
$459$		0			0
$460$	4.08492	+	5.58538i	0.190460	+	0.260420i
$461$	29.3893			1.36880			0.684399	−	0.729108i	$-0.260065\pi$
$461$	29.3893			1.36880			0.684399	+	0.729108i	$0.260065\pi$
$462$		0			0
$463$		−	12.1892i		−	0.566481i	−0.959049	−	0.283241i	$-0.908591\pi$
$463$		−	12.1892i		−	0.566481i	0.959049	−	0.283241i	$-0.0914095\pi$
$464$	−7.79518			−0.361882
$465$		0			0
$466$	−6.43899			−0.298280
$467$			17.8889i			0.827799i	0.910323	+	0.413899i	$0.135833\pi$
$467$			17.8889i			0.827799i	−0.910323	+	0.413899i	$0.864167\pi$
$468$		0			0
$469$	30.5445			1.41041
$470$	−8.96972	+	6.56009i	−0.413743	+	0.302595i
$471$		0			0
$472$			3.15516i			0.145228i
$473$		−	22.8099i		−	1.04880i
$474$		0			0
$475$	−1.51514	+	4.76491i	−0.0695193	+	0.218629i
$476$	2.12489			0.0973940
$477$		0			0
$478$		−	22.8742i		−	1.04624i
$479$	−1.15894			−0.0529534			−0.0264767	−	0.999649i	$-0.508429\pi$
$479$	−1.15894			−0.0529534			−0.0264767	+	0.999649i	$0.508429\pi$
$480$		0			0
$481$	25.7796			1.17545
$482$		−	4.96972i		−	0.226365i
$483$		0			0
$484$	4.03028			0.183194
$485$	−5.20012	−	7.11021i	−0.236125	−	0.322858i
$486$		0			0
$487$			30.6888i			1.39064i	0.718700	+	0.695320i	$0.244737\pi$
$487$			30.6888i			1.39064i	−0.718700	+	0.695320i	$0.755263\pi$
$488$		−	12.6400i		−	0.572187i
$489$		0			0
$490$	−13.2195	−	18.0752i	−0.597196	−	0.816556i
$491$	−3.67030			−0.165638			−0.0828192	−	0.996565i	$-0.526392\pi$
$491$	−3.67030			−0.165638			−0.0828192	+	0.996565i	$0.526392\pi$
$492$		0			0
$493$		−	4.01560i		−	0.180853i
$494$	2.51514			0.113161
$495$		0			0
$496$	3.67030			0.164801
$497$		−	45.9494i		−	2.06111i
$498$		0			0
$499$	−31.3893			−1.40518			−0.702590	−	0.711595i	$-0.747973\pi$
$499$	−31.3893			−1.40518			−0.702590	+	0.711595i	$0.747973\pi$
$500$	−3.55510	−	10.6001i	−0.158989	−	0.474049i
$501$		0			0
$502$			15.9201i			0.710548i
$503$		−	18.1542i		−	0.809458i	−0.914437	−	0.404729i	$-0.867366\pi$
$503$		−	18.1542i		−	0.809458i	0.914437	−	0.404729i	$-0.132634\pi$
$504$		0			0
$505$	−24.9054	+	18.2148i	−1.10828	+	0.810548i
$506$	8.16984			0.363194
$507$		0			0
$508$		−	14.3103i		−	0.634918i
$509$	11.5298			0.511050			0.255525	−	0.966802i	$-0.417752\pi$
$509$	11.5298			0.511050			0.255525	+	0.966802i	$0.417752\pi$
$510$		0			0
$511$	−11.1552			−0.493475
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	1.04965			0.0462982
$515$	6.04496	+	8.26537i	0.266373	+	0.364216i
$516$		0			0
$517$			13.1202i			0.577025i
$518$			42.2791i			1.85764i
$519$		0			0
$520$	−4.53951	+	3.32001i	−0.199071	+	0.145592i
$521$	42.5895			1.86588			0.932939	−	0.360035i	$-0.117235\pi$
$521$	42.5895			1.86588			0.932939	+	0.360035i	$0.117235\pi$
$522$		0			0
$523$		−	1.21571i		−	0.0531594i	−0.999647	−	0.0265797i	$-0.991538\pi$
$523$		−	1.21571i		−	0.0531594i	0.999647	−	0.0265797i	$-0.00846159\pi$
$524$	−6.56009			−0.286579
$525$		0			0
$526$	−11.9394			−0.520585
$527$			1.89071i			0.0823607i
$528$		0			0
$529$	13.4234			0.583626
$530$	−9.89948	+	7.24008i	−0.430006	+	0.314489i
$531$		0			0
$532$			4.12489i			0.178836i
$533$			22.3591i			0.968478i
$534$		0			0
$535$	−13.6947	−	18.7249i	−0.592072	−	0.809550i
$536$	7.40493			0.319844
