LMFDB - Embedded newform 1920.2.bh.a.703.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(703,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.703"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bh (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-8,0,0,0,0,0,0,0,4,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			703.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1920.703
Dual form			1920.2.bh.a.1087.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(2.82843 + 2.82843i) q^{7} +1.00000i q^{9} -2.82843 q^{11} +(1.00000 - 1.00000i) q^{13} +(0.707107 + 2.12132i) q^{15} +(-1.00000 + 1.00000i) q^{17} -4.00000i q^{21} +(3.00000 + 4.00000i) q^{25} +(0.707107 - 0.707107i) q^{27} -2.00000 q^{29} -8.48528i q^{31} +(2.00000 + 2.00000i) q^{33} +(-2.82843 - 8.48528i) q^{35} +(-7.00000 - 7.00000i) q^{37} -1.41421 q^{39} -12.0000 q^{41} +(5.65685 + 5.65685i) q^{43} +(1.00000 - 2.00000i) q^{45} +(-2.82843 - 2.82843i) q^{47} +9.00000i q^{49} +1.41421 q^{51} +(-7.00000 + 7.00000i) q^{53} +(5.65685 + 2.82843i) q^{55} +8.48528i q^{59} +2.00000i q^{61} +(-2.82843 + 2.82843i) q^{63} +(-3.00000 + 1.00000i) q^{65} +(5.65685 - 5.65685i) q^{67} -11.3137i q^{71} +(-9.00000 - 9.00000i) q^{73} +(0.707107 - 4.94975i) q^{75} +(-8.00000 - 8.00000i) q^{77} +2.82843 q^{79} -1.00000 q^{81} +(-2.82843 - 2.82843i) q^{83} +(3.00000 - 1.00000i) q^{85} +(1.41421 + 1.41421i) q^{87} +12.0000i q^{89} +5.65685 q^{91} +(-6.00000 + 6.00000i) q^{93} +(-13.0000 + 13.0000i) q^{97} -2.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5} + 4 q^{13} - 4 q^{17} + 12 q^{25} - 8 q^{29} + 8 q^{33} - 28 q^{37} - 48 q^{41} + 4 q^{45} - 28 q^{53} - 12 q^{65} - 36 q^{73} - 32 q^{77} - 4 q^{81} + 12 q^{85} - 24 q^{93} - 52 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 + 4 * q^13 - 4 * q^17 + 12 * q^25 - 8 * q^29 + 8 * q^33 - 28 * q^37 - 48 * q^41 + 4 * q^45 - 28 * q^53 - 12 * q^65 - 36 * q^73 - 32 * q^77 - 4 * q^81 + 12 * q^85 - 24 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	2.82843	+	2.82843i	1.06904	+	1.06904i	0.997433	+	0.0716124i	$0.0228145\pi$
$7$	2.82843	+	2.82843i	1.06904	+	1.06904i	0.0716124	+	0.997433i	$0.477186\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$		0			0
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$	0.707107	+	2.12132i	0.182574	+	0.547723i
$16$		0			0
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		−	4.00000i		−	0.872872i
$22$		0			0
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$		−	8.48528i		−	1.52400i	−0.647576	−	0.762001i	$-0.724217\pi$
$31$		−	8.48528i		−	1.52400i	0.647576	−	0.762001i	$-0.275783\pi$
$32$		0			0
$33$	2.00000	+	2.00000i	0.348155	+	0.348155i
$34$		0			0
$35$	−2.82843	−	8.48528i	−0.478091	−	1.43427i
$36$		0			0
$37$	−7.00000	−	7.00000i	−1.15079	−	1.15079i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−7.00000	−	7.00000i	−1.15079	−	1.15079i	−0.164399	−	0.986394i	$-0.552568\pi$
$38$		0			0
$39$	−1.41421			−0.226455
$40$		0			0
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$		0			0
$43$	5.65685	+	5.65685i	0.862662	+	0.862662i	0.991647	−	0.128984i	$-0.0411717\pi$
$43$	5.65685	+	5.65685i	0.862662	+	0.862662i	−0.128984	+	0.991647i	$0.541172\pi$
$44$		0			0
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$		0			0
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	0.470064	−	0.882632i	$-0.344231\pi$
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	−0.882632	+	0.470064i	$0.844231\pi$
$48$		0			0
$49$			9.00000i			1.28571i
$50$		0			0
$51$	1.41421			0.198030
$52$		0			0
$53$	−7.00000	+	7.00000i	−0.961524	+	0.961524i	−0.999287	−	0.0377628i	$-0.987977\pi$
$53$	−7.00000	+	7.00000i	−0.961524	+	0.961524i	0.0377628	+	0.999287i	$0.487977\pi$
$54$		0			0
$55$	5.65685	+	2.82843i	0.762770	+	0.381385i
$56$		0			0
$57$		0			0
$58$		0			0
$59$			8.48528i			1.10469i	0.833616	+	0.552345i	$0.186267\pi$
$59$			8.48528i			1.10469i	−0.833616	+	0.552345i	$0.813733\pi$
$60$		0			0
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$		0			0
$63$	−2.82843	+	2.82843i	−0.356348	+	0.356348i
$64$		0			0
$65$	−3.00000	+	1.00000i	−0.372104	+	0.124035i
$66$		0			0
$67$	5.65685	−	5.65685i	0.691095	−	0.691095i	−0.271378	−	0.962473i	$-0.587479\pi$
$67$	5.65685	−	5.65685i	0.691095	−	0.691095i	0.962473	+	0.271378i	$0.0874794\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.3137i		−	1.34269i	−0.741145	−	0.671345i	$-0.765717\pi$
$71$		−	11.3137i		−	1.34269i	0.741145	−	0.671345i	$-0.234283\pi$
$72$		0			0
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.998493	−	0.0548772i	$-0.982523\pi$
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.0548772	−	0.998493i	$-0.517477\pi$
$74$		0			0
$75$	0.707107	−	4.94975i	0.0816497	−	0.571548i
$76$		0			0
$77$	−8.00000	−	8.00000i	−0.911685	−	0.911685i
$78$		0			0
$79$	2.82843			0.318223			0.159111	−	0.987261i	$-0.449137\pi$
$79$	2.82843			0.318223			0.159111	+	0.987261i	$0.449137\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	0.534628	−	0.845088i	$-0.320452\pi$
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	−0.845088	+	0.534628i	$0.820452\pi$
$84$		0			0
$85$	3.00000	−	1.00000i	0.325396	−	0.108465i
$86$		0			0
$87$	1.41421	+	1.41421i	0.151620	+	0.151620i
$88$		0			0
$89$			12.0000i			1.27200i	0.771690	+	0.635999i	$0.219412\pi$
$89$			12.0000i			1.27200i	−0.771690	+	0.635999i	$0.780588\pi$
$90$		0			0
$91$	5.65685			0.592999
$92$		0			0
$93$	−6.00000	+	6.00000i	−0.622171	+	0.622171i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.0000	+	13.0000i	−1.31995	+	1.31995i	−0.406138	+	0.913812i	$0.633125\pi$
