LMFDB - Embedded newform 600.2.r.f.257.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(257,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("600.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.7
Root			$-0.0537601 - 1.73122i$ of defining polynomial
Character	$\chi$	$=$	600.257
Dual form			600.2.r.f.593.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47240 + 0.912166i) q^{3} +(1.78498 + 1.78498i) q^{7} +(1.33591 + 2.68614i) q^{9} +O(q^{10})$	$q+(1.47240 + 0.912166i) q^{3} +(1.78498 + 1.78498i) q^{7} +(1.33591 + 2.68614i) q^{9} -4.25639i q^{11} +(2.90544 - 2.90544i) q^{13} +(0.443864 - 0.443864i) q^{17} +7.74456i q^{19} +(1.00000 + 4.25639i) q^{21} +(1.94070 + 1.94070i) q^{23} +(-0.483219 + 5.17364i) q^{27} -10.0974 q^{29} +0.372281 q^{31} +(3.88253 - 6.26709i) q^{33} +(1.12046 + 1.12046i) q^{37} +(6.92820 - 1.62772i) q^{39} +7.42554i q^{41} +(6.68396 - 6.68396i) q^{43} +(5.65685 - 5.65685i) q^{47} -0.627719i q^{49} +(1.05842 - 0.248667i) q^{51} +(-7.59755 - 7.59755i) q^{53} +(-7.06432 + 11.4031i) q^{57} -5.34363 q^{59} -4.37228 q^{61} +(-2.41013 + 7.17926i) q^{63} +(1.22474 + 1.22474i) q^{67} +(1.08724 + 4.62772i) q^{69} -10.0974i q^{71} +(-7.90870 + 7.90870i) q^{73} +(7.59755 - 7.59755i) q^{77} -2.74456i q^{79} +(-5.43070 + 7.17687i) q^{81} +(8.04142 + 8.04142i) q^{83} +(-14.8673 - 9.21046i) q^{87} +0.497333 q^{89} +10.3723 q^{91} +(0.548146 + 0.339582i) q^{93} +(-6.47539 - 6.47539i) q^{97} +(11.4333 - 5.68614i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 16 q^{21} - 40 q^{31} - 52 q^{51} - 24 q^{61} + 28 q^{81} + 120 q^{91}+O(q^{100}) $ 16 * q + 16 * q^21 - 40 * q^31 - 52 * q^51 - 24 * q^61 + 28 * q^81 + 120 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.47240	+	0.912166i	0.850089	+	0.526639i
$3$	1.47240	+	0.912166i	0.850089	+	0.526639i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.78498	+	1.78498i	0.674658	+	0.674658i	0.958786	−	0.284129i	$-0.0917042\pi$
$7$	1.78498	+	1.78498i	0.674658	+	0.674658i	−0.284129	+	0.958786i	$0.591704\pi$
$8$		0			0
$9$	1.33591	+	2.68614i	0.445302	+	0.895380i
$10$		0			0
$11$		−	4.25639i		−	1.28335i	−0.766977	−	0.641675i	$-0.778240\pi$
$11$		−	4.25639i		−	1.28335i	0.766977	−	0.641675i	$-0.221760\pi$
$12$		0			0
$13$	2.90544	−	2.90544i	0.805824	−	0.805824i	−0.178175	−	0.983999i	$-0.557019\pi$
$13$	2.90544	−	2.90544i	0.805824	−	0.805824i	0.983999	+	0.178175i	$0.0570193\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.443864	−	0.443864i	0.107653	−	0.107653i	−0.651229	−	0.758882i	$-0.725746\pi$
$17$	0.443864	−	0.443864i	0.107653	−	0.107653i	0.758882	+	0.651229i	$0.225746\pi$
$18$		0			0
$19$			7.74456i			1.77672i	0.459143	+	0.888362i	$0.348156\pi$
$19$			7.74456i			1.77672i	−0.459143	+	0.888362i	$0.651844\pi$
$20$		0			0
$21$	1.00000	+	4.25639i	0.218218	+	0.928820i
$22$		0			0
$23$	1.94070	+	1.94070i	0.404664	+	0.404664i	0.879873	−	0.475209i	$-0.157628\pi$
$23$	1.94070	+	1.94070i	0.404664	+	0.404664i	−0.475209	+	0.879873i	$0.657628\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.483219	+	5.17364i	−0.0929956	+	0.995667i
$28$		0			0
$29$	−10.0974			−1.87503			−0.937516	−	0.347943i	$-0.886880\pi$
$29$	−10.0974			−1.87503			−0.937516	+	0.347943i	$0.886880\pi$
$30$		0			0
$31$	0.372281			0.0668637			0.0334318	−	0.999441i	$-0.489356\pi$
$31$	0.372281			0.0668637			0.0334318	+	0.999441i	$0.489356\pi$
$32$		0			0
$33$	3.88253	−	6.26709i	0.675862	−	1.09096i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.12046	+	1.12046i	0.184203	+	0.184203i	0.793184	−	0.608981i	$-0.208422\pi$
$37$	1.12046	+	1.12046i	0.184203	+	0.184203i	−0.608981	+	0.793184i	$0.708422\pi$
$38$		0			0
$39$	6.92820	−	1.62772i	1.10940	−	0.260644i
$40$		0			0
$41$			7.42554i			1.15967i	0.814733	+	0.579837i	$0.196884\pi$
$41$			7.42554i			1.15967i	−0.814733	+	0.579837i	$0.803116\pi$
$42$		0			0
$43$	6.68396	−	6.68396i	1.01929	−	1.01929i	0.0194835	−	0.999810i	$-0.493798\pi$
$43$	6.68396	−	6.68396i	1.01929	−	1.01929i	0.999810	−	0.0194835i	$-0.00620219\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.65685	−	5.65685i	0.825137	−	0.825137i	−0.161703	−	0.986840i	$-0.551699\pi$
$47$	5.65685	−	5.65685i	0.825137	−	0.825137i	0.986840	+	0.161703i	$0.0516985\pi$
$48$		0			0
$49$		−	0.627719i		−	0.0896741i
$50$		0			0
$51$	1.05842	−	0.248667i	0.148209	−	0.0348203i
$52$		0			0
$53$	−7.59755	−	7.59755i	−1.04360	−	1.04360i	−0.999005	−	0.0445992i	$-0.985799\pi$
$53$	−7.59755	−	7.59755i	−1.04360	−	1.04360i	−0.0445992	−	0.999005i	$-0.514201\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.06432	+	11.4031i	−0.935693	+	1.51037i
$58$		0			0
$59$	−5.34363			−0.695681			−0.347841	−	0.937554i	$-0.613085\pi$
$59$	−5.34363			−0.695681			−0.347841	+	0.937554i	$0.613085\pi$
$60$		0			0
$61$	−4.37228			−0.559813			−0.279907	−	0.960027i	$-0.590304\pi$
$61$	−4.37228			−0.559813			−0.279907	+	0.960027i	$0.590304\pi$
$62$		0			0
$63$	−2.41013	+	7.17926i	−0.303648	+	0.904502i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.22474	+	1.22474i	0.149626	+	0.149626i	0.777951	−	0.628325i	$-0.216259\pi$
$67$	1.22474	+	1.22474i	0.149626	+	0.149626i	−0.628325	+	0.777951i	$0.716259\pi$
$68$		0			0
$69$	1.08724	+	4.62772i	0.130888	+	0.557112i
$70$		0			0
$71$		−	10.0974i		−	1.19834i	−0.800624	−	0.599168i	$-0.795498\pi$
$71$		−	10.0974i		−	1.19834i	0.800624	−	0.599168i	$-0.204502\pi$
$72$		0			0
$73$	−7.90870	+	7.90870i	−0.925643	+	0.925643i	−0.997421	−	0.0717773i	$-0.977133\pi$
$73$	−7.90870	+	7.90870i	−0.925643	+	0.925643i	0.0717773	+	0.997421i	$0.477133\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.59755	−	7.59755i	0.865822	−	0.865822i
$78$		0			0
$79$		−	2.74456i		−	0.308787i	−0.988009	−	0.154394i	$-0.950658\pi$
$79$		−	2.74456i		−	0.308787i	0.988009	−	0.154394i	$-0.0493424\pi$
$80$		0			0
$81$	−5.43070	+	7.17687i	−0.603411	+	0.797430i
$82$		0			0
$83$	8.04142	+	8.04142i	0.882660	+	0.882660i	0.993804	−	0.111144i	$-0.0354515\pi$