$537$		0			0
$538$			15.9394i			0.687198i
$539$	−26.4390			−1.13881
$540$		0			0
$541$	−1.92007			−0.0825503			−0.0412751	−	0.999148i	$-0.513142\pi$
$541$	−1.92007			−0.0825503			−0.0412751	+	0.999148i	$0.513142\pi$
$542$		−	1.46548i		−	0.0629480i
$543$		0			0
$544$	0.515138			0.0220864
$545$	5.44112	−	3.97941i	0.233072	−	0.170459i
$546$		0			0
$547$			10.9697i			0.469032i	0.972112	+	0.234516i	$0.0753504\pi$
$547$			10.9697i			0.469032i	−0.972112	+	0.234516i	$0.924650\pi$
$548$		−	6.45459i		−	0.275726i
$549$		0			0
$550$	−12.5795	−	4.00000i	−0.536390	−	0.170561i
$551$	7.79518			0.332086
$552$		0			0
$553$		−	69.0890i		−	2.93796i
$554$	32.4995			1.38077
$555$		0			0
$556$	−23.0596			−0.977946
$557$		−	23.5005i		−	0.995746i	−0.867250	−	0.497873i	$-0.834114\pi$
$557$		−	23.5005i		−	0.995746i	0.867250	−	0.497873i	$-0.165886\pi$
$558$		0			0
$559$	−21.7309			−0.919117
$560$	−5.44490	−	7.44490i	−0.230089	−	0.314604i
$561$		0			0
$562$			1.04965i			0.0442770i
$563$		−	7.87890i		−	0.332056i	−0.986121	−	0.166028i	$-0.946906\pi$
$563$		−	7.87890i		−	0.332056i	0.986121	−	0.166028i	$-0.0530942\pi$
$564$		0			0
$565$	25.3444	+	34.6538i	1.06625	+	1.45790i
$566$	9.34060			0.392615
$567$		0			0
$568$		−	11.1396i		−	0.467406i
$569$	−1.09083			−0.0457299			−0.0228650	−	0.999739i	$-0.507279\pi$
$569$	−1.09083			−0.0457299			−0.0228650	+	0.999739i	$0.507279\pi$
$570$		0			0
$571$	21.4886			0.899272			0.449636	−	0.893212i	$-0.351554\pi$
$571$	21.4886			0.899272			0.449636	+	0.893212i	$0.351554\pi$
$572$			6.64002i			0.277633i
$573$		0			0
$574$	−36.6694			−1.53055
$575$	14.7455	+	4.68876i	0.614931	+	0.195535i
$576$		0			0
$577$		−	16.1055i		−	0.670481i	−0.942133	−	0.335241i	$-0.891182\pi$
$577$		−	16.1055i		−	0.670481i	0.942133	−	0.335241i	$-0.108818\pi$
$578$		−	16.7346i		−	0.696069i
$579$		0			0
$580$	−14.0693	+	10.2897i	−0.584197	+	0.427258i
$581$	−13.5298			−0.561311
$582$		0			0
$583$			14.4802i			0.599707i
$584$	−2.70436			−0.111907
$585$		0			0
$586$	25.5748			1.05648
$587$		−	0.480164i		−	0.0198185i	−0.999951	−	0.00990925i	$-0.996846\pi$
$587$		−	0.480164i		−	0.0198185i	0.999951	−	0.00990925i	$-0.00315426\pi$
$588$		0			0
$589$	−3.67030			−0.151232
$590$	4.16485	+	5.69467i	0.171464	+	0.234446i
$591$		0			0
$592$			10.2498i			0.421263i
$593$			40.4683i			1.66184i	0.556395	+	0.830918i	$0.312184\pi$
$593$			40.4683i			1.66184i	−0.556395	+	0.830918i	$0.687816\pi$
$594$		0			0
$595$	3.83515	−	2.80487i	0.157226	−	0.114989i
$596$	−16.0294			−0.656588
$597$		0			0
$598$		−	7.78337i		−	0.318286i
$599$	−36.1698			−1.47786			−0.738930	−	0.673782i	$-0.764669\pi$
$599$	−36.1698			−1.47786			−0.738930	+	0.673782i	$0.764669\pi$
$600$		0			0
$601$	24.3903			0.994899			0.497450	−	0.867493i	$-0.334270\pi$
$601$	24.3903			0.994899			0.497450	+	0.867493i	$0.334270\pi$
$602$		−	35.6391i		−	1.45254i
$603$		0			0
$604$	14.3103			0.582279
$605$	7.27414	−	5.32001i	0.295736	−	0.216289i
$606$		0			0
$607$			21.6897i			0.880357i	0.897910	+	0.440178i	$0.145085\pi$
$607$			21.6897i			0.880357i	−0.897910	+	0.440178i	$0.854915\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	−16.6850	−	22.8136i	−0.675555	−	0.923698i
