LMFDB - Embedded newform 975.2.n.c.824.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(749,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("975.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, degree $2$, not 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:	$7.78541419707$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			824.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	975.824
Dual form			975.2.n.c.749.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.292893 + 1.70711i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.292893 + 1.70711i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +(2.82843 - 2.82843i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(3.00000 + 2.00000i) q^{13} +1.41421i q^{14} +1.00000 q^{16} +(-1.29289 - 2.70711i) q^{18} +(-1.00000 + 1.00000i) q^{19} +(0.414214 - 2.41421i) q^{21} -4.00000i q^{22} +8.48528i q^{23} +(-5.12132 - 0.878680i) q^{24} +(3.53553 - 0.707107i) q^{26} +(1.41421 + 5.00000i) q^{27} +(-1.00000 - 1.00000i) q^{28} -2.82843i q^{29} +(-5.00000 + 5.00000i) q^{31} +(-3.53553 + 3.53553i) q^{32} +(-1.17157 + 6.82843i) q^{33} +(2.82843 + 1.00000i) q^{36} +(-1.00000 + 1.00000i) q^{37} +1.41421i q^{38} +(-6.24264 + 0.171573i) q^{39} +(1.41421 + 1.41421i) q^{41} +(-1.41421 - 2.00000i) q^{42} -6.00000 q^{43} +(2.82843 + 2.82843i) q^{44} +(6.00000 + 6.00000i) q^{46} +(2.82843 + 2.82843i) q^{47} +(-1.41421 + 1.00000i) q^{48} +5.00000i q^{49} +(-2.00000 + 3.00000i) q^{52} -5.65685 q^{53} +(4.53553 + 2.53553i) q^{54} -4.24264 q^{56} +(0.414214 - 2.41421i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-2.82843 + 2.82843i) q^{59} +8.00000 q^{61} +7.07107i q^{62} +(1.82843 + 3.82843i) q^{63} +7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-5.00000 - 5.00000i) q^{67} +(-8.48528 - 12.0000i) q^{69} +(-2.82843 - 2.82843i) q^{71} +(8.12132 - 3.87868i) q^{72} +(1.00000 - 1.00000i) q^{73} +1.41421i q^{74} +(-1.00000 - 1.00000i) q^{76} +5.65685i q^{77} +(-4.29289 + 4.53553i) q^{78} +10.0000 q^{79} +(-7.00000 - 5.65685i) q^{81} +2.00000 q^{82} +(5.65685 - 5.65685i) q^{83} +(2.41421 + 0.414214i) q^{84} +(-4.24264 + 4.24264i) q^{86} +(2.82843 + 4.00000i) q^{87} +12.0000 q^{88} +(9.89949 - 9.89949i) q^{89} +(-5.00000 + 1.00000i) q^{91} -8.48528 q^{92} +(2.07107 - 12.0711i) q^{93} +4.00000 q^{94} +(1.46447 - 8.53553i) q^{96} +(7.00000 + 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^6 - 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{6} - 4 q^{7} + 4 q^{9} - 4 q^{12} + 12 q^{13} + 4 q^{16} - 8 q^{18} - 4 q^{19} - 4 q^{21} - 12 q^{24} - 4 q^{28} - 20 q^{31} - 16 q^{33} - 4 q^{37} - 8 q^{39} - 24 q^{43} + 24 q^{46} - 8 q^{52} + 4 q^{54} - 4 q^{57} - 8 q^{58} + 32 q^{61} - 4 q^{63} + 16 q^{66} - 20 q^{67} + 24 q^{72} + 4 q^{73} - 4 q^{76} - 20 q^{78} + 40 q^{79} - 28 q^{81} + 8 q^{82} + 4 q^{84} + 48 q^{88} - 20 q^{91} - 20 q^{93} + 16 q^{94} + 20 q^{96} + 28 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^6 - 4 * q^7 + 4 * q^9 - 4 * q^12 + 12 * q^13 + 4 * q^16 - 8 * q^18 - 4 * q^19 - 4 * q^21 - 12 * q^24 - 4 * q^28 - 20 * q^31 - 16 * q^33 - 4 * q^37 - 8 * q^39 - 24 * q^43 + 24 * q^46 - 8 * q^52 + 4 * q^54 - 4 * q^57 - 8 * q^58 + 32 * q^61 - 4 * q^63 + 16 * q^66 - 20 * q^67 + 24 * q^72 + 4 * q^73 - 4 * q^76 - 20 * q^78 + 40 * q^79 - 28 * q^81 + 8 * q^82 + 4 * q^84 + 48 * q^88 - 20 * q^91 - 20 * q^93 + 16 * q^94 + 20 * q^96 + 28 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i	−0.411438	−	0.911438i	$-0.634973\pi$
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−0.292893	+	1.70711i	−0.119573	+	0.696923i
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$	2.12132	+	2.12132i	0.750000	+	0.750000i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$		0			0
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	−0.137675	−	0.990478i	$-0.543963\pi$
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	0.990478	+	0.137675i	$0.0439628\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$			1.41421i			0.377964i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$	−1.00000	+	1.00000i	−0.229416	+	0.229416i	−0.812449	−	0.583033i	$-0.801866\pi$
$19$	−1.00000	+	1.00000i	−0.229416	+	0.229416i	0.583033	+	0.812449i	$0.301866\pi$
$20$		0			0
$21$	0.414214	−	2.41421i	0.0903888	−	0.526825i
$22$		−	4.00000i		−	0.852803i
$23$			8.48528i			1.76930i	0.466252	+	0.884652i	$0.345604\pi$
$23$			8.48528i			1.76930i	−0.466252	+	0.884652i	$0.654396\pi$
$24$	−5.12132	−	0.878680i	−1.04539	−	0.179360i
$25$		0			0
$26$	3.53553	−	0.707107i	0.693375	−	0.138675i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$	−1.00000	−	1.00000i	−0.188982	−	0.188982i
$29$		−	2.82843i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$		0			0
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	−0.995261	−	0.0972349i	$-0.969000\pi$
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	0.0972349	+	0.995261i	$0.469000\pi$
$32$	−3.53553	+	3.53553i	−0.625000	+	0.625000i
$33$	−1.17157	+	6.82843i	−0.203945	+	1.18868i
$34$		0			0
$35$		0			0
$36$	2.82843	+	1.00000i	0.471405	+	0.166667i
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	−0.784512	−	0.620113i	$-0.787087\pi$
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	0.620113	+	0.784512i	$0.287087\pi$
$38$			1.41421i			0.229416i
$39$	−6.24264	+	0.171573i	−0.999623	+	0.0274736i
$40$		0			0
$41$	1.41421	+	1.41421i	0.220863	+	0.220863i	0.808862	−	0.587999i	$-0.200084\pi$
$41$	1.41421	+	1.41421i	0.220863	+	0.220863i	−0.587999	+	0.808862i	$0.700084\pi$
$42$	−1.41421	−	2.00000i	−0.218218	−	0.308607i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	2.82843	+	2.82843i	0.426401	+	0.426401i
$45$		0			0
$46$	6.00000	+	6.00000i	0.884652	+	0.884652i
$47$	2.82843	+	2.82843i	0.412568	+	0.412568i	0.882632	−	0.470064i	$-0.155769\pi$
$47$	2.82843	+	2.82843i	0.412568	+	0.412568i	−0.470064	+	0.882632i	$0.655769\pi$
$48$	−1.41421	+	1.00000i	−0.204124	+	0.144338i
$49$			5.00000i			0.714286i
$50$		0			0
$51$		0			0