$83$	8.04142	+	8.04142i	0.882660	+	0.882660i	−0.111144	+	0.993804i	$0.535452\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−14.8673	−	9.21046i	−1.59394	−	0.987465i
$88$		0			0
$89$	0.497333			0.0527172			0.0263586	−	0.999653i	$-0.491609\pi$
$89$	0.497333			0.0527172			0.0263586	+	0.999653i	$0.491609\pi$
$90$		0			0
$91$	10.3723			1.08731
$92$		0			0
$93$	0.548146	+	0.339582i	0.0568401	+	0.0352130i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.47539	−	6.47539i	−0.657476	−	0.657476i	0.297306	−	0.954782i	$-0.403912\pi$
$97$	−6.47539	−	6.47539i	−0.657476	−	0.657476i	−0.954782	+	0.297306i	$0.903912\pi$
$98$		0			0
$99$	11.4333	−	5.68614i	1.14909	−	0.571479i
$100$		0			0
$101$		−	15.4410i		−	1.53643i	−0.640189	−	0.768217i	$-0.721144\pi$
$101$		−	15.4410i		−	1.53643i	0.640189	−	0.768217i	$-0.278856\pi$
$102$		0			0
$103$	−5.81088	+	5.81088i	−0.572563	+	0.572563i	−0.932844	−	0.360281i	$-0.882681\pi$
$103$	−5.81088	+	5.81088i	−0.572563	+	0.572563i	0.360281	+	0.932844i	$0.382681\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.21299	−	5.21299i	0.503959	−	0.503959i	−0.408707	−	0.912666i	$-0.634020\pi$
$107$	5.21299	−	5.21299i	0.503959	−	0.503959i	0.912666	+	0.408707i	$0.134020\pi$
$108$		0			0
$109$		−	17.8614i		−	1.71081i	−0.517958	−	0.855406i	$-0.673308\pi$
$109$		−	17.8614i		−	1.71081i	0.517958	−	0.855406i	$-0.326692\pi$
$110$		0			0
$111$	0.627719	+	2.67181i	0.0595804	+	0.253597i
$112$		0			0
$113$	−2.38456	−	2.38456i	−0.224321	−	0.224321i	0.585994	−	0.810315i	$-0.300704\pi$
$113$	−2.38456	−	2.38456i	−0.224321	−	0.224321i	−0.810315	+	0.585994i	$0.800704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	11.6858	+	3.92302i	1.08035	+	0.362683i
$118$		0			0
$119$	1.58457			0.145258
$120$		0			0
$121$	−7.11684			−0.646986
$122$		0			0
$123$	−6.77332	+	10.9333i	−0.610730	+	0.985826i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.208564	+	0.208564i	0.0185070	+	0.0185070i	0.716300	−	0.697793i	$-0.245834\pi$
$127$	0.208564	+	0.208564i	0.0185070	+	0.0185070i	−0.697793	+	0.716300i	$0.745834\pi$
$128$		0			0
$129$	15.9383	−	3.74456i	1.40329	−	0.329690i
$130$		0			0
$131$		−	1.58457i		−	0.138445i	−0.997601	−	0.0692224i	$-0.977948\pi$
$131$		−	1.58457i		−	0.138445i	0.997601	−	0.0692224i	$-0.0220518\pi$
$132$		0			0
$133$	−13.8239	+	13.8239i	−1.19868	+	1.19868i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.15369	+	7.15369i	−0.611181	+	0.611181i	−0.943254	−	0.332073i	$-0.892252\pi$
$137$	−7.15369	+	7.15369i	−0.611181	+	0.611181i	0.332073	+	0.943254i	$0.392252\pi$
$138$		0			0
$139$		−	2.11684i		−	0.179548i	−0.995962	−	0.0897742i	$-0.971385\pi$
$139$		−	2.11684i		−	0.179548i	0.995962	−	0.0897742i	$-0.0286145\pi$
$140$		0			0
$141$	13.4891	−	3.16915i	1.13599	−	0.266890i
$142$		0			0
$143$	−12.3667	−	12.3667i	−1.03415	−	1.03415i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.572583	−	0.924251i	0.0472259	−	0.0762310i
$148$		0			0
$149$	−17.0256			−1.39479			−0.697394	−	0.716688i	$-0.745657\pi$
$149$	−17.0256			−1.39479			−0.697394	+	0.716688i	$0.745657\pi$
$150$		0			0
$151$	−8.37228			−0.681327			−0.340663	−	0.940185i	$-0.610652\pi$
$151$	−8.37228			−0.681327			−0.340663	+	0.940185i	$0.610652\pi$
$152$		0			0
$153$	1.78524	+	0.599320i	0.144328	+	0.0484522i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.5829	−	11.5829i	−0.924419	−	0.924419i	0.0729190	−	0.997338i	$-0.476769\pi$
$157$	−11.5829	−	11.5829i	−0.924419	−	0.924419i	−0.997338	+	0.0729190i	$0.976769\pi$
$158$		0			0
$159$	−4.25639	−	18.1168i	−0.337554	−	1.43676i
$160$		0			0
$161$			6.92820i			0.546019i
$162$		0			0
$163$	3.88280	−	3.88280i	0.304124	−	0.304124i	−0.538501	−	0.842625i	$-0.681009\pi$
$163$	3.88280	−	3.88280i	0.304124	−	0.304124i	0.842625	+	0.538501i	$0.181009\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	−0.808022	−	0.589152i	$-0.799462\pi$
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	0.589152	+	0.808022i	$0.299462\pi$
$168$		0			0
$169$		−	3.88316i		−	0.298704i
$170$		0			0
$171$	−20.8030	+	10.3460i	−1.59084	+	0.791180i
$172$		0			0
$173$	8.48528	+	8.48528i	0.645124	+	0.645124i	0.951811	−	0.306687i	$-0.0992203\pi$
$173$	8.48528	+	8.48528i	0.645124	+	0.645124i	−0.306687	+	0.951811i	$0.599220\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.86794	−	4.87428i	−0.591391	−	0.366373i
$178$		0			0
$179$	−2.67181			−0.199701			−0.0998504	−	0.995002i	$-0.531836\pi$
$179$	−2.67181			−0.199701			−0.0998504	+	0.995002i	$0.531836\pi$
$180$		0			0
$181$	−2.88316			−0.214303			−0.107152	−	0.994243i	$-0.534173\pi$
$181$	−2.88316			−0.214303			−0.107152	+	0.994243i	$0.534173\pi$
$182$		0			0
$183$	−6.43773	−	3.98825i	−0.475891	−	0.294820i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.88926	−	1.88926i	−0.138156	−	0.138156i
$188$		0			0
$189$	−10.0974	+	8.37228i	−0.734474	+	0.608994i
$190$		0			0
$191$			7.92287i			0.573279i	0.958039	+	0.286639i	$0.0925381\pi$
$191$			7.92287i			0.573279i	−0.958039	+	0.286639i	$0.907462\pi$
$192$		0			0
$193$	−1.01618	+	1.01618i	−0.0731463	+	0.0731463i	−0.742733	−	0.669587i	$-0.766471\pi$
$193$	−1.01618	+	1.01618i	−0.0731463	+	0.0731463i	0.669587	+	0.742733i	$0.266471\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.3074	−	14.3074i	1.01936	−	1.01936i	0.0195496	−	0.999809i	$-0.493777\pi$
$197$	14.3074	−	14.3074i	1.01936	−	1.01936i	0.999809	−	0.0195496i	$-0.00622322\pi$
$198$		0			0
$199$			10.3723i			0.735272i	0.929970	+	0.367636i	$0.119833\pi$
$199$			10.3723i			0.735272i	−0.929970	+	0.367636i	$0.880167\pi$
$200$		0			0
$201$	0.686141	+	2.92048i	0.0483966	+	0.205995i
$202$		0			0
$203$	−18.0235	−	18.0235i	−1.26500	−	1.26500i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.62040	+	7.80558i	−0.182130	+	0.542526i
$208$		0			0
$209$	32.9639			2.28016
$210$		0			0
$211$	−1.74456			−0.120101			−0.0600503	−	0.998195i	$-0.519126\pi$
$211$	−1.74456			−0.120101			−0.0600503	+	0.998195i	$0.519126\pi$