$611$	12.4995			0.505677
$612$		0			0
$613$			26.2304i			1.05944i	0.848174	+	0.529718i	$0.177702\pi$
$613$			26.2304i			1.05944i	−0.848174	+	0.529718i	$0.822298\pi$
$614$	9.43991			0.380964
$615$		0			0
$616$	−10.8898			−0.438762
$617$			22.7200i			0.914671i	0.889294	+	0.457335i	$0.151196\pi$
$617$			22.7200i			0.914671i	−0.889294	+	0.457335i	$0.848804\pi$
$618$		0			0
$619$	32.9192			1.32313			0.661566	−	0.749887i	$-0.269892\pi$
$619$	32.9192			1.32313			0.661566	+	0.749887i	$0.269892\pi$
$620$	6.62443	−	4.84484i	0.266043	−	0.194573i
$621$		0			0
$622$		−	17.4655i		−	0.700302i
$623$		−	31.3893i		−	1.25759i
$624$		0			0
$625$	−20.4087	−	14.4390i	−0.816349	−	0.577560i
$626$	10.4546			0.417849
$627$		0			0
$628$			18.0294i			0.719450i
$629$	−5.28005			−0.210529
$630$		0			0
$631$	17.2876			0.688209			0.344104	−	0.938931i	$-0.388183\pi$
$631$	17.2876			0.688209			0.344104	+	0.938931i	$0.388183\pi$
$632$		−	16.7493i		−	0.666252i
$633$		0			0
$634$	−4.33348			−0.172105
$635$	−18.8898	−	25.8283i	−0.749619	−	1.02497i
$636$		0			0
$637$			25.1883i			0.997997i
$638$			20.5795i			0.814749i
$639$		0			0
$640$	−1.32001	−	1.80487i	−0.0521780	−	0.0713439i
$641$	9.29942			0.367305			0.183653	−	0.982991i	$-0.441208\pi$
$641$	9.29942			0.367305			0.183653	+	0.982991i	$0.441208\pi$
$642$		0			0
$643$			3.40115i			0.134128i	0.997749	+	0.0670642i	$0.0213632\pi$
$643$			3.40115i			0.134128i	−0.997749	+	0.0670642i	$0.978637\pi$
$644$	12.7649			0.503008
$645$		0			0
$646$	−0.515138			−0.0202678
$647$		−	14.9348i		−	0.587146i	−0.955937	−	0.293573i	$-0.905156\pi$
$647$		−	14.9348i		−	0.587146i	0.955937	−	0.293573i	$-0.0948443\pi$
$648$		0			0
$649$	8.32970			0.326969
$650$	−3.81078	+	11.9844i	−0.149471	+	0.470067i
$651$		0			0
$652$			2.70058i			0.105763i
$653$			21.1202i			0.826497i	0.910618	+	0.413248i	$0.135606\pi$
$653$			21.1202i			0.826497i	−0.910618	+	0.413248i	$0.864394\pi$
$654$		0			0
$655$	−11.8401	+	8.65940i	−0.462633	+	0.338351i
$656$	−8.88979			−0.347088
$657$		0			0
$658$			20.4995i			0.799155i
$659$	27.6547			1.07727			0.538637	−	0.842538i	$-0.318939\pi$
$659$	27.6547			1.07727			0.538637	+	0.842538i	$0.318939\pi$
$660$		0			0
$661$	10.2342			0.398063			0.199032	−	0.979993i	$-0.436220\pi$
$661$	10.2342			0.398063			0.199032	+	0.979993i	$0.436220\pi$
$662$			4.56387i			0.177380i
$663$		0			0
$664$	−3.28005			−0.127291
$665$	5.44490	+	7.44490i	0.211144	+	0.288701i
$666$		0			0
$667$		−	24.1231i		−	0.934048i
$668$			8.95035i			0.346299i
$669$		0			0
$670$	13.3650	−	9.77460i	0.516334	−	0.377626i
$671$	−33.3700			−1.28823
$672$		0			0
$673$			13.4693i			0.519202i	0.965716	+	0.259601i	$0.0835911\pi$
$673$			13.4693i			0.519202i	−0.965716	+	0.259601i	$0.916409\pi$
$674$	13.0109			0.501161
$675$		0			0
$676$	−6.67408			−0.256695
$677$		−	15.1433i		−	0.582006i	−0.956722	−	0.291003i	$-0.906011\pi$
$677$		−	15.1433i		−	0.582006i	0.956722	−	0.291003i	$-0.0939890\pi$
$678$		0			0
$679$	−16.2498			−0.623609
$680$	0.929759	−	0.679988i	0.0356546	−	0.0260764i
$681$		0			0
$682$		−	9.68968i		−	0.371037i
$683$			15.8789i			0.607589i	0.952738	+	0.303795i	$0.0982536\pi$