$97$	−13.0000	+	13.0000i	−1.31995	+	1.31995i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$		−	2.82843i		−	0.284268i
$100$		0			0
$101$			4.00000i			0.398015i	0.979998	+	0.199007i	$0.0637718\pi$
$101$			4.00000i			0.398015i	−0.979998	+	0.199007i	$0.936228\pi$
$102$		0			0
$103$	−5.65685	+	5.65685i	−0.557386	+	0.557386i	−0.928562	−	0.371176i	$-0.878955\pi$
$103$	−5.65685	+	5.65685i	−0.557386	+	0.557386i	0.371176	+	0.928562i	$0.378955\pi$
$104$		0			0
$105$	−4.00000	+	8.00000i	−0.390360	+	0.780720i
$106$		0			0
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$108$		0			0
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$		0			0
$111$			9.89949i			0.939618i
$112$		0			0
$113$	5.00000	+	5.00000i	0.470360	+	0.470360i	0.902031	−	0.431671i	$-0.142076\pi$
$113$	5.00000	+	5.00000i	0.470360	+	0.470360i	−0.431671	+	0.902031i	$0.642076\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.00000	+	1.00000i	0.0924500	+	0.0924500i
$118$		0			0
$119$	−5.65685			−0.518563
$120$		0			0
$121$	−3.00000			−0.272727
$122$		0			0
$123$	8.48528	+	8.48528i	0.765092	+	0.765092i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$		0			0
$129$		−	8.00000i		−	0.704361i
$130$		0			0
$131$	−19.7990			−1.72985			−0.864923	−	0.501905i	$-0.832633\pi$
$131$	−19.7990			−1.72985			−0.864923	+	0.501905i	$0.832633\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.12132	+	0.707107i	−0.182574	+	0.0608581i
$136$		0			0
$137$	7.00000	−	7.00000i	0.598050	−	0.598050i	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	7.00000	−	7.00000i	0.598050	−	0.598050i	0.939793	+	0.341743i	$0.111017\pi$
$138$		0			0
$139$			16.9706i			1.43942i	0.694273	+	0.719712i	$0.255726\pi$
$139$			16.9706i			1.43942i	−0.694273	+	0.719712i	$0.744274\pi$
$140$		0			0
$141$			4.00000i			0.336861i
$142$		0			0
$143$	−2.82843	+	2.82843i	−0.236525	+	0.236525i
$144$		0			0
$145$	4.00000	+	2.00000i	0.332182	+	0.166091i
$146$		0			0
$147$	6.36396	−	6.36396i	0.524891	−	0.524891i
$148$		0			0
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$			8.48528i			0.690522i	0.938507	+	0.345261i	$0.112210\pi$
$151$			8.48528i			0.690522i	−0.938507	+	0.345261i	$0.887790\pi$
$152$		0			0
$153$	−1.00000	−	1.00000i	−0.0808452	−	0.0808452i
$154$		0			0
$155$	−8.48528	+	16.9706i	−0.681554	+	1.36311i
$156$		0			0
$157$	−13.0000	−	13.0000i	−1.03751	−	1.03751i	−0.999268	−	0.0382445i	$-0.987823\pi$
$157$	−13.0000	−	13.0000i	−1.03751	−	1.03751i	−0.0382445	−	0.999268i	$-0.512177\pi$
$158$		0			0
$159$	9.89949			0.785081
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−14.1421	−	14.1421i	−1.10770	−	1.10770i	−0.993453	−	0.114245i	$-0.963555\pi$
$163$	−14.1421	−	14.1421i	−1.10770	−	1.10770i	−0.114245	−	0.993453i	$-0.536445\pi$
$164$		0			0
$165$	−2.00000	−	6.00000i	−0.155700	−	0.467099i
$166$		0			0
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	0.297966	−	0.954577i	$-0.403692\pi$
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	−0.954577	+	0.297966i	$0.903692\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	−0.389026	−	0.921227i	$-0.627189\pi$
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	0.921227	+	0.389026i	$0.127189\pi$
$174$		0			0
$175$	−2.82843	+	19.7990i	−0.213809	+	1.49666i
$176$		0			0
$177$	6.00000	−	6.00000i	0.450988	−	0.450988i
$178$		0			0
$179$			2.82843i			0.211407i	0.994398	+	0.105703i	$0.0337094\pi$
$179$			2.82843i			0.211407i	−0.994398	+	0.105703i	$0.966291\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	1.41421	−	1.41421i	0.104542	−	0.104542i
$184$		0			0
$185$	7.00000	+	21.0000i	0.514650	+	1.54395i
$186$		0			0
$187$	2.82843	−	2.82843i	0.206835	−	0.206835i
$188$		0			0
$189$	4.00000			0.290957
$190$		0			0
$191$		−	16.9706i		−	1.22795i	−0.789327	−	0.613973i	$-0.789570\pi$
$191$		−	16.9706i		−	1.22795i	0.789327	−	0.613973i	$-0.210430\pi$
$192$		0			0
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	0.408768	−	0.912639i	$-0.365959\pi$
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	−0.912639	+	0.408768i	$0.865959\pi$
$194$		0			0
$195$	2.82843	+	1.41421i	0.202548	+	0.101274i
$196$		0			0
$197$	−11.0000	−	11.0000i	−0.783718	−	0.783718i	0.196738	−	0.980456i	$-0.436965\pi$
$197$	−11.0000	−	11.0000i	−0.783718	−	0.783718i	−0.980456	+	0.196738i	$0.936965\pi$
$198$		0			0
$199$	−8.48528			−0.601506			−0.300753	−	0.953702i	$-0.597238\pi$
$199$	−8.48528			−0.601506			−0.300753	+	0.953702i	$0.597238\pi$
$200$		0			0
$201$	−8.00000			−0.564276
$202$		0			0
$203$	−5.65685	−	5.65685i	−0.397033	−	0.397033i
$204$		0			0
$205$	24.0000	+	12.0000i	1.67623	+	0.838116i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	22.6274			1.55774			0.778868	−	0.627188i	$-0.215794\pi$
$211$	22.6274			1.55774			0.778868	+	0.627188i	$0.215794\pi$
$212$		0			0
$213$	−8.00000	+	8.00000i	−0.548151	+	0.548151i
$214$		0			0
$215$	−5.65685	−	16.9706i	−0.385794	−	1.15738i
$216$		0			0
$217$	24.0000	−	24.0000i	1.62923	−	1.62923i
$218$		0			0
$219$			12.7279i			0.860073i
$220$		0			0
$221$			2.00000i			0.134535i
$222$		0			0
$223$	−5.65685	+	5.65685i	−0.378811	+	0.378811i	−0.870673	−	0.491862i	$-0.836316\pi$
$223$	−5.65685	+	5.65685i	−0.378811	+	0.378811i	0.491862	+	0.870673i	$0.336316\pi$
$224$		0			0
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$		0			0
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$			11.3137i			0.744387i
$232$		0			0
$233$	3.00000	+	3.00000i	0.196537	+	0.196537i	0.798513	−	0.601977i	$-0.205620\pi$
$233$	3.00000	+	3.00000i	0.196537	+	0.196537i	−0.601977	+	0.798513i	$0.705620\pi$