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	−5.65685			−0.777029			−0.388514	−	0.921443i	$-0.627012\pi$
$53$	−5.65685			−0.777029			−0.388514	+	0.921443i	$0.627012\pi$
$54$	4.53553	+	2.53553i	0.617208	+	0.345042i
$55$		0			0
$56$	−4.24264			−0.566947
$57$	0.414214	−	2.41421i	0.0548639	−	0.319770i
$58$	−2.00000	−	2.00000i	−0.262613	−	0.262613i
$59$	−2.82843	+	2.82843i	−0.368230	+	0.368230i	−0.866831	−	0.498601i	$-0.833847\pi$
$59$	−2.82843	+	2.82843i	−0.368230	+	0.368230i	0.498601	+	0.866831i	$0.333847\pi$
$60$		0			0
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$			7.07107i			0.898027i
$63$	1.82843	+	3.82843i	0.230360	+	0.482336i
$64$			7.00000i			0.875000i
$65$		0			0
$66$	4.00000	+	5.65685i	0.492366	+	0.696311i
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$		0			0
$69$	−8.48528	−	12.0000i	−1.02151	−	1.44463i
$70$		0			0
$71$	−2.82843	−	2.82843i	−0.335673	−	0.335673i	0.519063	−	0.854736i	$-0.326281\pi$
$71$	−2.82843	−	2.82843i	−0.335673	−	0.335673i	−0.854736	+	0.519063i	$0.826281\pi$
$72$	8.12132	−	3.87868i	0.957107	−	0.457107i
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	−0.646160	−	0.763202i	$-0.723626\pi$
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	0.763202	+	0.646160i	$0.223626\pi$
$74$			1.41421i			0.164399i
$75$		0			0
$76$	−1.00000	−	1.00000i	−0.114708	−	0.114708i
$77$			5.65685i			0.644658i
$78$	−4.29289	+	4.53553i	−0.486074	+	0.513548i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	2.00000			0.220863
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	−0.324846	−	0.945767i	$-0.605313\pi$
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	0.945767	+	0.324846i	$0.105313\pi$
$84$	2.41421	+	0.414214i	0.263412	+	0.0451944i
$85$		0			0
$86$	−4.24264	+	4.24264i	−0.457496	+	0.457496i
$87$	2.82843	+	4.00000i	0.303239	+	0.428845i
$88$	12.0000			1.27920
$89$	9.89949	−	9.89949i	1.04934	−	1.04934i	0.0506267	−	0.998718i	$-0.483878\pi$
$89$	9.89949	−	9.89949i	1.04934	−	1.04934i	0.998718	−	0.0506267i	$-0.0161219\pi$
$90$		0			0
$91$	−5.00000	+	1.00000i	−0.524142	+	0.104828i
$92$	−8.48528			−0.884652
$93$	2.07107	−	12.0711i	0.214760	−	1.25171i
$94$	4.00000			0.412568
$95$		0			0
$96$	1.46447	−	8.53553i	0.149466	−	0.871154i
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	0.966691	−	0.255948i	$-0.0823876\pi$
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	−0.255948	+	0.966691i	$0.582388\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	−5.17157	−	10.8284i	−0.519763	−	1.08830i
$100$		0			0
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$		0			0
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	2.12132	+	10.6066i	0.208013	+	1.04006i
$105$		0			0
$106$	−4.00000	+	4.00000i	−0.388514	+	0.388514i
$107$	5.65685			0.546869			0.273434	−	0.961891i	$-0.411840\pi$
$107$	5.65685			0.546869			0.273434	+	0.961891i	$0.411840\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$		0			0
$111$	0.414214	−	2.41421i	0.0393154	−	0.229147i
$112$	−1.00000	+	1.00000i	−0.0944911	+	0.0944911i