$683$			15.8789i			0.607589i	−0.952738	+	0.303795i	$0.901746\pi$
$684$		0			0
$685$	−8.52013	−	11.6497i	−0.325537	−	0.445113i
$686$	−12.4352			−0.474778
$687$		0			0
$688$		−	8.64002i		−	0.329398i
$689$	13.7952			0.525555
$690$		0			0
$691$	27.3094			1.03890			0.519449	−	0.854501i	$-0.326137\pi$
$691$	27.3094			1.03890			0.519449	+	0.854501i	$0.326137\pi$
$692$		−	0.310323i		−	0.0117967i
$693$		0			0
$694$	−13.2195			−0.501805
$695$	−41.6197	+	30.4390i	−1.57873	+	1.15462i
$696$		0			0
$697$		−	4.57947i		−	0.173460i
$698$		−	20.4390i		−	0.773627i
$699$		0			0
$700$	−19.6547	−	6.24977i	−0.742878	−	0.236219i
$701$	20.9697			0.792016			0.396008	−	0.918247i	$-0.370395\pi$
$701$	20.9697			0.792016			0.396008	+	0.918247i	$0.370395\pi$
$702$		0			0
$703$		−	10.2498i		−	0.386577i
$704$	−2.64002			−0.0994996
$705$		0			0
$706$	10.7044			0.402864
$707$			56.9192i			2.14067i
$708$		0			0
$709$	−37.5592			−1.41056			−0.705282	−	0.708927i	$-0.749180\pi$
$709$	−37.5592			−1.41056			−0.705282	+	0.708927i	$0.749180\pi$
$710$	−14.7044	−	20.1055i	−0.551845	−	0.754546i
$711$		0			0
$712$		−	7.60975i		−	0.285187i
$713$			11.3581i			0.425366i
$714$		0			0
$715$	8.76491	+	11.9844i	0.327789	+	0.448191i
$716$	1.52982			0.0571720
$717$		0			0
$718$			4.31410i			0.161001i
$719$	3.94323			0.147058			0.0735288	−	0.997293i	$-0.476574\pi$
$719$	3.94323			0.147058			0.0735288	+	0.997293i	$0.476574\pi$
$720$		0			0
$721$	18.8898			0.703493
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	14.7493			0.548154
$725$	−11.8108	+	37.1433i	−0.438641	+	1.37947i
$726$		0			0
$727$			33.2139i			1.23183i	0.787811	+	0.615917i	$0.211214\pi$
$727$			33.2139i			1.23183i	−0.787811	+	0.615917i	$0.788786\pi$
$728$			10.3747i			0.384510i
$729$		0			0
$730$	−4.88102	+	3.56978i	−0.180655	+	0.132124i
$731$	4.45080			0.164619
$732$		0			0
$733$			8.62065i			0.318411i	0.987245	+	0.159205i	$0.0508932\pi$
$733$			8.62065i			0.318411i	−0.987245	+	0.159205i	$0.949107\pi$
$734$	−12.8099			−0.472821
$735$		0			0
$736$	3.09461			0.114069
$737$		−	19.5492i		−	0.720104i
$738$		0			0
$739$	45.1689			1.66157			0.830783	−	0.556597i	$-0.187893\pi$
$739$	45.1689			1.66157			0.830783	+	0.556597i	$0.187893\pi$
$740$	13.5298	+	18.4995i	0.497366	+	0.680057i
$741$		0			0
$742$			22.6244i			0.830569i
$743$		−	24.7905i		−	0.909475i	−0.890626	−	0.454737i	$-0.849733\pi$
$743$		−	24.7905i		−	0.909475i	0.890626	−	0.454737i	$-0.150267\pi$
$744$		0			0
$745$	−28.9310	+	21.1589i	−1.05995	+	0.775204i
$746$	−0.704357			−0.0257883
$747$		0			0
$748$		−	1.35998i		−	0.0497257i
$749$	−42.7943			−1.56367
$750$		0			0
$751$	−6.76869			−0.246993			−0.123497	−	0.992345i	$-0.539411\pi$
$751$	−6.76869			−0.246993			−0.123497	+	0.992345i	$0.539411\pi$
$752$			4.96972i			0.181227i
$753$		0			0
$754$	19.6060			0.714007
$755$	25.8283	−	18.8898i	0.939989	−	0.687470i
$756$		0			0
$757$			45.2101i			1.64319i	0.570072	+	0.821595i	$0.306915\pi$
$757$			45.2101i			1.64319i	−0.570072	+	0.821595i	$0.693085\pi$
$758$			6.12489i			0.222466i
$759$		0			0
$760$	1.32001	+	1.80487i	0.0478819	+	0.0654696i
$761$	−19.8851			−0.720834			−0.360417	−	0.932791i	$-0.617366\pi$