$234$		0			0
$235$	2.82843	+	8.48528i	0.184506	+	0.553519i
$236$		0			0
$237$	−2.00000	−	2.00000i	−0.129914	−	0.129914i
$238$		0			0
$239$	28.2843			1.82956			0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843			1.82956			0.914779	+	0.403955i	$0.132365\pi$
$240$		0			0
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	9.00000	−	18.0000i	0.574989	−	1.14998i
$246$		0			0
$247$		0			0
$248$		0			0
$249$			4.00000i			0.253490i
$250$		0			0
$251$	14.1421			0.892644			0.446322	−	0.894873i	$-0.352734\pi$
$251$	14.1421			0.892644			0.446322	+	0.894873i	$0.352734\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−2.82843	−	1.41421i	−0.177123	−	0.0885615i
$256$		0			0
$257$	21.0000	−	21.0000i	1.30994	−	1.30994i	0.388492	−	0.921452i	$-0.372996\pi$
$257$	21.0000	−	21.0000i	1.30994	−	1.30994i	0.921452	−	0.388492i	$-0.127004\pi$
$258$		0			0
$259$		−	39.5980i		−	2.46050i
$260$		0			0
$261$		−	2.00000i		−	0.123797i
$262$		0			0
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.253531	−	0.967327i	$-0.418408\pi$
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.967327	−	0.253531i	$-0.0815919\pi$
$264$		0			0
$265$	21.0000	−	7.00000i	1.29002	−	0.430007i
$266$		0			0
$267$	8.48528	−	8.48528i	0.519291	−	0.519291i
$268$		0			0
$269$	12.0000			0.731653			0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000			0.731653			0.365826	+	0.930683i	$0.380786\pi$
$270$		0			0
$271$			8.48528i			0.515444i	0.966219	+	0.257722i	$0.0829719\pi$
$271$			8.48528i			0.515444i	−0.966219	+	0.257722i	$0.917028\pi$
$272$		0			0
$273$	−4.00000	−	4.00000i	−0.242091	−	0.242091i
$274$		0			0
$275$	−8.48528	−	11.3137i	−0.511682	−	0.682242i
$276$		0			0
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	0.791466	−	0.611213i	$-0.209318\pi$
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	−0.611213	+	0.791466i	$0.709318\pi$
$278$		0			0
$279$	8.48528			0.508001
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$		0			0
$283$	−5.65685	−	5.65685i	−0.336265	−	0.336265i	0.518695	−	0.854960i	$-0.326418\pi$
$283$	−5.65685	−	5.65685i	−0.336265	−	0.336265i	−0.854960	+	0.518695i	$0.826418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−33.9411	−	33.9411i	−2.00348	−	2.00348i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$	18.3848			1.07773
$292$		0			0
$293$	−11.0000	+	11.0000i	−0.642627	+	0.642627i	−0.951200	−	0.308574i	$-0.900148\pi$
$293$	−11.0000	+	11.0000i	−0.642627	+	0.642627i	0.308574	+	0.951200i	$0.400148\pi$
$294$		0			0
$295$	8.48528	−	16.9706i	0.494032	−	0.988064i
$296$		0			0
$297$	−2.00000	+	2.00000i	−0.116052	+	0.116052i
$298$		0			0
$299$		0			0
$300$		0			0
$301$			32.0000i			1.84445i
$302$		0			0
$303$	2.82843	−	2.82843i	0.162489	−	0.162489i
$304$		0			0
$305$	2.00000	−	4.00000i	0.114520	−	0.229039i
$306$		0			0
$307$	−2.82843	+	2.82843i	−0.161427	+	0.161427i	−0.783199	−	0.621772i	$-0.786413\pi$
$307$	−2.82843	+	2.82843i	−0.161427	+	0.161427i	0.621772	+	0.783199i	$0.286413\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$			22.6274i			1.28308i	0.767088	+	0.641542i	$0.221705\pi$
$311$			22.6274i			1.28308i	−0.767088	+	0.641542i	$0.778295\pi$
$312$		0			0
$313$	−13.0000	−	13.0000i	−0.734803	−	0.734803i	0.236764	−	0.971567i	$-0.423913\pi$
$313$	−13.0000	−	13.0000i	−0.734803	−	0.734803i	−0.971567	+	0.236764i	$0.923913\pi$
$314$		0			0
$315$	8.48528	−	2.82843i	0.478091	−	0.159364i
$316$		0			0
$317$	11.0000	+	11.0000i	0.617822	+	0.617822i	0.944972	−	0.327151i	$-0.106088\pi$
$317$	11.0000	+	11.0000i	0.617822	+	0.617822i	−0.327151	+	0.944972i	$0.606088\pi$
$318$		0			0
$319$	5.65685			0.316723
$320$		0			0
$321$	8.00000			0.446516
$322$		0			0
$323$		0			0
$324$		0			0
$325$	7.00000	+	1.00000i	0.388290	+	0.0554700i
$326$		0			0
$327$	11.3137	+	11.3137i	0.625650	+	0.625650i
$328$		0			0
$329$		−	16.0000i		−	0.882109i
$330$		0			0
$331$	11.3137			0.621858			0.310929	−	0.950433i	$-0.399360\pi$
$331$	11.3137			0.621858			0.310929	+	0.950433i	$0.399360\pi$
$332$		0			0
$333$	7.00000	−	7.00000i	0.383598	−	0.383598i
$334$		0			0
$335$	−16.9706	+	5.65685i	−0.927201	+	0.309067i
$336$		0			0
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	−0.557685	−	0.830053i	$-0.688310\pi$
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	0.830053	+	0.557685i	$0.188310\pi$
$338$		0			0
$339$		−	7.07107i		−	0.384048i
$340$		0			0
$341$			24.0000i			1.29967i
$342$		0			0
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.6274	+	22.6274i	−1.21470	+	1.21470i	−0.245241	+	0.969462i	$0.578867\pi$
$347$	−22.6274	+	22.6274i	−1.21470	+	1.21470i	−0.969462	+	0.245241i	$0.921133\pi$
$348$		0			0
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$		−	1.41421i		−	0.0754851i
$352$		0			0
$353$	−17.0000	−	17.0000i	−0.904819	−	0.904819i	0.0910295	−	0.995848i	$-0.470984\pi$
$353$	−17.0000	−	17.0000i	−0.904819	−	0.904819i	−0.995848	+	0.0910295i	$0.970984\pi$
$354$		0			0
$355$	−11.3137	+	22.6274i	−0.600469	+	1.20094i
$356$		0			0
$357$	4.00000	+	4.00000i	0.211702	+	0.211702i
$358$		0			0
$359$	−5.65685			−0.298557			−0.149279	−	0.988795i	$-0.547695\pi$
$359$	−5.65685			−0.298557			−0.149279	+	0.988795i	$0.547695\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	2.12132	+	2.12132i	0.111340	+	0.111340i
$364$		0			0
$365$	9.00000	+	27.0000i	0.471082	+	1.41324i
$366$		0			0
$367$	19.7990	+	19.7990i	1.03350	+	1.03350i	0.999419	+	0.0340797i	$0.0108500\pi$
$367$	19.7990	+	19.7990i	1.03350	+	1.03350i	0.0340797	+	0.999419i	$0.489150\pi$
$368$		0			0
$369$		−	12.0000i		−	0.624695i
$370$		0			0
$371$	−39.5980			−2.05582