$113$	−14.1421			−1.33038			−0.665190	−	0.746674i	$-0.731650\pi$
$113$	−14.1421			−1.33038			−0.665190	+	0.746674i	$0.731650\pi$
$114$	−1.41421	−	2.00000i	−0.132453	−	0.187317i
$115$		0			0
$116$	2.82843			0.262613
$117$	8.65685	−	6.48528i	0.800326	−	0.599564i
$118$			4.00000i			0.368230i
$119$		0			0
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$	5.65685	−	5.65685i	0.512148	−	0.512148i
$123$	−3.41421	−	0.585786i	−0.307849	−	0.0528186i
$124$	−5.00000	−	5.00000i	−0.449013	−	0.449013i
$125$		0			0
$126$	4.00000	+	1.41421i	0.356348	+	0.125988i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−2.12132	−	2.12132i	−0.187500	−	0.187500i
$129$	8.48528	−	6.00000i	0.747087	−	0.528271i
$130$		0			0
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	−6.82843	−	1.17157i	−0.594338	−	0.101972i
$133$		−	2.00000i		−	0.173422i
$134$	−7.07107			−0.610847
$135$		0			0
$136$		0			0
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	0.143831	−	0.989602i	$-0.454058\pi$
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	−0.989602	+	0.143831i	$0.954058\pi$
$138$	−14.4853	−	2.48528i	−1.23307	−	0.211561i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−6.82843	−	1.17157i	−0.575057	−	0.0986642i
$142$	−4.00000			−0.335673
$143$	14.1421	−	2.82843i	1.18262	−	0.236525i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$		0			0
$146$		−	1.41421i		−	0.117041i
$147$	−5.00000	−	7.07107i	−0.412393	−	0.583212i
$148$	−1.00000	−	1.00000i	−0.0821995	−	0.0821995i
$149$	−1.41421	−	1.41421i	−0.115857	−	0.115857i	0.646802	−	0.762658i	$-0.276106\pi$
$149$	−1.41421	−	1.41421i	−0.115857	−	0.115857i	−0.762658	+	0.646802i	$0.776106\pi$
$150$		0			0
$151$	1.00000	+	1.00000i	0.0813788	+	0.0813788i	0.746625	−	0.665246i	$-0.231673\pi$
$151$	1.00000	+	1.00000i	0.0813788	+	0.0813788i	−0.665246	+	0.746625i	$0.731673\pi$
$152$	−4.24264			−0.344124
$153$		0			0
$154$	4.00000	+	4.00000i	0.322329	+	0.322329i
$155$		0			0
$156$	−0.171573	−	6.24264i	−0.0137368	−	0.499811i
$157$			14.0000i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$			14.0000i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$	7.07107	−	7.07107i	0.562544	−	0.562544i
$159$	8.00000	−	5.65685i	0.634441	−	0.448618i
$160$		0			0
$161$	−8.48528	−	8.48528i	−0.668734	−	0.668734i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	−0.666858	−	0.745184i	$-0.732361\pi$
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	0.745184	+	0.666858i	$0.232361\pi$
$164$	−1.41421	+	1.41421i	−0.110432	+	0.110432i
$165$		0			0
$166$		−	8.00000i		−	0.620920i
$167$	2.82843	+	2.82843i	0.218870	+	0.218870i	0.808022	−	0.589152i	$-0.200538\pi$
$167$	2.82843	+	2.82843i	0.218870	+	0.218870i	−0.589152	+	0.808022i	$0.700538\pi$
$168$	6.00000	−	4.24264i	0.462910	−	0.327327i
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	1.82843	+	3.82843i	0.139823	+	0.292767i
$172$		−	6.00000i		−	0.457496i
$173$		−	8.48528i		−	0.645124i	−0.946548	−	0.322562i	$-0.895456\pi$
$173$		−	8.48528i		−	0.645124i	0.946548	−	0.322562i	$-0.104544\pi$