$761$	−19.8851			−0.720834			−0.360417	+	0.932791i	$0.617366\pi$
$762$		0			0
$763$		−	12.4352i		−	0.450185i
$764$	18.1249			0.655735
$765$		0			0
$766$	18.6400			0.673491
$767$		−	7.93567i		−	0.286540i
$768$		0			0
$769$	−8.07615			−0.291233			−0.145617	−	0.989341i	$-0.546517\pi$
$769$	−8.07615			−0.291233			−0.145617	+	0.989341i	$0.546517\pi$
$770$	−19.6547	+	14.3747i	−0.708306	+	0.518027i
$771$		0			0
$772$		−	4.56009i		−	0.164121i
$773$			45.9456i			1.65255i	0.563267	+	0.826275i	$0.309544\pi$
$773$			45.9456i			1.65255i	−0.563267	+	0.826275i	$0.690456\pi$
$774$		0			0
$775$	5.56101	−	17.4886i	0.199757	−	0.628211i
$776$	−3.93945			−0.141418
$777$		0			0
$778$		−	13.9201i		−	0.499059i
$779$	8.88979			0.318510
$780$		0			0
$781$	−29.4087			−1.05233
$782$			1.59415i			0.0570067i
$783$		0			0
$784$	−10.0147			−0.357667
$785$	23.7990	+	32.5407i	0.849422	+	1.16143i
$786$		0			0
$787$		−	17.8439i		−	0.636067i	−0.948079	−	0.318034i	$-0.896978\pi$
$787$		−	17.8439i		−	0.636067i	0.948079	−	0.318034i	$-0.103022\pi$
$788$		−	2.14048i		−	0.0762515i
$789$		0			0
$790$	−22.1093	−	30.2304i	−0.786613	−	1.07555i
$791$	79.1983			2.81597
$792$		0			0
$793$			31.7914i			1.12895i
$794$	−28.3784			−1.00711
$795$		0			0
$796$	16.5639			0.587091
$797$			37.3326i			1.32239i	0.750215	+	0.661194i	$0.229950\pi$
$797$			37.3326i			1.32239i	−0.750215	+	0.661194i	$0.770050\pi$
$798$		0			0
$799$	−2.56009			−0.0905696
$800$	−4.76491	−	1.51514i	−0.168465	−	0.0535682i
$801$		0			0
$802$			5.54920i			0.195949i
$803$			7.13957i			0.251950i
$804$		0			0
$805$	23.0390	−	16.8498i	0.812020	−	0.593878i
$806$	−9.23131			−0.325159
$807$		0			0
$808$			13.7990i			0.485446i
$809$	−38.6950			−1.36044			−0.680221	−	0.733007i	$-0.738116\pi$
$809$	−38.6950			−1.36044			−0.680221	+	0.733007i	$0.738116\pi$
$810$		0			0
$811$	13.3444			0.468585			0.234292	−	0.972166i	$-0.424723\pi$
$811$	13.3444			0.468585			0.234292	+	0.972166i	$0.424723\pi$
$812$			32.1542i			1.12839i
$813$		0			0
$814$	27.0596			0.948440
$815$	3.56479	+	4.87420i	0.124869	+	0.170736i
$816$		0			0
$817$			8.64002i			0.302276i
$818$		−	5.01090i		−	0.175202i
$819$		0			0
$820$	−16.0450	+	11.7346i	−0.560314	+	0.409791i
$821$	37.3482			1.30346			0.651730	−	0.758451i	$-0.274044\pi$
$821$	37.3482			1.30346			0.651730	+	0.758451i	$0.274044\pi$
$822$		0			0
$823$			51.5630i			1.79737i	0.438593	+	0.898686i	$0.355477\pi$
$823$			51.5630i			1.79737i	−0.438593	+	0.898686i	$0.644523\pi$
$824$	4.57947			0.159533
$825$		0			0
$826$	13.0147			0.452839
$827$			48.5639i			1.68873i	0.535767	+	0.844366i	$0.320022\pi$
$827$			48.5639i			1.68873i	−0.535767	+	0.844366i	$0.679978\pi$
$828$		0			0
$829$	−0.325919			−0.0113196			−0.00565982	−	0.999984i	$-0.501802\pi$
$829$	−0.325919			−0.0113196			−0.00565982	+	0.999984i	$0.501802\pi$
$830$	−5.92007	+	4.32970i	−0.205489	+	0.150286i
$831$		0			0
$832$			2.51514i			0.0871967i
$833$		−	5.15894i		−	0.178747i
$834$		0			0
$835$	11.8146	+	16.1542i	0.408860	+	0.559041i
$836$	2.64002			0.0913071
$837$		0			0
$838$			15.8889i			0.548872i
$839$	−17.1202			−0.591055			−0.295527	−	0.955334i	$-0.595495\pi$
$839$	−17.1202			−0.591055			−0.295527	+	0.955334i	$0.595495\pi$