$372$		0			0
$373$	1.00000	−	1.00000i	0.0517780	−	0.0517780i	−0.680744	−	0.732522i	$-0.738343\pi$
$373$	1.00000	−	1.00000i	0.0517780	−	0.0517780i	0.732522	+	0.680744i	$0.238343\pi$
$374$		0			0
$375$	−6.36396	+	9.19239i	−0.328634	+	0.474693i
$376$		0			0
$377$	−2.00000	+	2.00000i	−0.103005	+	0.103005i
$378$		0			0
$379$		−	22.6274i		−	1.16229i	−0.813799	−	0.581146i	$-0.802604\pi$
$379$		−	22.6274i		−	1.16229i	0.813799	−	0.581146i	$-0.197396\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	22.6274	−	22.6274i	1.15621	−	1.15621i	0.170923	−	0.985284i	$-0.445325\pi$
$383$	22.6274	−	22.6274i	1.15621	−	1.15621i	0.985284	−	0.170923i	$-0.0546748\pi$
$384$		0			0
$385$	8.00000	+	24.0000i	0.407718	+	1.22315i
$386$		0			0
$387$	−5.65685	+	5.65685i	−0.287554	+	0.287554i
$388$		0			0
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	14.0000	+	14.0000i	0.706207	+	0.706207i
$394$		0			0
$395$	−5.65685	−	2.82843i	−0.284627	−	0.142314i
$396$		0			0
$397$	−21.0000	−	21.0000i	−1.05396	−	1.05396i	−0.998459	−	0.0555012i	$-0.982324\pi$
$397$	−21.0000	−	21.0000i	−1.05396	−	1.05396i	−0.0555012	−	0.998459i	$-0.517676\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	−8.48528	−	8.48528i	−0.422682	−	0.422682i
$404$		0			0
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$		0			0
$407$	19.7990	+	19.7990i	0.981399	+	0.981399i
$408$		0			0
$409$		−	34.0000i		−	1.68119i	−0.541663	−	0.840596i	$-0.682205\pi$
$409$		−	34.0000i		−	1.68119i	0.541663	−	0.840596i	$-0.317795\pi$
$410$		0			0
$411$	−9.89949			−0.488306
$412$		0			0
$413$	−24.0000	+	24.0000i	−1.18096	+	1.18096i
$414$		0			0
$415$	2.82843	+	8.48528i	0.138842	+	0.416526i
$416$		0			0
$417$	12.0000	−	12.0000i	0.587643	−	0.587643i
$418$		0			0
$419$			19.7990i			0.967244i	0.875277	+	0.483622i	$0.160679\pi$
$419$			19.7990i			0.967244i	−0.875277	+	0.483622i	$0.839321\pi$
$420$		0			0
$421$			26.0000i			1.26716i	0.773676	+	0.633581i	$0.218416\pi$
$421$			26.0000i			1.26716i	−0.773676	+	0.633581i	$0.781584\pi$
$422$		0			0
$423$	2.82843	−	2.82843i	0.137523	−	0.137523i
$424$		0			0
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$	−5.65685	+	5.65685i	−0.273754	+	0.273754i
$428$		0			0
$429$	4.00000			0.193122
$430$		0			0
$431$		−	5.65685i		−	0.272481i	−0.990676	−	0.136241i	$-0.956498\pi$
$431$		−	5.65685i		−	0.272481i	0.990676	−	0.136241i	$-0.0435020\pi$
$432$		0			0
$433$	−9.00000	−	9.00000i	−0.432512	−	0.432512i	0.456970	−	0.889482i	$-0.348935\pi$
$433$	−9.00000	−	9.00000i	−0.432512	−	0.432512i	−0.889482	+	0.456970i	$0.848935\pi$
$434$		0			0
$435$	−1.41421	−	4.24264i	−0.0678064	−	0.203419i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−8.48528			−0.404980			−0.202490	−	0.979284i	$-0.564903\pi$
$439$	−8.48528			−0.404980			−0.202490	+	0.979284i	$0.564903\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−5.65685	−	5.65685i	−0.268765	−	0.268765i	0.559837	−	0.828603i	$-0.310864\pi$
$443$	−5.65685	−	5.65685i	−0.268765	−	0.268765i	−0.828603	+	0.559837i	$0.810864\pi$
$444$		0			0
$445$	12.0000	−	24.0000i	0.568855	−	1.13771i
$446$		0			0
$447$	−8.48528	−	8.48528i	−0.401340	−	0.401340i
$448$		0			0
$449$		−	18.0000i		−	0.849473i	−0.905317	−	0.424736i	$-0.860367\pi$
$449$		−	18.0000i		−	0.849473i	0.905317	−	0.424736i	$-0.139633\pi$
$450$		0			0
$451$	33.9411			1.59823
$452$		0			0
$453$	6.00000	−	6.00000i	0.281905	−	0.281905i
$454$		0			0
$455$	−11.3137	−	5.65685i	−0.530395	−	0.265197i
$456$		0			0
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	−0.263099	−	0.964769i	$-0.584744\pi$
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	0.964769	+	0.263099i	$0.0847444\pi$
$458$		0			0
$459$			1.41421i			0.0660098i
$460$		0			0
$461$			12.0000i			0.558896i	0.960161	+	0.279448i	$0.0901514\pi$
$461$			12.0000i			0.558896i	−0.960161	+	0.279448i	$0.909849\pi$
$462$		0			0
$463$	−25.4558	+	25.4558i	−1.18303	+	1.18303i	−0.204079	+	0.978954i	$0.565420\pi$
$463$	−25.4558	+	25.4558i	−1.18303	+	1.18303i	−0.978954	+	0.204079i	$0.934580\pi$
$464$		0			0
$465$	18.0000	−	6.00000i	0.834730	−	0.278243i
$466$		0			0
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	−0.299634	−	0.954054i	$-0.596865\pi$
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	0.954054	+	0.299634i	$0.0968646\pi$
$468$		0			0
$469$	32.0000			1.47762
$470$		0			0
$471$			18.3848i			0.847126i
$472$		0			0
$473$	−16.0000	−	16.0000i	−0.735681	−	0.735681i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.00000	−	7.00000i	−0.320508	−	0.320508i
$478$		0			0
$479$	−11.3137			−0.516937			−0.258468	−	0.966020i	$-0.583218\pi$
$479$	−11.3137			−0.516937			−0.258468	+	0.966020i	$0.583218\pi$
$480$		0			0
$481$	−14.0000			−0.638345
$482$		0			0
$483$		0			0
$484$		0			0
$485$	39.0000	−	13.0000i	1.77090	−	0.590300i
$486$		0			0
$487$	11.3137	+	11.3137i	0.512673	+	0.512673i	0.915345	−	0.402671i	$-0.131918\pi$
$487$	11.3137	+	11.3137i	0.512673	+	0.512673i	−0.402671	+	0.915345i	$0.631918\pi$
$488$		0			0
$489$			20.0000i			0.904431i
$490$		0			0
$491$	−14.1421			−0.638226			−0.319113	−	0.947717i	$-0.603385\pi$
$491$	−14.1421			−0.638226			−0.319113	+	0.947717i	$0.603385\pi$
$492$		0			0
$493$	2.00000	−	2.00000i	0.0900755	−	0.0900755i
$494$		0			0
$495$	−2.82843	+	5.65685i	−0.127128	+	0.254257i
$496$		0			0
$497$	32.0000	−	32.0000i	1.43540	−	1.43540i
$498$		0			0
$499$			16.9706i			0.759707i	0.925047	+	0.379853i	$0.124026\pi$
$499$			16.9706i			0.759707i	−0.925047	+	0.379853i	$0.875974\pi$
$500$		0			0
$501$			12.0000i			0.536120i
$502$		0			0
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	−0.492163	−	0.870503i	$-0.663794\pi$