$212$		0			0
$213$	9.21046	−	14.8673i	0.631090	−	1.01869i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.664513	+	0.664513i	0.0451101	+	0.0451101i
$218$		0			0
$219$	−18.8588	+	4.43070i	−1.27436	+	0.299399i
$220$		0			0
$221$		−	2.57924i		−	0.173499i
$222$		0			0
$223$	8.71632	−	8.71632i	0.583688	−	0.583688i	−0.352227	−	0.935915i	$-0.614575\pi$
$223$	8.71632	−	8.71632i	0.583688	−	0.583688i	0.935915	+	0.352227i	$0.114575\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	−0.794714	−	0.606984i	$-0.792379\pi$
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	0.606984	+	0.794714i	$0.292379\pi$
$228$		0			0
$229$		−	10.3723i		−	0.685420i	−0.939441	−	0.342710i	$-0.888655\pi$
$229$		−	10.3723i		−	0.685420i	0.939441	−	0.342710i	$-0.111345\pi$
$230$		0			0
$231$	18.1168	−	4.25639i	1.19200	−	0.280050i
$232$		0			0
$233$	11.4790	+	11.4790i	0.752011	+	0.752011i	0.974854	−	0.222843i	$-0.0715338\pi$
$233$	11.4790	+	11.4790i	0.752011	+	0.752011i	−0.222843	+	0.974854i	$0.571534\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.50350	−	4.04109i	0.162620	−	0.262497i
$238$		0			0
$239$	−13.2665			−0.858138			−0.429069	−	0.903272i	$-0.641158\pi$
$239$	−13.2665			−0.858138			−0.429069	+	0.903272i	$0.641158\pi$
$240$		0			0
$241$	21.2337			1.36778			0.683891	−	0.729584i	$-0.260286\pi$
$241$	21.2337			1.36778			0.683891	+	0.729584i	$0.260286\pi$
$242$		0			0
$243$	−14.5426	+	5.61350i	−0.932911	+	0.360106i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	22.5014	+	22.5014i	1.43173	+	1.43173i
$248$		0			0
$249$	4.50506	+	19.1753i	0.285496	+	1.21518i
$250$		0			0
$251$			26.0357i			1.64336i	0.569952	+	0.821678i	$0.306962\pi$
$251$			26.0357i			1.64336i	−0.569952	+	0.821678i	$0.693038\pi$
$252$		0			0
$253$	8.26037	−	8.26037i	0.519325	−	0.519325i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.3074	+	14.3074i	−0.892470	+	0.892470i	−0.994755	−	0.102285i	$-0.967385\pi$
$257$	−14.3074	+	14.3074i	−0.892470	+	0.892470i	0.102285	+	0.994755i	$0.467385\pi$
$258$		0			0
$259$			4.00000i			0.248548i
$260$		0			0
$261$	−13.4891	−	27.1229i	−0.834956	−	1.67887i
$262$		0			0
$263$	18.9113	+	18.9113i	1.16612	+	1.16612i	0.983112	+	0.183007i	$0.0585830\pi$
$263$	18.9113	+	18.9113i	1.16612	+	1.16612i	0.183007	+	0.983112i	$0.441417\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.732272	+	0.453650i	0.0448143	+	0.0277630i
$268$		0			0
$269$	0.589907			0.0359673			0.0179836	−	0.999838i	$-0.494275\pi$
$269$	0.589907			0.0359673			0.0179836	+	0.999838i	$0.494275\pi$
$270$		0			0
$271$	−16.2337			−0.986126			−0.493063	−	0.869994i	$-0.664123\pi$
$271$	−16.2337			−0.986126			−0.493063	+	0.869994i	$0.664123\pi$
$272$		0			0
$273$	15.2721	+	9.46124i	0.924311	+	0.572620i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.8562	+	15.8562i	0.952708	+	0.952708i	0.998931	−	0.0462230i	$-0.0147185\pi$
$277$	15.8562	+	15.8562i	0.952708	+	0.952708i	−0.0462230	+	0.998931i	$0.514718\pi$
$278$		0			0
$279$	0.497333	+	1.00000i	0.0297746	+	0.0598684i
$280$		0			0
$281$		−	20.7846i		−	1.23991i	−0.784639	−	0.619953i	$-0.787152\pi$
$281$		−	20.7846i		−	1.23991i	0.784639	−	0.619953i	$-0.212848\pi$
$282$		0			0
$283$	10.3970	−	10.3970i	0.618038	−	0.618038i	−0.326990	−	0.945028i	$-0.606034\pi$
$283$	10.3970	−	10.3970i	0.618038	−	0.618038i	0.945028	+	0.326990i	$0.106034\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.2544	+	13.2544i	−0.782383	+	0.782383i
$288$		0			0
$289$			16.6060i			0.976822i
$290$		0			0
$291$	−3.62772	−	15.4410i	−0.212661	−	0.905166i
$292$		0			0
$293$	2.99367	+	2.99367i	0.174892	+	0.174892i	0.789125	−	0.614233i	$-0.210534\pi$
$293$	2.99367	+	2.99367i	0.174892	+	0.174892i	−0.614233	+	0.789125i	$0.710534\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	22.0210	+	2.05677i	1.27779	+	0.119346i
$298$		0			0
$299$	11.2772			0.652175
$300$		0			0
$301$	23.8614			1.37535
$302$		0			0
$303$	14.0847	−	22.7353i	0.809147	−	1.30611i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−14.8012	−	14.8012i	−0.844750	−	0.844750i	0.144722	−	0.989472i	$-0.453771\pi$
$307$	−14.8012	−	14.8012i	−0.844750	−	0.844750i	−0.989472	+	0.144722i	$0.953771\pi$
$308$		0			0
$309$	−13.8564	+	3.25544i	−0.788263	+	0.185195i
$310$		0			0
$311$			19.2000i			1.08873i	0.838847	+	0.544367i	$0.183230\pi$
$311$			19.2000i			1.08873i	−0.838847	+	0.544367i	$0.816770\pi$
$312$		0			0
$313$	−1.99354	+	1.99354i	−0.112682	+	0.112682i	−0.761199	−	0.648518i	$-0.775389\pi$
$313$	−1.99354	+	1.99354i	−0.112682	+	0.112682i	0.648518	+	0.761199i	$0.275389\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.53825	−	9.53825i	0.535722	−	0.535722i	−0.386548	−	0.922269i	$-0.626333\pi$
$317$	9.53825	−	9.53825i	0.535722	−	0.535722i	0.922269	+	0.386548i	$0.126333\pi$
$318$		0			0
$319$			42.9783i			2.40632i
$320$		0			0
$321$	12.4307	−	2.92048i	0.693814	−	0.163005i
$322$		0			0
$323$	3.43753	+	3.43753i	0.191269	+	0.191269i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	16.2926	−	26.2991i	0.900981	−	1.45434i
$328$		0			0
$329$	20.1947			1.11337
$330$		0			0
$331$	20.6277			1.13380			0.566901	−	0.823786i	$-0.308142\pi$
$331$	20.6277			1.13380			0.566901	+	0.823786i	$0.308142\pi$
$332$		0			0
$333$	−1.51289	+	4.50656i	−0.0829057	+	0.246958i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.67423	−	3.67423i	−0.200148	−	0.200148i	0.599915	−	0.800064i	$-0.295201\pi$
$337$	−3.67423	−	3.67423i	−0.200148	−	0.200148i	−0.800064	+	0.599915i	$0.795201\pi$
$338$		0			0
$339$	−1.33591	−	5.68614i	−0.0725565	−	0.308829i
$340$		0			0
$341$		−	1.58457i		−	0.0858095i
$342$		0			0
$343$	13.6153	−	13.6153i	0.735157	−	0.735157i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.9228	+	11.9228i	−0.640050	+	0.640050i	−0.950568	−	0.310517i	$-0.899498\pi$
$347$	−11.9228	+	11.9228i	−0.640050	+	0.640050i	0.310517	+	0.950568i	$0.399498\pi$
$348$		0			0
$349$			27.4891i			1.47146i	0.677275	+	0.735730i	$0.263161\pi$