$840$		0			0
$841$	31.7649			1.09534
$842$			2.38647i			0.0822432i
$843$		0			0
$844$	15.2838			0.526091
$845$	−12.0459	+	8.80986i	−0.414391	+	0.303069i
$846$		0			0
$847$		−	16.6244i		−	0.571222i
$848$			5.48486i			0.188351i
$849$		0			0
$850$	0.780505	−	2.45459i	0.0267711	−	0.0841916i
$851$	−31.7190			−1.08731
$852$		0			0
$853$			24.9092i			0.852874i	0.904517	+	0.426437i	$0.140231\pi$
$853$			24.9092i			0.852874i	−0.904517	+	0.426437i	$0.859769\pi$
$854$	−52.1386			−1.78415
$855$		0			0
$856$	−10.3747			−0.354598
$857$			11.6509i			0.397988i	0.980001	+	0.198994i	$0.0637674\pi$
$857$			11.6509i			0.397988i	−0.980001	+	0.198994i	$0.936233\pi$
$858$		0			0
$859$	5.35998			0.182880			0.0914400	−	0.995811i	$-0.470853\pi$
$859$	5.35998			0.182880			0.0914400	+	0.995811i	$0.470853\pi$
$860$	−11.4049	−	15.5942i	−0.388905	−	0.531756i
$861$		0			0
$862$		−	2.35906i		−	0.0803499i
$863$		−	41.0790i		−	1.39835i	−0.714953	−	0.699173i	$-0.753552\pi$
$863$		−	41.0790i		−	1.39835i	0.714953	−	0.699173i	$-0.246448\pi$
$864$		0			0
$865$	−0.409630	−	0.560094i	−0.0139278	−	0.0190438i
$866$	0.640023			0.0217489
$867$		0			0
$868$		−	15.1396i		−	0.513870i
$869$	−44.2186			−1.50001
$870$		0			0
$871$	−18.6244			−0.631065
$872$		−	3.01468i		−	0.102090i
$873$		0			0
$874$	−3.09461			−0.104677
$875$	−43.7240	+	14.6644i	−1.47814	+	0.495747i
$876$		0			0
$877$			45.9532i			1.55173i	0.630899	+	0.775865i	$0.282686\pi$
$877$			45.9532i			1.55173i	−0.630899	+	0.775865i	$0.717314\pi$
$878$		−	25.4499i		−	0.858892i
$879$		0			0
$880$	−4.76491	+	3.48486i	−0.160625	+	0.117475i
$881$	6.90917			0.232776			0.116388	−	0.993204i	$-0.462868\pi$
$881$	6.90917			0.232776			0.116388	+	0.993204i	$0.462868\pi$
$882$		0			0
$883$		−	48.5213i		−	1.63287i	−0.577435	−	0.816437i	$-0.695946\pi$
$883$		−	48.5213i		−	1.63287i	0.577435	−	0.816437i	$-0.304054\pi$
$884$	−1.29564			−0.0435772
$885$		0			0
$886$	−35.6685			−1.19831
$887$		−	23.7990i		−	0.799091i	−0.916713	−	0.399546i	$-0.869168\pi$
$887$		−	23.7990i		−	0.799091i	0.916713	−	0.399546i	$-0.130832\pi$
$888$		0			0
$889$	−59.0284			−1.97975
$890$	−10.0450	−	13.7346i	−0.336708	−	0.460386i
$891$		0			0
$892$		−	3.75023i		−	0.125567i
$893$		−	4.96972i		−	0.166305i
$894$		0			0
$895$	2.76113	−	2.01938i	0.0922943	−	0.0675003i
$896$	−4.12489			−0.137803
$897$		0			0
$898$			11.4399i			0.381755i
$899$	−28.6107			−0.954219
$900$		0			0
$901$	−2.82546			−0.0941298
$902$			23.4693i			0.781441i
$903$		0			0
$904$	19.2001			0.638586
$905$	26.6206	−	19.4693i	0.884900	−	0.647180i
$906$		0			0
$907$			17.9726i			0.596770i	0.954446	+	0.298385i	$0.0964479\pi$
$907$			17.9726i			0.596770i	−0.954446	+	0.298385i	$0.903552\pi$
$908$		−	24.1542i		−	0.801587i
$909$		0			0
$910$	13.6947	+	18.7249i	0.453974	+	0.620726i
$911$	−19.5592			−0.648024			−0.324012	−	0.946053i	$-0.605032\pi$
$911$	−19.5592			−0.648024			−0.324012	+	0.946053i	$0.605032\pi$
$912$		0			0
$913$			8.65940i			0.286584i
$914$	19.4849			0.644502
$915$		0			0
$916$	−13.0596			−0.431503
$917$			27.0596i			0.893588i
$918$		0			0
$919$	−35.4948			−1.17087			−0.585433	−	0.810720i	$-0.699076\pi$