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	0.870503	+	0.492163i	$0.163794\pi$
$504$		0			0
$505$	4.00000	−	8.00000i	0.177998	−	0.355995i
$506$		0			0
$507$	7.77817	−	7.77817i	0.345441	−	0.345441i
$508$		0			0
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$		0			0
$511$		−	50.9117i		−	2.25220i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.9706	−	5.65685i	0.747812	−	0.249271i
$516$		0			0
$517$	8.00000	+	8.00000i	0.351840	+	0.351840i
$518$		0			0
$519$	−9.89949			−0.434540
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$	14.1421	+	14.1421i	0.618392	+	0.618392i	0.945119	−	0.326727i	$-0.105946\pi$
$523$	14.1421	+	14.1421i	0.618392	+	0.618392i	−0.326727	+	0.945119i	$0.605946\pi$
$524$		0			0
$525$	16.0000	−	12.0000i	0.698297	−	0.523723i
$526$		0			0
$527$	8.48528	+	8.48528i	0.369625	+	0.369625i
$528$		0			0
$529$			23.0000i			1.00000i
$530$		0			0
$531$	−8.48528			−0.368230
$532$		0			0
$533$	−12.0000	+	12.0000i	−0.519778	+	0.519778i
$534$		0			0
$535$	16.9706	−	5.65685i	0.733701	−	0.244567i
$536$		0			0
$537$	2.00000	−	2.00000i	0.0863064	−	0.0863064i
$538$		0			0
$539$		−	25.4558i		−	1.09646i
$540$		0			0
$541$		−	16.0000i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$541$		−	16.0000i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	32.0000	+	16.0000i	1.37073	+	0.685365i
$546$		0			0
$547$	−16.9706	+	16.9706i	−0.725609	+	0.725609i	−0.969742	−	0.244133i	$-0.921497\pi$
$547$	−16.9706	+	16.9706i	−0.725609	+	0.725609i	0.244133	+	0.969742i	$0.421497\pi$
$548$		0			0
$549$	−2.00000			−0.0853579
$550$		0			0
$551$		0			0
$552$		0			0
$553$	8.00000	+	8.00000i	0.340195	+	0.340195i
$554$		0			0
$555$	9.89949	−	19.7990i	0.420210	−	0.840420i
$556$		0			0
$557$	−5.00000	−	5.00000i	−0.211857	−	0.211857i	0.593199	−	0.805056i	$-0.297865\pi$
$557$	−5.00000	−	5.00000i	−0.211857	−	0.211857i	−0.805056	+	0.593199i	$0.797865\pi$
$558$		0			0
$559$	11.3137			0.478519
$560$		0			0
$561$	−4.00000			−0.168880
$562$		0			0
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	0.967623	−	0.252399i	$-0.0812196\pi$
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	−0.252399	+	0.967623i	$0.581220\pi$
$564$		0			0
$565$	−5.00000	−	15.0000i	−0.210352	−	0.631055i
$566$		0			0
$567$	−2.82843	−	2.82843i	−0.118783	−	0.118783i
$568$		0			0
$569$			26.0000i			1.08998i	0.838444	+	0.544988i	$0.183466\pi$
$569$			26.0000i			1.08998i	−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	16.9706			0.710196			0.355098	−	0.934829i	$-0.384448\pi$
$571$	16.9706			0.710196			0.355098	+	0.934829i	$0.384448\pi$
$572$		0			0
$573$	−12.0000	+	12.0000i	−0.501307	+	0.501307i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	15.0000	−	15.0000i	0.624458	−	0.624458i	−0.322210	−	0.946668i	$-0.604426\pi$
$577$	15.0000	−	15.0000i	0.624458	−	0.624458i	0.946668	+	0.322210i	$0.104426\pi$
$578$		0			0
$579$			9.89949i			0.411409i
$580$		0			0
$581$		−	16.0000i		−	0.663792i
$582$		0			0
$583$	19.7990	−	19.7990i	0.819990	−	0.819990i
$584$		0			0
$585$	−1.00000	−	3.00000i	−0.0413449	−	0.124035i
$586$		0			0
$587$	5.65685	−	5.65685i	0.233483	−	0.233483i	−0.580662	−	0.814145i	$-0.697206\pi$
$587$	5.65685	−	5.65685i	0.233483	−	0.233483i	0.814145	+	0.580662i	$0.197206\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$			15.5563i			0.639903i
$592$		0			0
$593$	−13.0000	−	13.0000i	−0.533846	−	0.533846i	0.387869	−	0.921715i	$-0.373211\pi$
$593$	−13.0000	−	13.0000i	−0.533846	−	0.533846i	−0.921715	+	0.387869i	$0.873211\pi$
$594$		0			0
$595$	11.3137	+	5.65685i	0.463817	+	0.231908i
$596$		0			0
$597$	6.00000	+	6.00000i	0.245564	+	0.245564i
$598$		0			0
$599$	−45.2548			−1.84906			−0.924531	−	0.381106i	$-0.875543\pi$
$599$	−45.2548			−1.84906			−0.924531	+	0.381106i	$0.875543\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$	5.65685	+	5.65685i	0.230365	+	0.230365i
$604$		0			0
$605$	6.00000	+	3.00000i	0.243935	+	0.121967i
$606$		0			0
$607$	−25.4558	−	25.4558i	−1.03322	−	1.03322i	−0.999429	−	0.0337920i	$-0.989242\pi$
$607$	−25.4558	−	25.4558i	−1.03322	−	1.03322i	−0.0337920	−	0.999429i	$-0.510758\pi$
$608$		0			0
$609$			8.00000i			0.324176i
$610$		0			0
$611$	−5.65685			−0.228852
$612$		0			0
$613$	−15.0000	+	15.0000i	−0.605844	+	0.605844i	−0.941857	−	0.336013i	$-0.890921\pi$
$613$	−15.0000	+	15.0000i	−0.605844	+	0.605844i	0.336013	+	0.941857i	$0.390921\pi$
$614$		0			0
$615$	−8.48528	−	25.4558i	−0.342160	−	1.02648i
$616$		0			0
$617$	−5.00000	+	5.00000i	−0.201292	+	0.201292i	−0.800554	−	0.599261i	$-0.795461\pi$
$617$	−5.00000	+	5.00000i	−0.201292	+	0.201292i	0.599261	+	0.800554i	$0.295461\pi$
$618$		0			0
$619$		−	11.3137i		−	0.454736i	−0.973809	−	0.227368i	$-0.926988\pi$
$619$		−	11.3137i		−	0.454736i	0.973809	−	0.227368i	$-0.0730121\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−33.9411	+	33.9411i	−1.35982	+	1.35982i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.0000			0.558217
$630$		0			0
$631$		−	8.48528i		−	0.337794i	−0.985634	−	0.168897i	$-0.945980\pi$
$631$		−	8.48528i		−	0.337794i	0.985634	−	0.168897i	$-0.0540205\pi$
$632$		0			0
$633$	−16.0000	−	16.0000i	−0.635943	−	0.635943i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.00000	+	9.00000i	0.356593	+	0.356593i
$638$		0			0
$639$	11.3137			0.447563
$640$		0			0
$641$	20.0000			0.789953			0.394976	−	0.918691i	$-0.370753\pi$
$641$	20.0000			0.789953			0.394976	+	0.918691i	$0.370753\pi$
$642$		0			0
$643$	31.1127	+	31.1127i	1.22697	+	1.22697i	0.965106	+	0.261859i	$0.0843355\pi$