$349$			27.4891i			1.47146i	−0.677275	+	0.735730i	$0.736839\pi$
$350$		0			0
$351$	13.6277	+	16.4356i	0.727394	+	0.877270i
$352$		0			0
$353$	13.2544	+	13.2544i	0.705461	+	0.705461i	0.965577	−	0.260116i	$-0.0837609\pi$
$353$	13.2544	+	13.2544i	0.705461	+	0.705461i	−0.260116	+	0.965577i	$0.583761\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.33312	+	1.44539i	0.123482	+	0.0764984i
$358$		0			0
$359$	1.58457			0.0836306			0.0418153	−	0.999125i	$-0.486686\pi$
$359$	1.58457			0.0836306			0.0418153	+	0.999125i	$0.486686\pi$
$360$		0			0
$361$	−40.9783			−2.15675
$362$		0			0
$363$	−10.4788	−	6.49174i	−0.549995	−	0.340728i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.99354	+	1.99354i	0.104062	+	0.104062i	0.757221	−	0.653159i	$-0.226557\pi$
$367$	1.99354	+	1.99354i	0.104062	+	0.104062i	−0.653159	+	0.757221i	$0.726557\pi$
$368$		0			0
$369$	−19.9460	+	9.91983i	−1.03835	+	0.516406i
$370$		0			0
$371$		−	27.1229i		−	1.40815i
$372$		0			0
$373$	1.78498	−	1.78498i	0.0924226	−	0.0924226i	−0.659384	−	0.751806i	$-0.729183\pi$
$373$	1.78498	−	1.78498i	0.0924226	−	0.0924226i	0.751806	+	0.659384i	$0.229183\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.3372	+	29.3372i	−1.51094	+	1.51094i
$378$		0			0
$379$		−	26.4891i		−	1.36065i	−0.732908	−	0.680327i	$-0.761838\pi$
$379$		−	26.4891i		−	1.36065i	0.732908	−	0.680327i	$-0.238162\pi$
$380$		0			0
$381$	0.116844	+	0.497333i	0.00598610	+	0.0254792i
$382$		0			0
$383$	−14.3074	−	14.3074i	−0.731073	−	0.731073i	0.239759	−	0.970832i	$-0.422931\pi$
$383$	−14.3074	−	14.3074i	−0.731073	−	0.731073i	−0.970832	+	0.239759i	$0.922931\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	26.8832	+	9.02490i	1.36655	+	0.458761i
$388$		0			0
$389$	9.10268			0.461524			0.230762	−	0.973010i	$-0.425878\pi$
$389$	9.10268			0.461524			0.230762	+	0.973010i	$0.425878\pi$
$390$		0			0
$391$	1.72281			0.0871264
$392$		0			0
$393$	1.44539	−	2.33312i	0.0729105	−	0.117690i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	12.7034	+	12.7034i	0.637565	+	0.637565i	0.949954	−	0.312389i	$-0.101129\pi$
$397$	12.7034	+	12.7034i	0.637565	+	0.637565i	−0.312389	+	0.949954i	$0.601129\pi$
$398$		0			0
$399$	−32.9639	+	7.74456i	−1.65026	+	0.387713i
$400$		0			0
$401$			26.6256i			1.32962i	0.747014	+	0.664809i	$0.231487\pi$
$401$			26.6256i			1.32962i	−0.747014	+	0.664809i	$0.768513\pi$
$402$		0			0
$403$	1.08164	−	1.08164i	0.0538804	−	0.0538804i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.76913	−	4.76913i	0.236397	−	0.236397i
$408$		0			0
$409$		−	20.4891i		−	1.01312i	−0.862204	−	0.506561i	$-0.830916\pi$
$409$		−	20.4891i		−	1.01312i	0.862204	−	0.506561i	$-0.169084\pi$
$410$		0			0
$411$	−17.0584	+	4.00772i	−0.841430	+	0.197686i
$412$		0			0
$413$	−9.53825	−	9.53825i	−0.469347	−	0.469347i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.93091	−	3.11684i	0.0945572	−	0.152632i
$418$		0			0
$419$	12.7692			0.623815			0.311907	−	0.950113i	$-0.399032\pi$
$419$	12.7692			0.623815			0.311907	+	0.950113i	$0.399032\pi$
$420$		0			0
$421$	−16.7446			−0.816080			−0.408040	−	0.912964i	$-0.633788\pi$
$421$	−16.7446			−0.816080			−0.408040	+	0.912964i	$0.633788\pi$
$422$		0			0
$423$	22.7521	+	7.63807i	1.10625	+	0.371376i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.80442	−	7.80442i	−0.377682	−	0.377682i
$428$		0			0
$429$	−6.92820	−	29.4891i	−0.334497	−	1.42375i
$430$		0			0
$431$			29.2974i			1.41121i	0.708608	+	0.705603i	$0.249324\pi$
$431$			29.2974i			1.41121i	−0.708608	+	0.705603i	$0.750676\pi$
$432$		0			0
$433$	6.12372	−	6.12372i	0.294287	−	0.294287i	−0.544484	−	0.838771i	$-0.683274\pi$
$433$	6.12372	−	6.12372i	0.294287	−	0.294287i	0.838771	+	0.544484i	$0.183274\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.0299	+	15.0299i	−0.718976	+	0.718976i
$438$		0			0
$439$		−	14.3723i		−	0.685952i	−0.939344	−	0.342976i	$-0.888565\pi$
$439$		−	14.3723i		−	0.685952i	0.939344	−	0.342976i	$-0.111435\pi$
$440$		0			0
$441$	1.68614	−	0.838574i	0.0802924	−	0.0399321i
$442$		0			0
$443$	−5.37823	−	5.37823i	−0.255528	−	0.255528i	0.567705	−	0.823232i	$-0.307832\pi$
$443$	−5.37823	−	5.37823i	−0.255528	−	0.255528i	−0.823232	+	0.567705i	$0.807832\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−25.0684	−	15.5301i	−1.18569	−	0.734550i
$448$		0			0
$449$	−14.3537			−0.677395			−0.338697	−	0.940895i	$-0.609986\pi$
$449$	−14.3537			−0.677395			−0.338697	+	0.940895i	$0.609986\pi$
$450$		0			0
$451$	31.6060			1.48827
$452$		0			0
$453$	−12.3273	−	7.63691i	−0.579188	−	0.358813i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.351668	−	0.351668i	−0.0164503	−	0.0164503i	0.698834	−	0.715284i	$-0.253703\pi$
$457$	−0.351668	−	0.351668i	−0.0164503	−	0.0164503i	−0.715284	+	0.698834i	$0.753703\pi$
$458$		0			0
$459$	2.08191	+	2.51087i	0.0971751	+	0.117198i
$460$		0			0
$461$		−	3.75906i		−	0.175077i	−0.996161	−	0.0875383i	$-0.972100\pi$
$461$		−	3.75906i		−	0.175077i	0.996161	−	0.0875383i	$-0.0279000\pi$
$462$		0			0
$463$	−20.5078	+	20.5078i	−0.953079	+	0.953079i	−0.998947	−	0.0458684i	$-0.985395\pi$
$463$	−20.5078	+	20.5078i	−0.953079	+	0.953079i	0.0458684	+	0.998947i	$0.485395\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	−0.769514	−	0.638630i	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$		0			0
$469$			4.37228i			0.201893i
$470$		0			0
$471$	−6.48913	−	27.6202i	−0.299003	−	1.27267i
$472$		0			0
$473$	−28.4495	−	28.4495i	−1.30811	−	1.30811i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	10.2585	−	30.5577i	0.469703	−	1.39914i
$478$		0			0
$479$	28.7075			1.31168			0.655839	−	0.754901i	$-0.272315\pi$
$479$	28.7075			1.31168			0.655839	+	0.754901i	$0.272315\pi$
$480$		0			0
$481$	6.51087			0.296870
$482$		0			0
$483$	−6.31967	+	10.2011i	−0.287555	+	0.464165i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	11.1658	+	11.1658i	0.505971	+	0.505971i	0.913287	−	0.407316i	$-0.133535\pi$