$174$	4.82843	+	0.828427i	0.366042	+	0.0628029i
$175$		0			0
$176$	2.82843	−	2.82843i	0.213201	−	0.213201i
$177$	1.17157	−	6.82843i	0.0880608	−	0.513256i
$178$		−	14.0000i		−	1.04934i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−2.82843	+	4.24264i	−0.209657	+	0.314485i
$183$	−11.3137	+	8.00000i	−0.836333	+	0.591377i
$184$	−18.0000	+	18.0000i	−1.32698	+	1.32698i
$185$		0			0
$186$	−7.07107	−	10.0000i	−0.518476	−	0.733236i
$187$		0			0
$188$	−2.82843	+	2.82843i	−0.206284	+	0.206284i
$189$	−6.41421	−	3.58579i	−0.466565	−	0.260828i
$190$		0			0
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	−7.00000	−	9.89949i	−0.505181	−	0.714435i
$193$	19.0000	−	19.0000i	1.36765	−	1.36765i	0.503871	−	0.863779i	$-0.331909\pi$
$193$	19.0000	−	19.0000i	1.36765	−	1.36765i	0.863779	−	0.503871i	$-0.168091\pi$
$194$	9.89949			0.710742
$195$		0			0
$196$	−5.00000			−0.357143
$197$	15.5563	−	15.5563i	1.10834	−	1.10834i	0.114976	−	0.993368i	$-0.463321\pi$
$197$	15.5563	−	15.5563i	1.10834	−	1.10834i	0.993368	−	0.114976i	$-0.0366790\pi$
$198$	−11.3137	−	4.00000i	−0.804030	−	0.284268i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$	12.0711	+	2.07107i	0.851427	+	0.146082i
$202$	6.00000	−	6.00000i	0.422159	−	0.422159i
$203$	2.82843	+	2.82843i	0.198517	+	0.198517i
$204$		0			0
$205$		0			0
$206$	4.24264	−	4.24264i	0.295599	−	0.295599i
$207$	24.0000	+	8.48528i	1.66812	+	0.589768i
$208$	3.00000	+	2.00000i	0.208013	+	0.138675i
$209$			5.65685i			0.391293i
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$		−	5.65685i		−	0.388514i
$213$	6.82843	+	1.17157i	0.467876	+	0.0802749i
$214$	4.00000	−	4.00000i	0.273434	−	0.273434i
$215$		0			0
$216$	−7.60660	+	13.6066i	−0.517564	+	0.925812i
$217$		−	10.0000i		−	0.678844i
$218$			1.41421i			0.0957826i
$219$	−0.414214	+	2.41421i	−0.0279900	+	0.163137i
$220$		0			0
$221$		0			0
$222$	−1.41421	−	2.00000i	−0.0949158	−	0.134231i
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	0.971921	−	0.235307i	$-0.0756095\pi$
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	−0.235307	+	0.971921i	$0.575609\pi$
$224$		−	7.07107i		−	0.472456i
$225$		0			0
$226$	−10.0000	+	10.0000i	−0.665190	+	0.665190i
$227$	−5.65685	+	5.65685i	−0.375459	+	0.375459i	−0.869461	−	0.494002i	$-0.835534\pi$
$227$	−5.65685	+	5.65685i	−0.375459	+	0.375459i	0.494002	+	0.869461i	$0.335534\pi$
$228$	2.41421	+	0.414214i	0.159885	+	0.0274320i
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	0.673293	−	0.739375i	$-0.264879\pi$
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	−0.739375	+	0.673293i	$0.764879\pi$
$230$		0			0
$231$	−5.65685	−	8.00000i	−0.372194	−	0.526361i
$232$	6.00000	−	6.00000i	0.393919	−	0.393919i
$233$		−	25.4558i		−	1.66767i	−0.552015	−	0.833834i	$-0.686141\pi$
$233$		−	25.4558i		−	1.66767i	0.552015	−	0.833834i	$-0.313859\pi$
$234$	1.53553	−	10.7071i	0.100381	−	0.699945i
$235$		0			0
$236$	−2.82843	−	2.82843i	−0.184115	−	0.184115i
$237$	−14.1421	+	10.0000i	−0.918630	+	0.649570i
$238$		0			0