$643$	31.1127	+	31.1127i	1.22697	+	1.22697i	0.261859	+	0.965106i	$0.415665\pi$
$644$		0			0
$645$	−8.00000	+	16.0000i	−0.315000	+	0.629999i
$646$		0			0
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	0.520358	−	0.853948i	$-0.325799\pi$
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	−0.853948	+	0.520358i	$0.825799\pi$
$648$		0			0
$649$		−	24.0000i		−	0.942082i
$650$		0			0
$651$	−33.9411			−1.33026
$652$		0			0
$653$	29.0000	−	29.0000i	1.13486	−	1.13486i	0.145499	−	0.989358i	$-0.453521\pi$
$653$	29.0000	−	29.0000i	1.13486	−	1.13486i	0.989358	−	0.145499i	$-0.0464789\pi$
$654$		0			0
$655$	39.5980	+	19.7990i	1.54722	+	0.773611i
$656$		0			0
$657$	9.00000	−	9.00000i	0.351123	−	0.351123i
$658$		0			0
$659$			14.1421i			0.550899i	0.961315	+	0.275450i	$0.0888267\pi$
$659$			14.1421i			0.550899i	−0.961315	+	0.275450i	$0.911173\pi$
$660$		0			0
$661$		−	10.0000i		−	0.388955i	−0.980907	−	0.194477i	$-0.937699\pi$
$661$		−	10.0000i		−	0.388955i	0.980907	−	0.194477i	$-0.0623011\pi$
$662$		0			0
$663$	1.41421	−	1.41421i	0.0549235	−	0.0549235i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	8.00000			0.309298
$670$		0			0
$671$		−	5.65685i		−	0.218380i
$672$		0			0
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$		0			0
$675$	4.94975	+	0.707107i	0.190516	+	0.0272166i
$676$		0			0
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$		0			0
$679$	−73.5391			−2.82217
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.82843	+	2.82843i	0.108227	+	0.108227i	0.759147	−	0.650920i	$-0.225617\pi$
$683$	2.82843	+	2.82843i	0.108227	+	0.108227i	−0.650920	+	0.759147i	$0.725617\pi$
$684$		0			0
$685$	−21.0000	+	7.00000i	−0.802369	+	0.267456i
$686$		0			0
$687$	4.24264	+	4.24264i	0.161867	+	0.161867i
$688$		0			0
$689$			14.0000i			0.533358i
$690$		0			0
$691$	−5.65685			−0.215197			−0.107598	−	0.994194i	$-0.534316\pi$
$691$	−5.65685			−0.215197			−0.107598	+	0.994194i	$0.534316\pi$
$692$		0			0
$693$	8.00000	−	8.00000i	0.303895	−	0.303895i
$694$		0			0
$695$	16.9706	−	33.9411i	0.643730	−	1.28746i
$696$		0			0
$697$	12.0000	−	12.0000i	0.454532	−	0.454532i
$698$		0			0
$699$		−	4.24264i		−	0.160471i
$700$		0			0
$701$			6.00000i			0.226617i	0.993560	+	0.113308i	$0.0361448\pi$
$701$			6.00000i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	4.00000	−	8.00000i	0.150649	−	0.301297i
$706$		0			0
$707$	−11.3137	+	11.3137i	−0.425496	+	0.425496i
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$			2.82843i			0.106074i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	8.48528	−	2.82843i	0.317332	−	0.105777i
$716$		0			0
$717$	−20.0000	−	20.0000i	−0.746914	−	0.746914i
$718$		0			0
$719$	22.6274			0.843860			0.421930	−	0.906628i	$-0.361353\pi$
$719$	22.6274			0.843860			0.421930	+	0.906628i	$0.361353\pi$
$720$		0			0
$721$	−32.0000			−1.19174
$722$		0			0
$723$	11.3137	+	11.3137i	0.420761	+	0.420761i
$724$		0			0
$725$	−6.00000	−	8.00000i	−0.222834	−	0.297113i
$726$		0			0
$727$	33.9411	+	33.9411i	1.25881	+	1.25881i	0.951663	+	0.307143i	$0.0993731\pi$
$727$	33.9411	+	33.9411i	1.25881	+	1.25881i	0.307143	+	0.951663i	$0.400627\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−11.3137			−0.418453
$732$		0			0
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	−0.927604	−	0.373566i	$-0.878135\pi$
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	0.373566	+	0.927604i	$0.378135\pi$
$734$		0			0
$735$	−19.0919	+	6.36396i	−0.704215	+	0.234738i
$736$		0			0
$737$	−16.0000	+	16.0000i	−0.589368	+	0.589368i
$738$		0			0
$739$			16.9706i			0.624272i	0.950037	+	0.312136i	$0.101045\pi$
$739$			16.9706i			0.624272i	−0.950037	+	0.312136i	$0.898955\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.9706	+	16.9706i	−0.622590	+	0.622590i	−0.946193	−	0.323603i	$-0.895106\pi$
$743$	−16.9706	+	16.9706i	−0.622590	+	0.622590i	0.323603	+	0.946193i	$0.395106\pi$
$744$		0			0
$745$	−24.0000	−	12.0000i	−0.879292	−	0.439646i
$746$		0			0
$747$	2.82843	−	2.82843i	0.103487	−	0.103487i
$748$		0			0
$749$	−32.0000			−1.16925
$750$		0			0
$751$		−	14.1421i		−	0.516054i	−0.966138	−	0.258027i	$-0.916928\pi$
$751$		−	14.1421i		−	0.516054i	0.966138	−	0.258027i	$-0.0830723\pi$
$752$		0			0
$753$	−10.0000	−	10.0000i	−0.364420	−	0.364420i
$754$		0			0
$755$	8.48528	−	16.9706i	0.308811	−	0.617622i
$756$		0			0
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	0.610380	−	0.792108i	$-0.291017\pi$
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	−0.792108	+	0.610380i	$0.791017\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$		0			0
$763$	−45.2548	−	45.2548i	−1.63833	−	1.63833i
$764$		0			0
$765$	1.00000	+	3.00000i	0.0361551	+	0.108465i
$766$		0			0
$767$	8.48528	+	8.48528i	0.306386	+	0.306386i
$768$		0			0
$769$			16.0000i			0.576975i	0.957484	+	0.288487i	$0.0931523\pi$
$769$			16.0000i			0.576975i	−0.957484	+	0.288487i	$0.906848\pi$
$770$		0			0
$771$	−29.6985			−1.06956
$772$		0			0
$773$	7.00000	−	7.00000i	0.251773	−	0.251773i	−0.569925	−	0.821697i	$-0.693028\pi$
$773$	7.00000	−	7.00000i	0.251773	−	0.251773i	0.821697	+	0.569925i	$0.193028\pi$
$774$		0			0
$775$	33.9411	−	25.4558i	1.21920	−	0.914401i
$776$		0			0
$777$	−28.0000	+	28.0000i	−1.00449	+	1.00449i
$778$		0			0
$779$		0			0
$780$		0			0
$781$			32.0000i			1.14505i
$782$		0			0
$783$	−1.41421	+	1.41421i	−0.0505399	+	0.0505399i
$784$		0			0
$785$	13.0000	+	39.0000i	0.463990	+	1.39197i
$786$		0			0
$787$	−19.7990	+	19.7990i	−0.705758	+	0.705758i	−0.965640	−	0.259882i	$-0.916316\pi$
$787$	−19.7990	+	19.7990i	−0.705758	+	0.705758i	0.259882	+	0.965640i	$0.416316\pi$