$487$	11.1658	+	11.1658i	0.505971	+	0.505971i	−0.407316	+	0.913287i	$0.633535\pi$
$488$		0			0
$489$	9.25878	−	2.17527i	0.418696	−	0.0983689i
$490$		0			0
$491$			28.7075i			1.29555i	0.761832	+	0.647775i	$0.224300\pi$
$491$			28.7075i			1.29555i	−0.761832	+	0.647775i	$0.775700\pi$
$492$		0			0
$493$	−4.48185	+	4.48185i	−0.201852	+	0.201852i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.0235	−	18.0235i	0.808466	−	0.808466i
$498$		0			0
$499$		−	17.6277i		−	0.789125i	−0.918869	−	0.394563i	$-0.870896\pi$
$499$		−	17.6277i		−	0.789125i	0.918869	−	0.394563i	$-0.129104\pi$
$500$		0			0
$501$	−6.74456	+	1.58457i	−0.301325	+	0.0707935i
$502$		0			0
$503$	16.2481	+	16.2481i	0.724466	+	0.724466i	0.969512	−	0.245046i	$-0.0788029\pi$
$503$	16.2481	+	16.2481i	0.724466	+	0.724466i	−0.245046	+	0.969512i	$0.578803\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.54208	−	5.71755i	0.157309	−	0.253925i
$508$		0			0
$509$	−2.17448			−0.0963822			−0.0481911	−	0.998838i	$-0.515346\pi$
$509$	−2.17448			−0.0963822			−0.0481911	+	0.998838i	$0.515346\pi$
$510$		0			0
$511$	−28.2337			−1.24898
$512$		0			0
$513$	−40.0675	−	3.74232i	−1.76903	−	0.165228i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−24.0778	−	24.0778i	−1.05894	−	1.05894i
$518$		0			0
$519$	4.75372	+	20.2337i	0.208665	+	0.888160i
$520$		0			0
$521$			26.6256i			1.16649i	0.812297	+	0.583244i	$0.198217\pi$
$521$			26.6256i			1.16649i	−0.812297	+	0.583244i	$0.801783\pi$
$522$		0			0
$523$	−15.2960	+	15.2960i	−0.668847	+	0.668847i	−0.957449	−	0.288602i	$-0.906810\pi$
$523$	−15.2960	+	15.2960i	−0.668847	+	0.668847i	0.288602	+	0.957449i	$0.406810\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.165242	−	0.165242i	0.00719807	−	0.00719807i
$528$		0			0
$529$		−	15.4674i		−	0.672495i
$530$		0			0
$531$	−7.13859	−	14.3537i	−0.309789	−	0.622899i
$532$		0			0
$533$	21.5744	+	21.5744i	0.934493	+	0.934493i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.93397	−	2.43714i	−0.169763	−	0.105170i
$538$		0			0
$539$	−2.67181			−0.115083
$540$		0			0
$541$	23.1168			0.993871			0.496935	−	0.867788i	$-0.334459\pi$
$541$	23.1168			0.993871			0.496935	+	0.867788i	$0.334459\pi$
$542$		0			0
$543$	−4.24515	−	2.62992i	−0.182177	−	0.112861i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−24.6380	−	24.6380i	−1.05344	−	1.05344i	−0.998489	−	0.0549561i	$-0.982498\pi$
$547$	−24.6380	−	24.6380i	−1.05344	−	1.05344i	−0.0549561	−	0.998489i	$-0.517502\pi$
$548$		0			0
$549$	−5.84096	−	11.7446i	−0.249286	−	0.501246i
$550$		0			0
$551$		−	78.1996i		−	3.33141i
$552$		0			0
$553$	4.89898	−	4.89898i	0.208326	−	0.208326i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.76280	+	7.76280i	−0.328920	+	0.328920i	−0.852176	−	0.523256i	$-0.824717\pi$
$557$	−7.76280	+	7.76280i	−0.328920	+	0.328920i	0.523256	+	0.852176i	$0.324717\pi$
$558$		0			0
$559$		−	38.8397i		−	1.64274i
$560$		0			0
$561$	−1.05842	−	4.50506i	−0.0446866	−	0.190204i
$562$		0			0
$563$	25.7863	+	25.7863i	1.08676	+	1.08676i	0.995860	+	0.0909046i	$0.0289758\pi$
$563$	25.7863	+	25.7863i	1.08676	+	1.08676i	0.0909046	+	0.995860i	$0.471024\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.5042	+	3.11687i	−0.945088	+	0.130896i
$568$		0			0
$569$	11.7745			0.493613			0.246806	−	0.969065i	$-0.420619\pi$
$569$	11.7745			0.493613			0.246806	+	0.969065i	$0.420619\pi$
$570$		0			0
$571$	−42.8397			−1.79278			−0.896392	−	0.443262i	$-0.853821\pi$
$571$	−42.8397			−1.79278			−0.896392	+	0.443262i	$0.853821\pi$
$572$		0			0
$573$	−7.22697	+	11.6656i	−0.301911	+	0.487338i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.61850	−	6.61850i	−0.275532	−	0.275532i	0.555791	−	0.831322i	$-0.312416\pi$
$577$	−6.61850	−	6.61850i	−0.275532	−	0.275532i	−0.831322	+	0.555791i	$0.812416\pi$
$578$		0			0
$579$	−2.42315	+	0.569297i	−0.100703	+	0.0236592i
$580$		0			0
$581$			28.7075i			1.19099i
$582$		0			0
$583$	−32.3381	+	32.3381i	−1.33931	+	1.33931i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.43753	−	3.43753i	0.141882	−	0.141882i	−0.632598	−	0.774480i	$-0.718011\pi$
$587$	3.43753	−	3.43753i	0.141882	−	0.141882i	0.774480	+	0.632598i	$0.218011\pi$
$588$		0			0
$589$			2.88316i			0.118798i
$590$		0			0
$591$	34.1168	−	8.01544i	1.40338	−	0.329711i
$592$		0			0
$593$	1.33159	+	1.33159i	0.0546819	+	0.0546819i	0.733919	−	0.679237i	$-0.237689\pi$
$593$	1.33159	+	1.33159i	0.0546819	+	0.0546819i	−0.679237	+	0.733919i	$0.737689\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.46124	+	15.2721i	−0.387223	+	0.625046i
$598$		0			0
$599$	18.0202			0.736286			0.368143	−	0.929769i	$-0.379994\pi$
$599$	18.0202			0.736286			0.368143	+	0.929769i	$0.379994\pi$
$600$		0			0
$601$	7.74456			0.315907			0.157954	−	0.987447i	$-0.449510\pi$
$601$	7.74456			0.315907			0.157954	+	0.987447i	$0.449510\pi$
$602$		0			0
$603$	−1.65369	+	4.92598i	−0.0673435	+	0.200602i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.1659	+	23.1659i	0.940274	+	0.940274i	0.998314	−	0.0580405i	$-0.0184853\pi$
$607$	23.1659	+	23.1659i	0.940274	+	0.940274i	−0.0580405	+	0.998314i	$0.518485\pi$
$608$		0			0
$609$	−10.0974	−	42.9783i	−0.409165	−	1.74157i
$610$		0			0
$611$		−	32.8713i		−	1.32983i
$612$		0			0
$613$	−22.9573	+	22.9573i	−0.927237	+	0.927237i	−0.997527	−	0.0702897i	$-0.977608\pi$
$613$	−22.9573	+	22.9573i	−0.927237	+	0.927237i	0.0702897	+	0.997527i	$0.477608\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.6741	−	26.6741i	1.07386	−	1.07386i	0.0768115	−	0.997046i	$-0.475526\pi$
$617$	26.6741	−	26.6741i	1.07386	−	1.07386i	0.997046	−	0.0768115i	$-0.0244740\pi$
$618$		0			0
$619$			15.8614i			0.637524i	0.947835	+	0.318762i	$0.103267\pi$
$619$			15.8614i			0.637524i	−0.947835	+	0.318762i	$0.896733\pi$
$620$		0			0
$621$	−10.9783	+	9.10268i	−0.440542	+	0.365278i
$622$		0			0
$623$	0.887728	+	0.887728i	0.0355661	+	0.0355661i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	48.5359	+	30.0685i	1.93834	+	1.20082i
$628$		0			0