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	0.0818647	−	0.996643i	$-0.473912\pi$
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	−0.996643	+	0.0818647i	$0.973912\pi$
$240$		0			0
$241$	−17.0000	−	17.0000i	−1.09507	−	1.09507i	−0.994979	−	0.100088i	$-0.968088\pi$
$241$	−17.0000	−	17.0000i	−1.09507	−	1.09507i	−0.100088	−	0.994979i	$-0.531912\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$			8.00000i			0.512148i
$245$		0			0
$246$	−2.82843	+	2.00000i	−0.180334	+	0.127515i
$247$	−5.00000	+	1.00000i	−0.318142	+	0.0636285i
$248$	−21.2132			−1.34704
$249$	−2.34315	+	13.6569i	−0.148491	+	0.865468i
$250$		0			0
$251$	−25.4558			−1.60676			−0.803379	−	0.595468i	$-0.796967\pi$
$251$	−25.4558			−1.60676			−0.803379	+	0.595468i	$0.796967\pi$
$252$	−3.82843	+	1.82843i	−0.241168	+	0.115180i
$253$	24.0000	+	24.0000i	1.50887	+	1.50887i
$254$		0			0
$255$		0			0
$256$	−17.0000			−1.06250
$257$		−	8.48528i		−	0.529297i	−0.964345	−	0.264649i	$-0.914744\pi$
$257$		−	8.48528i		−	0.529297i	0.964345	−	0.264649i	$-0.0852560\pi$
$258$	1.75736	−	10.2426i	0.109408	−	0.637679i
$259$		−	2.00000i		−	0.124274i
$260$		0			0
$261$	−8.00000	−	2.82843i	−0.495188	−	0.175075i
$262$	8.00000	+	8.00000i	0.494242	+	0.494242i
$263$	−22.6274			−1.39527			−0.697633	−	0.716455i	$-0.745763\pi$
$263$	−22.6274			−1.39527			−0.697633	+	0.716455i	$0.745763\pi$
$264$	−16.9706	+	12.0000i	−1.04447	+	0.738549i
$265$		0			0
$266$	−1.41421	−	1.41421i	−0.0867110	−	0.0867110i
$267$	−4.10051	+	23.8995i	−0.250947	+	1.46263i
$268$	5.00000	−	5.00000i	0.305424	−	0.305424i
$269$		−	19.7990i		−	1.20717i	−0.797300	−	0.603583i	$-0.793739\pi$
$269$		−	19.7990i		−	1.20717i	0.797300	−	0.603583i	$-0.206261\pi$
$270$		0			0
$271$	19.0000	+	19.0000i	1.15417	+	1.15417i	0.985709	+	0.168459i	$0.0538791\pi$
$271$	19.0000	+	19.0000i	1.15417	+	1.15417i	0.168459	+	0.985709i	$0.446121\pi$
$272$		0			0
$273$	6.07107	−	6.41421i	0.367438	−	0.388206i
$274$	−14.0000			−0.845771
$275$		0			0
$276$	12.0000	−	8.48528i	0.722315	−	0.510754i
$277$	−12.0000			−0.721010			−0.360505	−	0.932757i	$-0.617396\pi$
$277$	−12.0000			−0.721010			−0.360505	+	0.932757i	$0.617396\pi$
$278$	2.82843	−	2.82843i	0.169638	−	0.169638i
$279$	9.14214	+	19.1421i	0.547325	+	1.14601i
$280$		0			0
$281$	−9.89949	+	9.89949i	−0.590554	+	0.590554i	−0.937781	−	0.347227i	$-0.887123\pi$
$281$	−9.89949	+	9.89949i	−0.590554	+	0.590554i	0.347227	+	0.937781i	$0.387123\pi$
$282$	−5.65685	+	4.00000i	−0.336861	+	0.238197i
$283$	−12.0000			−0.713326			−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000			−0.713326			−0.356663	+	0.934233i	$0.616086\pi$
$284$	2.82843	−	2.82843i	0.167836	−	0.167836i
$285$		0			0
$286$	8.00000	−	12.0000i	0.473050	−	0.709575i
$287$	−2.82843			−0.166957
$288$	6.46447	+	13.5355i	0.380922	+	0.797589i
$289$	17.0000			1.00000
$290$		0			0
$291$	−16.8995	−	2.89949i	−0.990666	−	0.169971i
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	0.934444	−	0.356110i	$-0.115897\pi$