$788$		0			0
$789$	−28.0000			−0.996826
$790$		0			0
$791$			28.2843i			1.00567i
$792$		0			0
$793$	2.00000	+	2.00000i	0.0710221	+	0.0710221i
$794$		0			0
$795$	−19.7990	−	9.89949i	−0.702198	−	0.351099i
$796$		0			0
$797$	15.0000	+	15.0000i	0.531327	+	0.531327i	0.920967	−	0.389640i	$-0.127401\pi$
$797$	15.0000	+	15.0000i	0.531327	+	0.531327i	−0.389640	+	0.920967i	$0.627401\pi$
$798$		0			0
$799$	5.65685			0.200125
$800$		0			0
$801$	−12.0000			−0.423999
$802$		0			0
$803$	25.4558	+	25.4558i	0.898317	+	0.898317i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.48528	−	8.48528i	−0.298696	−	0.298696i
$808$		0			0
$809$			12.0000i			0.421898i	0.977497	+	0.210949i	$0.0676553\pi$
$809$			12.0000i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$810$		0			0
$811$	−39.5980			−1.39047			−0.695237	−	0.718781i	$-0.744700\pi$
$811$	−39.5980			−1.39047			−0.695237	+	0.718781i	$0.744700\pi$
$812$		0			0
$813$	6.00000	−	6.00000i	0.210429	−	0.210429i
$814$		0			0
$815$	14.1421	+	42.4264i	0.495377	+	1.48613i
$816$		0			0
$817$		0			0
$818$		0			0
$819$			5.65685i			0.197666i
$820$		0			0
$821$			10.0000i			0.349002i	0.984657	+	0.174501i	$0.0558313\pi$
$821$			10.0000i			0.349002i	−0.984657	+	0.174501i	$0.944169\pi$
$822$		0			0
$823$	−28.2843	+	28.2843i	−0.985928	+	0.985928i	−0.999902	−	0.0139746i	$-0.995552\pi$
$823$	−28.2843	+	28.2843i	−0.985928	+	0.985928i	0.0139746	+	0.999902i	$0.495552\pi$
$824$		0			0
$825$	−2.00000	+	14.0000i	−0.0696311	+	0.487417i
$826$		0			0
$827$	36.7696	−	36.7696i	1.27860	−	1.27860i	0.337153	−	0.941450i	$-0.390536\pi$
$827$	36.7696	−	36.7696i	1.27860	−	1.27860i	0.941450	−	0.337153i	$-0.109464\pi$
$828$		0			0
$829$	16.0000			0.555703			0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000			0.555703			0.277851	+	0.960624i	$0.410378\pi$
$830$		0			0
$831$		−	4.24264i		−	0.147176i
$832$		0			0
$833$	−9.00000	−	9.00000i	−0.311832	−	0.311832i
$834$		0			0
$835$	8.48528	+	25.4558i	0.293645	+	0.880936i
$836$		0			0
$837$	−6.00000	−	6.00000i	−0.207390	−	0.207390i
$838$		0			0
$839$	22.6274			0.781185			0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274			0.781185			0.390593	+	0.920564i	$0.372270\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	8.48528	+	8.48528i	0.292249	+	0.292249i
$844$		0			0
$845$	11.0000	−	22.0000i	0.378412	−	0.756823i
$846$		0			0
$847$	−8.48528	−	8.48528i	−0.291558	−	0.291558i
$848$		0			0
$849$			8.00000i			0.274559i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−23.0000	+	23.0000i	−0.787505	+	0.787505i	−0.981085	−	0.193580i	$-0.937990\pi$
$853$	−23.0000	+	23.0000i	−0.787505	+	0.787505i	0.193580	+	0.981085i	$0.437990\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.0000	+	13.0000i	−0.444072	+	0.444072i	−0.893378	−	0.449306i	$-0.851671\pi$
$857$	−13.0000	+	13.0000i	−0.444072	+	0.444072i	0.449306	+	0.893378i	$0.351671\pi$
$858$		0			0
$859$		−	16.9706i		−	0.579028i	−0.957174	−	0.289514i	$-0.906506\pi$
$859$		−	16.9706i		−	0.579028i	0.957174	−	0.289514i	$-0.0934937\pi$
$860$		0			0
$861$			48.0000i			1.63584i
$862$		0			0
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	−0.657326	−	0.753607i	$-0.728312\pi$
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	0.753607	+	0.657326i	$0.228312\pi$
$864$		0			0
$865$	−21.0000	+	7.00000i	−0.714021	+	0.238007i
$866$		0			0
$867$	10.6066	−	10.6066i	0.360219	−	0.360219i
$868$		0			0
$869$	−8.00000			−0.271381
$870$		0			0
$871$		−	11.3137i		−	0.383350i
$872$		0			0
$873$	−13.0000	−	13.0000i	−0.439983	−	0.439983i
$874$		0			0
$875$	25.4558	−	36.7696i	0.860565	−	1.24304i
$876$		0			0
$877$	3.00000	+	3.00000i	0.101303	+	0.101303i	0.755942	−	0.654639i	$-0.227179\pi$
$877$	3.00000	+	3.00000i	0.101303	+	0.101303i	−0.654639	+	0.755942i	$0.727179\pi$
$878$		0			0
$879$	15.5563			0.524703
$880$		0			0
$881$	4.00000			0.134763			0.0673817	−	0.997727i	$-0.478535\pi$
$881$	4.00000			0.134763			0.0673817	+	0.997727i	$0.478535\pi$
$882$		0			0
$883$	−31.1127	−	31.1127i	−1.04703	−	1.04703i	−0.998838	−	0.0481873i	$-0.984656\pi$
$883$	−31.1127	−	31.1127i	−1.04703	−	1.04703i	−0.0481873	−	0.998838i	$-0.515344\pi$
$884$		0			0
$885$	−18.0000	+	6.00000i	−0.605063	+	0.201688i
$886$		0			0
$887$	19.7990	+	19.7990i	0.664785	+	0.664785i	0.956504	−	0.291719i	$-0.0942272\pi$
$887$	19.7990	+	19.7990i	0.664785	+	0.664785i	−0.291719	+	0.956504i	$0.594227\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.82843			0.0947559
$892$		0			0
$893$		0			0
$894$		0			0
$895$	2.82843	−	5.65685i	0.0945439	−	0.189088i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			16.9706i			0.566000i
$900$		0			0
$901$		−	14.0000i		−	0.466408i
$902$		0			0
$903$	22.6274	−	22.6274i	0.752993	−	0.752993i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.9706	−	16.9706i	0.563498	−	0.563498i	−0.366801	−	0.930299i	$-0.619547\pi$
$907$	16.9706	−	16.9706i	0.563498	−	0.563498i	0.930299	+	0.366801i	$0.119547\pi$
$908$		0			0
$909$	−4.00000			−0.132672
$910$		0			0
$911$			45.2548i			1.49936i	0.661801	+	0.749680i	$0.269792\pi$
$911$			45.2548i			1.49936i	−0.661801	+	0.749680i	$0.730208\pi$
$912$		0			0
$913$	8.00000	+	8.00000i	0.264761	+	0.264761i
$914$		0			0
$915$	−4.24264	+	1.41421i	−0.140257	+	0.0467525i
$916$		0			0
$917$	−56.0000	−	56.0000i	−1.84928	−	1.84928i
$918$		0			0
$919$	−19.7990			−0.653108			−0.326554	−	0.945178i	$-0.605888\pi$
$919$	−19.7990			−0.653108			−0.326554	+	0.945178i	$0.605888\pi$
$920$		0			0
$921$	4.00000			0.131804
$922$		0			0
$923$	−11.3137	−	11.3137i	−0.372395	−	0.372395i
$924$		0			0
$925$	7.00000	−	49.0000i	0.230159	−	1.61111i