$629$	0.994667			0.0396600
$630$		0			0
$631$	14.6060			0.581454			0.290727	−	0.956806i	$-0.406103\pi$
$631$	14.6060			0.581454			0.290727	+	0.956806i	$0.406103\pi$
$632$		0			0
$633$	−2.56869	−	1.59133i	−0.102096	−	0.0632497i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.82380	−	1.82380i	−0.0722615	−	0.0722615i
$638$		0			0
$639$	27.1229	−	13.4891i	1.07297	−	0.533622i
$640$		0			0
$641$		−	10.6873i		−	0.422121i	−0.977473	−	0.211061i	$-0.932308\pi$
$641$		−	10.6873i		−	0.422121i	0.977473	−	0.211061i	$-0.0676918\pi$
$642$		0			0
$643$	−14.4884	+	14.4884i	−0.571366	+	0.571366i	−0.932510	−	0.361144i	$-0.882386\pi$
$643$	−14.4884	+	14.4884i	−0.571366	+	0.571366i	0.361144	+	0.932510i	$0.382386\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$		0			0
$649$			22.7446i			0.892802i
$650$		0			0
$651$	0.372281	+	1.58457i	0.0145909	+	0.0621044i
$652$		0			0
$653$	−31.2779	−	31.2779i	−1.22400	−	1.22400i	−0.966198	−	0.257803i	$-0.917001\pi$
$653$	−31.2779	−	31.2779i	−1.22400	−	1.22400i	−0.257803	−	0.966198i	$-0.582999\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−31.8092	−	10.6786i	−1.24099	−	0.416612i
$658$		0			0
$659$	33.9585			1.32284			0.661418	−	0.750017i	$-0.269955\pi$
$659$	33.9585			1.32284			0.661418	+	0.750017i	$0.269955\pi$
$660$		0			0
$661$	5.76631			0.224284			0.112142	−	0.993692i	$-0.464229\pi$
$661$	5.76631			0.224284			0.112142	+	0.993692i	$0.464229\pi$
$662$		0			0
$663$	2.35269	−	3.79767i	0.0913711	−	0.147489i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−19.5959	−	19.5959i	−0.758757	−	0.758757i
$668$		0			0
$669$	20.7846	−	4.88316i	0.803579	−	0.188794i
$670$		0			0
$671$			18.6101i			0.718436i
$672$		0			0
$673$	26.3187	−	26.3187i	1.01451	−	1.01451i	0.0146180	−	0.999893i	$-0.495347\pi$
$673$	26.3187	−	26.3187i	1.01451	−	1.01451i	0.999893	−	0.0146180i	$-0.00465323\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.2481	+	16.2481i	−0.624464	+	0.624464i	−0.946670	−	0.322205i	$-0.895576\pi$
$677$	−16.2481	+	16.2481i	−0.624464	+	0.624464i	0.322205	+	0.946670i	$0.395576\pi$
$678$		0			0
$679$		−	23.1168i		−	0.887143i
$680$		0			0
$681$	−6.74456	+	1.58457i	−0.258452	+	0.0607210i
$682$		0			0
$683$	−11.0351	−	11.0351i	−0.422246	−	0.422246i	0.463730	−	0.885976i	$-0.346511\pi$
$683$	−11.0351	−	11.0351i	−0.422246	−	0.422246i	−0.885976	+	0.463730i	$0.846511\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	9.46124	−	15.2721i	0.360969	−	0.582668i
$688$		0			0
$689$	−44.1485			−1.68192
$690$		0			0
$691$	30.3505			1.15459			0.577294	−	0.816536i	$-0.304109\pi$
$691$	30.3505			1.15459			0.577294	+	0.816536i	$0.304109\pi$
$692$		0			0
$693$	30.5577	+	10.2585i	1.16079	+	0.389687i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.29593	+	3.29593i	0.124842	+	0.124842i
$698$		0			0
$699$	6.43087	+	27.3723i	0.243238	+	1.03531i
$700$		0			0
$701$			13.2665i			0.501069i	0.968108	+	0.250534i	$0.0806063\pi$
$701$			13.2665i			0.501069i	−0.968108	+	0.250534i	$0.919394\pi$
$702$		0			0
$703$	−8.67750	+	8.67750i	−0.327278	+	0.327278i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.5618	−	27.5618i	1.03657	−	1.03657i
$708$		0			0
$709$		−	27.8614i		−	1.04636i	−0.852223	−	0.523179i	$-0.824746\pi$
$709$		−	27.8614i		−	1.04636i	0.852223	−	0.523179i	$-0.175254\pi$
$710$		0			0
$711$	7.37228	−	3.66648i	0.276482	−	0.137504i
$712$		0			0
$713$	0.722486	+	0.722486i	0.0270573	+	0.0270573i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−19.5336	−	12.1012i	−0.729494	−	0.451929i
$718$		0			0
$719$	−45.1431			−1.68355			−0.841777	−	0.539825i	$-0.818490\pi$
$719$	−45.1431			−1.68355			−0.841777	+	0.539825i	$0.818490\pi$
$720$		0			0
$721$	−20.7446			−0.772568
$722$		0			0
$723$	31.2644	+	19.3686i	1.16274	+	0.720328i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−17.6024	−	17.6024i	−0.652836	−	0.652836i	0.300839	−	0.953675i	$-0.402733\pi$
$727$	−17.6024	−	17.6024i	−0.652836	−	0.652836i	−0.953675	+	0.300839i	$0.902733\pi$
$728$		0			0
$729$	−26.5330	−	5.00000i	−0.982704	−	0.185185i
$730$		0			0
$731$		−	5.93354i		−	0.219460i
$732$		0			0
$733$	34.2929	−	34.2929i	1.26664	−	1.26664i	0.318820	−	0.947815i	$-0.396713\pi$
$733$	34.2929	−	34.2929i	1.26664	−	1.26664i	0.947815	−	0.318820i	$-0.103287\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.21299	−	5.21299i	0.192023	−	0.192023i
$738$		0			0
$739$			24.4674i			0.900047i	0.893017	+	0.450023i	$0.148584\pi$
$739$			24.4674i			0.900047i	−0.893017	+	0.450023i	$0.851416\pi$
$740$		0			0
$741$	12.6060	+	53.6559i	0.463092	+	1.97110i
$742$		0			0
$743$	−8.32004	−	8.32004i	−0.305233	−	0.305233i	0.537824	−	0.843057i	$-0.319246\pi$
$743$	−8.32004	−	8.32004i	−0.305233	−	0.305233i	−0.843057	+	0.537824i	$0.819246\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−10.8578	+	32.3430i	−0.397266	+	1.18337i
$748$		0			0
$749$	18.6101			0.679999
$750$		0			0
$751$	−44.0000			−1.60558			−0.802791	−	0.596260i	$-0.796653\pi$
$751$	−44.0000			−1.60558			−0.802791	+	0.596260i	$0.796653\pi$
$752$		0			0
$753$	−23.7488	+	38.3348i	−0.865456	+	1.39700i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	21.5895	+	21.5895i	0.784682	+	0.784682i	0.980617	−	0.195935i	$-0.0627741\pi$
$757$	21.5895	+	21.5895i	0.784682	+	0.784682i	−0.195935	+	0.980617i	$0.562774\pi$
$758$		0			0
$759$	19.6974	−	4.62772i	0.714969	−	0.167976i
$760$		0			0
$761$		−	9.01011i		−	0.326616i	−0.986575	−	0.163308i	$-0.947784\pi$
$761$		−	9.01011i		−	0.326616i	0.986575	−	0.163308i	$-0.0522165\pi$
$762$		0			0
$763$	31.8822	−	31.8822i	1.15421	−	1.15421i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.5256	+	15.5256i	−0.560597	+	0.560597i
$768$		0			0
$769$			30.4891i			1.09947i	0.835340	+	0.549733i	$0.185271\pi$
$769$			30.4891i			1.09947i	−0.835340	+	0.549733i	$0.814729\pi$
$770$		0			0
$771$	−34.1168	+	8.01544i	−1.22869	+	0.288669i
$772$		0			0
$773$	−36.7696	−	36.7696i	−1.32251	−	1.32251i	−0.911739	−	0.410770i	$-0.865260\pi$