$919$	−35.4948			−1.17087			−0.585433	+	0.810720i	$0.699076\pi$
$920$	5.58538	−	4.08492i	0.184144	−	0.134676i
$921$		0			0
$922$		−	29.3893i		−	0.967886i
$923$			28.0175i			0.922209i
$924$		0			0
$925$	48.8392	+	15.5298i	1.60582	+	0.510617i
$926$	−12.1892			−0.400563
$927$		0			0
$928$			7.79518i			0.255889i
$929$	17.9532			0.589026			0.294513	−	0.955648i	$-0.404843\pi$
$929$	17.9532			0.589026			0.294513	+	0.955648i	$0.404843\pi$
$930$		0			0
$931$	10.0147			0.328218
$932$			6.43899i			0.210916i
$933$		0			0
$934$	17.8889			0.585342
$935$	−1.79518	−	2.45459i	−0.0587088	−	0.0802735i
$936$		0			0
$937$		−	5.66652i		−	0.185117i	−0.995707	−	0.0925585i	$-0.970495\pi$
$937$		−	5.66652i		−	0.185117i	0.995707	−	0.0925585i	$-0.0295045\pi$
$938$		−	30.5445i		−	0.997313i
$939$		0			0
$940$	6.56009	+	8.96972i	0.213967	+	0.292560i
$941$	24.7044			0.805339			0.402670	−	0.915345i	$-0.368082\pi$
$941$	24.7044			0.805339			0.402670	+	0.915345i	$0.368082\pi$
$942$		0			0
$943$		−	27.5104i		−	0.895863i
$944$	3.15516			0.102692
$945$		0			0
$946$	−22.8099			−0.741613
$947$		−	13.5904i		−	0.441628i	−0.975316	−	0.220814i	$-0.929129\pi$
$947$		−	13.5904i		−	0.441628i	0.975316	−	0.220814i	$-0.0708713\pi$
$948$		0			0
$949$	6.80183			0.220797
$950$	4.76491	+	1.51514i	0.154594	+	0.0491576i
$951$		0			0
$952$		−	2.12489i		−	0.0688679i
$953$			24.7375i			0.801326i	0.916225	+	0.400663i	$0.131220\pi$
$953$			24.7375i			0.801326i	−0.916225	+	0.400663i	$0.868780\pi$
$954$		0			0
$955$	32.7131	−	23.9251i	1.05857	−	0.774197i
$956$	−22.8742			−0.739804
$957$		0			0
$958$			1.15894i			0.0374437i
$959$	−26.6244			−0.859748
$960$		0			0
$961$	−17.5289			−0.565448
$962$		−	25.7796i		−	0.831167i
$963$		0			0
$964$	−4.96972			−0.160064
$965$	−6.01938	−	8.23039i	−0.193771	−	0.264946i
$966$		0			0
$967$		−	35.6897i		−	1.14770i	−0.818960	−	0.573851i	$-0.805449\pi$
$967$		−	35.6897i		−	1.14770i	0.818960	−	0.573851i	$-0.194551\pi$
$968$		−	4.03028i		−	0.129538i
$969$		0			0
$970$	−7.11021	+	5.20012i	−0.228295	+	0.166966i
$971$	−16.4995			−0.529495			−0.264748	−	0.964318i	$-0.585289\pi$
$971$	−16.4995			−0.529495			−0.264748	+	0.964318i	$0.585289\pi$
$972$		0			0
$973$			95.1184i			3.04935i
$974$	30.6888			0.983331
$975$		0			0
$976$	−12.6400			−0.404597
$977$		−	49.8501i		−	1.59485i	−0.603420	−	0.797423i	$-0.706196\pi$
$977$		−	49.8501i		−	1.59485i	0.603420	−	0.797423i	$-0.293804\pi$
$978$		0			0
$979$	−20.0899			−0.642076
$980$	−18.0752	+	13.2195i	−0.577392	+	0.422281i
$981$		0			0
$982$			3.67030i			0.117124i
$983$		−	5.19014i		−	0.165540i	−0.996569	−	0.0827698i	$-0.973623\pi$
$983$		−	5.19014i		−	0.165540i	0.996569	−	0.0827698i	$-0.0263766\pi$
$984$		0			0
$985$	−2.82546	−	3.86330i	−0.0900267	−	0.123095i
$986$	−4.01560			−0.127883
$987$		0			0
$988$		−	2.51514i		−	0.0800172i
$989$	26.7375			0.850203
$990$		0			0
$991$	−32.4272			−1.03008			−0.515042	−	0.857165i	$-0.672224\pi$
$991$	−32.4272			−1.03008			−0.515042	+	0.857165i	$0.672224\pi$
$992$		−	3.67030i		−	0.116532i
$993$		0			0
$994$	−45.9494			−1.45743
$995$	29.8957	−	21.8645i	0.947757	−	0.693152i
$996$		0			0
$997$			10.1992i			0.323012i	0.986872	+	0.161506i	$0.0516351\pi$