$926$		0			0
$927$	−5.65685	−	5.65685i	−0.185795	−	0.185795i
$928$		0			0
$929$			18.0000i			0.590561i	0.955411	+	0.295280i	$0.0954131\pi$
$929$			18.0000i			0.590561i	−0.955411	+	0.295280i	$0.904587\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	16.0000	−	16.0000i	0.523816	−	0.523816i
$934$		0			0
$935$	−8.48528	+	2.82843i	−0.277498	+	0.0924995i
$936$		0			0
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	−0.754410	−	0.656404i	$-0.772077\pi$
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	0.656404	+	0.754410i	$0.272077\pi$
$938$		0			0
$939$			18.3848i			0.599965i
$940$		0			0
$941$		−	52.0000i		−	1.69515i	−0.530674	−	0.847576i	$-0.678061\pi$
$941$		−	52.0000i		−	1.69515i	0.530674	−	0.847576i	$-0.321939\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−8.00000	−	4.00000i	−0.260240	−	0.130120i
$946$		0			0
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	−0.831404	−	0.555669i	$-0.812462\pi$
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	0.555669	+	0.831404i	$0.312462\pi$
$948$		0			0
$949$	−18.0000			−0.584305
$950$		0			0
$951$		−	15.5563i		−	0.504449i
$952$		0			0
$953$	25.0000	+	25.0000i	0.809829	+	0.809829i	0.984608	−	0.174778i	$-0.0559209\pi$
$953$	25.0000	+	25.0000i	0.809829	+	0.809829i	−0.174778	+	0.984608i	$0.555921\pi$
$954$		0			0
$955$	−16.9706	+	33.9411i	−0.549155	+	1.09831i
$956$		0			0
$957$	−4.00000	−	4.00000i	−0.129302	−	0.129302i
$958$		0			0
$959$	39.5980			1.27869
$960$		0			0
$961$	−41.0000			−1.32258
$962$		0			0
$963$	−5.65685	−	5.65685i	−0.182290	−	0.182290i
$964$		0			0
$965$	7.00000	+	21.0000i	0.225338	+	0.676014i
$966$		0			0
$967$	22.6274	+	22.6274i	0.727649	+	0.727649i	0.970151	−	0.242502i	$-0.0779682\pi$
$967$	22.6274	+	22.6274i	0.727649	+	0.727649i	−0.242502	+	0.970151i	$0.577968\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.7990			−0.635380			−0.317690	−	0.948195i	$-0.602907\pi$
$971$	−19.7990			−0.635380			−0.317690	+	0.948195i	$0.602907\pi$
$972$		0			0
$973$	−48.0000	+	48.0000i	−1.53881	+	1.53881i
$974$		0			0
$975$	−4.24264	−	5.65685i	−0.135873	−	0.181164i
$976$		0			0
$977$	1.00000	−	1.00000i	0.0319928	−	0.0319928i	−0.690929	−	0.722922i	$-0.742798\pi$
$977$	1.00000	−	1.00000i	0.0319928	−	0.0319928i	0.722922	+	0.690929i	$0.242798\pi$
$978$		0			0
$979$		−	33.9411i		−	1.08476i
$980$		0			0
$981$		−	16.0000i		−	0.510841i
$982$		0			0
$983$	33.9411	−	33.9411i	1.08255	−	1.08255i	0.0862831	−	0.996271i	$-0.472501\pi$
$983$	33.9411	−	33.9411i	1.08255	−	1.08255i	0.996271	−	0.0862831i	$-0.0274990\pi$
$984$		0			0
$985$	11.0000	+	33.0000i	0.350489	+	1.05147i
$986$		0			0
$987$	−11.3137	+	11.3137i	−0.360119	+	0.360119i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		−	59.3970i		−	1.88681i	−0.331647	−	0.943403i	$-0.607604\pi$
$991$		−	59.3970i		−	1.88681i	0.331647	−	0.943403i	$-0.392396\pi$
$992$		0			0
$993$	−8.00000	−	8.00000i	−0.253872	−	0.253872i
$994$		0			0
$995$	16.9706	+	8.48528i	0.538003	+	0.269002i
$996$		0			0
$997$	−15.0000	−	15.0000i	−0.475055	−	0.475055i	0.428491	−	0.903546i	$-0.359045\pi$
$997$	−15.0000	−	15.0000i	−0.475055	−	0.475055i	−0.903546	+	0.428491i	$0.859045\pi$
$998$		0			0
$999$	−9.89949			−0.313206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bh.a.703.1	✓	4
4.3	odd	2	inner	1920.2.bh.a.703.2	yes	4
5.2	odd	4		1920.2.bh.h.1087.1	yes	4
8.3	odd	2		1920.2.bh.h.703.1	yes	4
8.5	even	2		1920.2.bh.h.703.2	yes	4
20.7	even	4		1920.2.bh.h.1087.2	yes	4
40.27	even	4	inner	1920.2.bh.a.1087.1	yes	4
40.37	odd	4	inner	1920.2.bh.a.1087.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.bh.a.703.1	✓	4	1.1	even	1	trivial
1920.2.bh.a.703.2	yes	4	4.3	odd	2	inner
1920.2.bh.a.1087.1	yes	4	40.27	even	4	inner
1920.2.bh.a.1087.2	yes	4	40.37	odd	4	inner
1920.2.bh.h.703.1	yes	4	8.3	odd	2
1920.2.bh.h.703.2	yes	4	8.5	even	2
1920.2.bh.h.1087.1	yes	4	5.2	odd	4
1920.2.bh.h.1087.2	yes	4	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bh (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(2.82843 + 2.82843i) q^{7} +1.00000i q^{9} -2.82843 q^{11} +(1.00000 - 1.00000i) q^{13} +(0.707107 + 2.12132i) q^{15} +(-1.00000 + 1.00000i) q^{17} -4.00000i q^{21} +(3.00000 + 4.00000i) q^{25} +(0.707107 - 0.707107i) q^{27} -2.00000 q^{29} -8.48528i q^{31} +(2.00000 + 2.00000i) q^{33} +(-2.82843 - 8.48528i) q^{35} +(-7.00000 - 7.00000i) q^{37} -1.41421 q^{39} -12.0000 q^{41} +(5.65685 + 5.65685i) q^{43} +(1.00000 - 2.00000i) q^{45} +(-2.82843 - 2.82843i) q^{47} +9.00000i q^{49} +1.41421 q^{51} +(-7.00000 + 7.00000i) q^{53} +(5.65685 + 2.82843i) q^{55} +8.48528i q^{59} +2.00000i q^{61} +(-2.82843 + 2.82843i) q^{63} +(-3.00000 + 1.00000i) q^{65} +(5.65685 - 5.65685i) q^{67} -11.3137i q^{71} +(-9.00000 - 9.00000i) q^{73} +(0.707107 - 4.94975i) q^{75} +(-8.00000 - 8.00000i) q^{77} +2.82843 q^{79} -1.00000 q^{81} +(-2.82843 - 2.82843i) q^{83} +(3.00000 - 1.00000i) q^{85} +(1.41421 + 1.41421i) q^{87} +12.0000i q^{89} +5.65685 q^{91} +(-6.00000 + 6.00000i) q^{93} +(-13.0000 + 13.0000i) q^{97} -2.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5} + 4 q^{13} - 4 q^{17} + 12 q^{25} - 8 q^{29} + 8 q^{33} - 28 q^{37} - 48 q^{41} + 4 q^{45} - 28 q^{53} - 12 q^{65} - 36 q^{73} - 32 q^{77} - 4 q^{81} + 12 q^{85} - 24 q^{93} - 52 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 + 4 * q^13 - 4 * q^17 + 12 * q^25 - 8 * q^29 + 8 * q^33 - 28 * q^37 - 48 * q^41 + 4 * q^45 - 28 * q^53 - 12 * q^65 - 36 * q^73 - 32 * q^77 - 4 * q^81 + 12 * q^85 - 24 * q^93 - 52 * q^97

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