$773$	−36.7696	−	36.7696i	−1.32251	−	1.32251i	−0.410770	−	0.911739i	$-0.634740\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.64866	+	5.88959i	−0.130895	+	0.211288i
$778$		0			0
$779$	−57.5075			−2.06042
$780$		0			0
$781$	−42.9783			−1.53788
$782$		0			0
$783$	4.87923	−	52.2400i	0.174370	−	1.86691i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.78498	−	1.78498i	−0.0636275	−	0.0636275i	0.674577	−	0.738205i	$-0.264326\pi$
$787$	−1.78498	−	1.78498i	−0.0636275	−	0.0636275i	−0.738205	+	0.674577i	$0.764326\pi$
$788$		0			0
$789$	10.5947	+	45.0951i	0.377181	+	1.60543i
$790$		0			0
$791$		−	8.51278i		−	0.302680i
$792$		0			0
$793$	−12.7034	+	12.7034i	−0.451111	+	0.451111i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.3074	+	14.3074i	−0.506793	+	0.506793i	−0.913541	−	0.406747i	$-0.866663\pi$
$797$	−14.3074	+	14.3074i	−0.506793	+	0.506793i	0.406747	+	0.913541i	$0.366663\pi$
$798$		0			0
$799$		−	5.02175i		−	0.177657i
$800$		0			0
$801$	0.664391	+	1.33591i	0.0234751	+	0.0472020i
$802$		0			0
$803$	33.6625	+	33.6625i	1.18792	+	1.18792i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.868578	+	0.538093i	0.0305754	+	0.0189418i
$808$		0			0
$809$	−47.3176			−1.66360			−0.831799	−	0.555077i	$-0.812689\pi$
$809$	−47.3176			−1.66360			−0.831799	+	0.555077i	$0.812689\pi$
$810$		0			0
$811$	38.3723			1.34743			0.673717	−	0.738990i	$-0.264697\pi$
$811$	38.3723			1.34743			0.673717	+	0.738990i	$0.264697\pi$
$812$		0			0
$813$	−23.9024	−	14.8078i	−0.838295	−	0.519333i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	51.7643	+	51.7643i	1.81100	+	1.81100i
$818$		0			0
$819$	13.8564	+	27.8614i	0.484182	+	0.973556i
$820$		0			0
$821$		−	19.2000i		−	0.670086i	−0.942203	−	0.335043i	$-0.891249\pi$
$821$		−	19.2000i		−	0.670086i	0.942203	−	0.335043i	$-0.108751\pi$
$822$		0			0
$823$	−18.5143	+	18.5143i	−0.645367	+	0.645367i	−0.951870	−	0.306503i	$-0.900841\pi$
$823$	−18.5143	+	18.5143i	−0.645367	+	0.645367i	0.306503	+	0.951870i	$0.400841\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.09439	+	9.09439i	−0.316243	+	0.316243i	−0.847322	−	0.531079i	$-0.821787\pi$
$827$	−9.09439	+	9.09439i	−0.316243	+	0.316243i	0.531079	+	0.847322i	$0.321787\pi$
$828$		0			0
$829$			24.7446i			0.859414i	0.902968	+	0.429707i	$0.141383\pi$
$829$			24.7446i			0.859414i	−0.902968	+	0.429707i	$0.858617\pi$
$830$		0			0
$831$	8.88316	+	37.8102i	0.308153	+	1.31162i
$832$		0			0
$833$	−0.278622	−	0.278622i	−0.00965367	−	0.00965367i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.179893	+	1.92605i	−0.00621803	+	0.0665739i
$838$		0			0
$839$	14.4463			0.498742			0.249371	−	0.968408i	$-0.419776\pi$
$839$	14.4463			0.498742			0.249371	+	0.968408i	$0.419776\pi$
$840$		0			0
$841$	72.9565			2.51574
$842$		0			0
$843$	18.9590	−	30.6032i	0.652983	−	1.05403i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.7034	−	12.7034i	−0.436494	−	0.436494i
$848$		0			0
$849$	24.7923	−	5.82473i	0.850871	−	0.199904i
$850$		0			0
$851$			4.34896i			0.149081i
$852$		0			0
$853$	26.3575	−	26.3575i	0.902464	−	0.902464i	−0.0931846	−	0.995649i	$-0.529705\pi$
$853$	26.3575	−	26.3575i	0.902464	−	0.902464i	0.995649	+	0.0931846i	$0.0297047\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	34.5502	−	34.5502i	1.18021	−	1.18021i	0.200525	−	0.979689i	$-0.435735\pi$
$857$	34.5502	−	34.5502i	1.18021	−	1.18021i	0.979689	−	0.200525i	$-0.0642647\pi$
$858$		0			0
$859$		−	16.8614i		−	0.575304i	−0.957735	−	0.287652i	$-0.907125\pi$
$859$		−	16.8614i		−	0.575304i	0.957735	−	0.287652i	$-0.0928746\pi$
$860$		0			0
$861$	−31.6060	+	7.42554i	−1.07713	+	0.253062i
$862$		0			0
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	0.604240	−	0.796802i	$-0.293477\pi$
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	−0.796802	+	0.604240i	$0.793477\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.1474	+	24.4506i	−0.514433	+	0.830385i
$868$		0			0
$869$	−11.6819			−0.396282
$870$		0			0
$871$	7.11684			0.241145
$872$		0			0
$873$	8.74329	−	26.0443i	0.295916	−	0.881467i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.80442	+	7.80442i	0.263536	+	0.263536i	0.826489	−	0.562953i	$-0.190335\pi$
$877$	7.80442	+	7.80442i	0.263536	+	0.263536i	−0.562953	+	0.826489i	$0.690335\pi$
$878$		0			0
$879$	1.67715	+	7.13859i	0.0565688	+	0.240779i
$880$		0			0
$881$		−	30.8820i		−	1.04044i	−0.854032	−	0.520220i	$-0.825850\pi$
$881$		−	30.8820i		−	1.04044i	0.854032	−	0.520220i	$-0.174150\pi$
$882$		0			0
$883$	32.2339	−	32.2339i	1.08476	−	1.08476i	0.0886970	−	0.996059i	$-0.471730\pi$
$883$	32.2339	−	32.2339i	1.08476	−	1.08476i	0.996059	−	0.0886970i	$-0.0282703\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	−0.216523	−	0.976277i	$-0.569472\pi$
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	0.976277	+	0.216523i	$0.0694717\pi$
$888$		0			0
$889$			0.744563i			0.0249718i
$890$		0			0
$891$	30.5475	+	23.1152i	1.02338	+	0.774388i
$892$		0			0
$893$	43.8099	+	43.8099i	1.46604	+	1.46604i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	16.6045	+	10.2866i	0.554407	+	0.343461i
$898$		0			0
$899$	−3.75906			−0.125372
$900$		0			0
$901$	−6.74456			−0.224694
$902$		0			0
$903$	35.1335	+	21.7656i	1.16917	+	0.724312i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	20.7940	+	20.7940i	0.690454	+	0.690454i	0.962332	−	0.271878i	$-0.0876446\pi$
$907$	20.7940	+	20.7940i	0.690454	+	0.690454i	−0.271878	+	0.962332i	$0.587645\pi$
$908$		0			0
$909$	41.4766	−	20.6277i	1.37569	−	0.684178i
$910$		0			0
$911$		−	1.17981i		−	0.0390890i	−0.999809	−	0.0195445i	$-0.993778\pi$
$911$		−	1.17981i		−	0.0390890i	0.999809	−	0.0195445i	$-0.00622160\pi$
$912$		0			0
$913$	34.2274	−	34.2274i	1.13276	−	1.13276i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.82843	−	2.82843i	0.0934029	−	0.0934029i
$918$		0			0
$919$			40.8397i			1.34718i	0.739107	+	0.673588i	$0.235248\pi$
$919$			40.8397i			1.34718i	−0.739107	+	0.673588i	$0.764752\pi$