$997$			10.1992i			0.323012i	−0.986872	+	0.161506i	$0.948365\pi$
$998$			31.3893i			0.993612i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.d.1369.1		6
3.2	odd	2		190.2.b.b.39.6	yes	6
5.2	odd	4		8550.2.a.cl.1.1		3
5.3	odd	4		8550.2.a.ck.1.3		3
5.4	even	2	inner	1710.2.d.d.1369.4		6
12.11	even	2		1520.2.d.j.609.2		6
15.2	even	4		950.2.a.i.1.3		3
15.8	even	4		950.2.a.n.1.1		3
15.14	odd	2		190.2.b.b.39.1	✓	6
60.23	odd	4		7600.2.a.bi.1.3		3
60.47	odd	4		7600.2.a.cd.1.1		3
60.59	even	2		1520.2.d.j.609.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.1	✓	6	15.14	odd	2
190.2.b.b.39.6	yes	6	3.2	odd	2
950.2.a.i.1.3		3	15.2	even	4
950.2.a.n.1.1		3	15.8	even	4
1520.2.d.j.609.2		6	12.11	even	2
1520.2.d.j.609.5		6	60.59	even	2
1710.2.d.d.1369.1		6	1.1	even	1	trivial
1710.2.d.d.1369.4		6	5.4	even	2	inner
7600.2.a.bi.1.3		3	60.23	odd	4
7600.2.a.cd.1.1		3	60.47	odd	4
8550.2.a.ck.1.3		3	5.3	odd	4
8550.2.a.cl.1.1		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.80487 + 1.32001i) q^{5} +4.12489i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.80487 + 1.32001i) q^{5} +4.12489i q^{7} +1.00000i q^{8} +(1.32001 + 1.80487i) q^{10} +2.64002 q^{11} -2.51514i q^{13} +4.12489 q^{14} +1.00000 q^{16} +0.515138i q^{17} -1.00000 q^{19} +(1.80487 - 1.32001i) q^{20} -2.64002i q^{22} +3.09461i q^{23} +(1.51514 - 4.76491i) q^{25} -2.51514 q^{26} -4.12489i q^{28} -7.79518 q^{29} +3.67030 q^{31} -1.00000i q^{32} +0.515138 q^{34} +(-5.44490 - 7.44490i) q^{35} +10.2498i q^{37} +1.00000i q^{38} +(-1.32001 - 1.80487i) q^{40} -8.88979 q^{41} -8.64002i q^{43} -2.64002 q^{44} +3.09461 q^{46} +4.96972i q^{47} -10.0147 q^{49} +(-4.76491 - 1.51514i) q^{50} +2.51514i q^{52} +5.48486i q^{53} +(-4.76491 + 3.48486i) q^{55} -4.12489 q^{56} +7.79518i q^{58} +3.15516 q^{59} -12.6400 q^{61} -3.67030i q^{62} -1.00000 q^{64} +(3.32001 + 4.53951i) q^{65} -7.40493i q^{67} -0.515138i q^{68} +(-7.44490 + 5.44490i) q^{70} -11.1396 q^{71} +2.70436i q^{73} +10.2498 q^{74} +1.00000 q^{76} +10.8898i q^{77} -16.7493 q^{79} +(-1.80487 + 1.32001i) q^{80} +8.88979i q^{82} +3.28005i q^{83} +(-0.679988 - 0.929759i) q^{85} -8.64002 q^{86} +2.64002i q^{88} -7.60975 q^{89} +10.3747 q^{91} -3.09461i q^{92} +4.96972 q^{94} +(1.80487 - 1.32001i) q^{95} +3.93945i q^{97} +10.0147i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^5	\( 6 q - 6 q^{4} - 2 q^{5} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 2 q^{20} + 10 q^{25} - 16 q^{26} - 16 q^{29} + 8 q^{31} + 4 q^{34} - 8 q^{35} - 4 q^{41} + 6 q^{49} + 4 q^{50} + 4 q^{55} - 8 q^{56} + 4 q^{59} - 60 q^{61} - 6 q^{64} + 12 q^{65} - 20 q^{70} + 16 q^{71} + 28 q^{74} + 6 q^{76} - 2 q^{80} - 12 q^{85} - 36 q^{86} - 28 q^{89} + 12 q^{91} + 28 q^{94} + 2 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 2 * q^20 + 10 * q^25 - 16 * q^26 - 16 * q^29 + 8 * q^31 + 4 * q^34 - 8 * q^35 - 4 * q^41 + 6 * q^49 + 4 * q^50 + 4 * q^55 - 8 * q^56 + 4 * q^59 - 60 * q^61 - 6 * q^64 + 12 * q^65 - 20 * q^70 + 16 * q^71 + 28 * q^74 + 6 * q^76 - 2 * q^80 - 12 * q^85 - 36 * q^86 - 28 * q^89 + 12 * q^91 + 28 * q^94 + 2 * q^95

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