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	−0.356110	+	0.934444i	$0.615897\pi$
$294$	−8.53553	−	1.46447i	−0.497802	−	0.0854094i
$295$		0			0
$296$	−4.24264			−0.246598
$297$	18.1421	+	10.1421i	1.05271	+	0.588506i
$298$	−2.00000			−0.115857
$299$	−16.9706	+	25.4558i	−0.981433	+	1.47215i
$300$		0			0
$301$	6.00000	−	6.00000i	0.345834	−	0.345834i
$302$	1.41421			0.0813788
$303$	−12.0000	+	8.48528i	−0.689382	+	0.487467i
$304$	−1.00000	+	1.00000i	−0.0573539	+	0.0573539i
$305$		0			0
$306$		0			0
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	−0.0293286	−	0.999570i	$-0.509337\pi$
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	0.999570	+	0.0293286i	$0.00933691\pi$
$308$	−5.65685			−0.322329
$309$	−8.48528	+	6.00000i	−0.482711	+	0.341328i
$310$		0			0
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$	−13.6066	−	12.8787i	−0.770322	−	0.729112i
$313$		−	8.00000i		−	0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$		−	8.00000i		−	0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$	9.89949	+	9.89949i	0.558661	+	0.558661i
$315$		0			0
$316$			10.0000i			0.562544i
$317$	7.07107	−	7.07107i	0.397151	−	0.397151i	−0.480076	−	0.877227i	$-0.659391\pi$
$317$	7.07107	−	7.07107i	0.397151	−	0.397151i	0.877227	+	0.480076i	$0.159391\pi$
$318$	1.65685	−	9.65685i	0.0929118	−	0.541529i
$319$	−8.00000	−	8.00000i	−0.447914	−	0.447914i
$320$		0			0
$321$	−8.00000	+	5.65685i	−0.446516	+	0.315735i
$322$	−12.0000			−0.668734
$323$		0			0
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$		0			0
$326$		−	1.41421i		−	0.0783260i
$327$	0.414214	−	2.41421i	0.0229061	−	0.133506i
$328$			6.00000i			0.331295i
$329$	−5.65685			−0.311872
$330$		0			0
$331$	7.00000	−	7.00000i	0.384755	−	0.384755i	−0.488057	−	0.872812i	$-0.662294\pi$
$331$	7.00000	−	7.00000i	0.384755	−	0.384755i	0.872812	+	0.488057i	$0.162294\pi$
$332$	5.65685	+	5.65685i	0.310460	+	0.310460i
$333$	1.82843	+	3.82843i	0.100197	+	0.209797i
$334$	4.00000			0.218870
$335$		0			0
$336$	0.414214	−	2.41421i	0.0225972	−	0.131706i
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	12.0208	+	4.94975i	0.653846	+	0.269231i
$339$	20.0000	−	14.1421i	1.08625	−	0.768095i
$340$		0			0
$341$			28.2843i			1.53168i
$342$	4.00000	+	1.41421i	0.216295	+	0.0764719i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−12.7279	−	12.7279i	−0.686244	−	0.686244i
$345$		0			0
$346$	−6.00000	−	6.00000i	−0.322562	−	0.322562i
$347$	14.1421			0.759190			0.379595	−	0.925153i	$-0.376063\pi$
$347$	14.1421			0.759190			0.379595	+	0.925153i	$0.376063\pi$
$348$	−4.00000	+	2.82843i	−0.214423	+	0.151620i
$349$	17.0000	+	17.0000i	0.909989	+	0.909989i	0.996271	−	0.0862816i	$-0.0274985\pi$
$349$	17.0000	+	17.0000i	0.909989	+	0.909989i	−0.0862816	+	0.996271i	$0.527498\pi$
$350$		0			0
$351$	−5.75736	+	17.8284i	−0.307305	+	0.951611i
$352$			20.0000i			1.06600i
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	−0.0212513	−	0.999774i	$-0.506765\pi$
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	0.999774	+	0.0212513i	$0.00676499\pi$