$920$		0			0
$921$	−8.29211	−	35.2944i	−0.273234	−	1.16299i
$922$		0			0
$923$	−29.3372	−	29.3372i	−0.965647	−	0.965647i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−23.3716	−	7.84604i	−0.767625	−	0.257698i
$928$		0			0
$929$	−10.0974			−0.331283			−0.165642	−	0.986186i	$-0.552970\pi$
$929$	−10.0974			−0.331283			−0.165642	+	0.986186i	$0.552970\pi$
$930$		0			0
$931$	4.86141			0.159326
$932$		0			0
$933$	−17.5136	+	28.2701i	−0.573370	+	0.925521i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	0.764571	−	0.644539i	$-0.222951\pi$
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	−0.644539	+	0.764571i	$0.722951\pi$
$938$		0			0
$939$	−4.75372	+	1.11684i	−0.155132	+	0.0364468i
$940$		0			0
$941$			9.50744i			0.309934i	0.987920	+	0.154967i	$0.0495271\pi$
$941$			9.50744i			0.309934i	−0.987920	+	0.154967i	$0.950473\pi$
$942$		0			0
$943$	−14.4107	+	14.4107i	−0.469278	+	0.469278i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.60388	−	4.60388i	0.149606	−	0.149606i	−0.628336	−	0.777942i	$-0.716264\pi$
$947$	4.60388	−	4.60388i	0.149606	−	0.149606i	0.777942	+	0.628336i	$0.216264\pi$
$948$		0			0
$949$			45.9565i			1.49181i
$950$		0			0
$951$	22.7446	−	5.34363i	0.737543	−	0.173279i
$952$		0			0
$953$	11.0351	+	11.0351i	0.357462	+	0.357462i	0.862876	−	0.505415i	$-0.168661\pi$
$953$	11.0351	+	11.0351i	0.357462	+	0.357462i	−0.505415	+	0.862876i	$0.668661\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−39.2033	+	63.2811i	−1.26726	+	2.04559i
$958$		0			0
$959$	−25.5383			−0.824676
$960$		0			0
$961$	−30.8614			−0.995529
$962$		0			0
$963$	20.9669	+	7.03875i	0.675649	+	0.226821i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.30319	+	9.30319i	0.299170	+	0.299170i	0.840689	−	0.541519i	$-0.182150\pi$
$967$	9.30319	+	9.30319i	0.299170	+	0.299170i	−0.541519	+	0.840689i	$0.682150\pi$
$968$		0			0
$969$	1.92581	+	8.19702i	0.0618661	+	0.263326i
$970$		0			0
$971$			20.6920i			0.664039i	0.943273	+	0.332020i	$0.107730\pi$
$971$			20.6920i			0.664039i	−0.943273	+	0.332020i	$0.892270\pi$
$972$		0			0
$973$	3.77852	−	3.77852i	0.121134	−	0.121134i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.27229	+	3.27229i	−0.104690	+	0.104690i	−0.757512	−	0.652822i	$-0.773585\pi$
$977$	−3.27229	+	3.27229i	−0.104690	+	0.104690i	0.652822	+	0.757512i	$0.273585\pi$
$978$		0			0
$979$		−	2.11684i		−	0.0676546i
$980$		0			0
$981$	47.9783	−	23.8612i	1.53183	−	0.761829i
$982$		0			0
$983$	16.0828	+	16.0828i	0.512963	+	0.512963i	0.915433	−	0.402470i	$-0.131848\pi$
$983$	16.0828	+	16.0828i	0.512963	+	0.512963i	−0.402470	+	0.915433i	$0.631848\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	29.7346	+	18.4209i	0.946464	+	0.586344i
$988$		0			0
$989$	25.9431			0.824942
$990$		0			0
$991$	−16.8397			−0.534929			−0.267465	−	0.963568i	$-0.586186\pi$
$991$	−16.8397			−0.534929			−0.267465	+	0.963568i	$0.586186\pi$
$992$		0			0
$993$	30.3722	+	18.8159i	0.963833	+	0.597104i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−33.4586	−	33.4586i	−1.05964	−	1.05964i	−0.998105	−	0.0615399i	$-0.980399\pi$
$997$	−33.4586	−	33.4586i	−1.05964	−	1.05964i	−0.0615399	−	0.998105i	$-0.519601\pi$
$998$		0			0
$999$	−6.33830	+	5.25544i	−0.200535	+	0.166275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.r.f.257.7	yes	16
3.2	odd	2	inner	600.2.r.f.257.3	yes	16
4.3	odd	2		1200.2.v.m.257.2		16
5.2	odd	4	inner	600.2.r.f.593.6	yes	16
5.3	odd	4	inner	600.2.r.f.593.3	yes	16
5.4	even	2	inner	600.2.r.f.257.2	✓	16
12.11	even	2		1200.2.v.m.257.6		16
15.2	even	4	inner	600.2.r.f.593.2	yes	16
15.8	even	4	inner	600.2.r.f.593.7	yes	16
15.14	odd	2	inner	600.2.r.f.257.6	yes	16
20.3	even	4		1200.2.v.m.593.6		16
20.7	even	4		1200.2.v.m.593.3		16
20.19	odd	2		1200.2.v.m.257.7		16
60.23	odd	4		1200.2.v.m.593.2		16
60.47	odd	4		1200.2.v.m.593.7		16
60.59	even	2		1200.2.v.m.257.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.r.f.257.2	✓	16	5.4	even	2	inner
600.2.r.f.257.3	yes	16	3.2	odd	2	inner
600.2.r.f.257.6	yes	16	15.14	odd	2	inner
600.2.r.f.257.7	yes	16	1.1	even	1	trivial
600.2.r.f.593.2	yes	16	15.2	even	4	inner
600.2.r.f.593.3	yes	16	5.3	odd	4	inner
600.2.r.f.593.6	yes	16	5.2	odd	4	inner
600.2.r.f.593.7	yes	16	15.8	even	4	inner
1200.2.v.m.257.2		16	4.3	odd	2
1200.2.v.m.257.3		16	60.59	even	2
1200.2.v.m.257.6		16	12.11	even	2
1200.2.v.m.257.7		16	20.19	odd	2
1200.2.v.m.593.2		16	60.23	odd	4
1200.2.v.m.593.3		16	20.7	even	4
1200.2.v.m.593.6		16	20.3	even	4
1200.2.v.m.593.7		16	60.47	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47240 + 0.912166i) q^{3} +(1.78498 + 1.78498i) q^{7} +(1.33591 + 2.68614i) q^{9} +O(q^{10})\)	\(q+(1.47240 + 0.912166i) q^{3} +(1.78498 + 1.78498i) q^{7} +(1.33591 + 2.68614i) q^{9} -4.25639i q^{11} +(2.90544 - 2.90544i) q^{13} +(0.443864 - 0.443864i) q^{17} +7.74456i q^{19} +(1.00000 + 4.25639i) q^{21} +(1.94070 + 1.94070i) q^{23} +(-0.483219 + 5.17364i) q^{27} -10.0974 q^{29} +0.372281 q^{31} +(3.88253 - 6.26709i) q^{33} +(1.12046 + 1.12046i) q^{37} +(6.92820 - 1.62772i) q^{39} +7.42554i q^{41} +(6.68396 - 6.68396i) q^{43} +(5.65685 - 5.65685i) q^{47} -0.627719i q^{49} +(1.05842 - 0.248667i) q^{51} +(-7.59755 - 7.59755i) q^{53} +(-7.06432 + 11.4031i) q^{57} -5.34363 q^{59} -4.37228 q^{61} +(-2.41013 + 7.17926i) q^{63} +(1.22474 + 1.22474i) q^{67} +(1.08724 + 4.62772i) q^{69} -10.0974i q^{71} +(-7.90870 + 7.90870i) q^{73} +(7.59755 - 7.59755i) q^{77} -2.74456i q^{79} +(-5.43070 + 7.17687i) q^{81} +(8.04142 + 8.04142i) q^{83} +(-14.8673 - 9.21046i) q^{87} +0.497333 q^{89} +10.3723 q^{91} +(0.548146 + 0.339582i) q^{93} +(-6.47539 - 6.47539i) q^{97} +(11.4333 - 5.68614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 16 q^{21} - 40 q^{31} - 52 q^{51} - 24 q^{61} + 28 q^{81} + 120 q^{91}+O(q^{100}) \) 16 * q + 16 * q^21 - 40 * q^31 - 52 * q^51 - 24 * q^61 + 28 * q^81 + 120 * q^91

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