$354$	−4.00000	−	5.65685i	−0.212598	−	0.300658i
$355$		0			0
$356$	9.89949	+	9.89949i	0.524672	+	0.524672i
$357$		0			0
$358$		0			0
$359$	−2.82843	+	2.82843i	−0.149279	+	0.149279i	−0.777796	−	0.628517i	$-0.783662\pi$
$359$	−2.82843	+	2.82843i	−0.149279	+	0.149279i	0.628517	+	0.777796i	$0.283662\pi$
$360$		0			0
$361$			17.0000i			0.894737i
$362$		0			0
$363$	5.00000	+	7.07107i	0.262432	+	0.371135i
$364$	−1.00000	−	5.00000i	−0.0524142	−	0.262071i
$365$		0			0
$366$	−2.34315	+	13.6569i	−0.122478	+	0.713855i
$367$			8.00000i			0.417597i	0.977959	+	0.208798i	$0.0669552\pi$
$367$			8.00000i			0.417597i	−0.977959	+	0.208798i	$0.933045\pi$
$368$			8.48528i			0.442326i
$369$	5.41421	−	2.58579i	0.281853	−	0.134611i
$370$		0			0
$371$	5.65685	−	5.65685i	0.293689	−	0.293689i
$372$	12.0711	+	2.07107i	0.625856	+	0.107380i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$			12.0000i			0.618853i
$377$	5.65685	−	8.48528i	0.291343	−	0.437014i
$378$	−7.07107	+	2.00000i	−0.363696	+	0.102869i
$379$	−19.0000	+	19.0000i	−0.975964	+	0.975964i	−0.999718	−	0.0237534i	$-0.992438\pi$
$379$	−19.0000	+	19.0000i	−0.975964	+	0.975964i	0.0237534	+	0.999718i	$0.492438\pi$
$380$		0			0
$381$		0			0
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	−11.3137	+	11.3137i	−0.578103	+	0.578103i	−0.934380	−	0.356277i	$-0.884046\pi$
$383$	−11.3137	+	11.3137i	−0.578103	+	0.578103i	0.356277	+	0.934380i	$0.384046\pi$
$384$	5.12132	+	0.878680i	0.261346	+	0.0448399i
$385$		0			0
$386$		−	26.8701i		−	1.36765i
$387$	−6.00000	+	16.9706i	−0.304997	+	0.862662i
$388$	−7.00000	+	7.00000i	−0.355371	+	0.355371i
$389$	16.9706			0.860442			0.430221	−	0.902724i	$-0.358436\pi$
$389$	16.9706			0.860442			0.430221	+	0.902724i	$0.358436\pi$
$390$		0			0
$391$		0			0
$392$	−10.6066	+	10.6066i	−0.535714	+	0.535714i
$393$	−11.3137	−	16.0000i	−0.570701	−	0.807093i
$394$		−	22.0000i		−	1.10834i
$395$		0			0
$396$	10.8284	−	5.17157i	0.544149	−	0.259881i
$397$	17.0000	−	17.0000i	0.853206	−	0.853206i	−0.137321	−	0.990527i	$-0.543849\pi$
$397$	17.0000	−	17.0000i	0.853206	−	0.853206i	0.990527	+	0.137321i	$0.0438492\pi$
$398$		0			0
$399$	2.00000	+	2.82843i	0.100125	+	0.141598i
$400$		0			0
$401$	15.5563	−	15.5563i	0.776847	−	0.776847i	−0.202446	−	0.979293i	$-0.564889\pi$
$401$	15.5563	−	15.5563i	0.776847	−	0.776847i	0.979293	+	0.202446i	$0.0648892\pi$
$402$	10.0000	−	7.07107i	0.498755	−	0.352673i
$403$	−25.0000	+	5.00000i	−1.24534	+	0.249068i
$404$			8.48528i			0.422159i
$405$		0			0
$406$	4.00000			0.198517
$407$			5.65685i			0.280400i
$408$		0			0
$409$	23.0000	−	23.0000i	1.13728	−	1.13728i	0.148340	−	0.988936i	$-0.452607\pi$
$409$	23.0000	−	23.0000i	1.13728	−	1.13728i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$		0			0
$411$	23.8995	+	4.10051i	1.17888	+	0.202263i
$412$			6.00000i			0.295599i
$413$		−	5.65685i		−	0.278356i
$414$	22.9706	−	10.9706i	1.12894	−	0.539174i
$415$		0			0
$416$	−17.6777	+	3.53553i	−0.866719	+	0.173344i
$417$	−5.65685	+	4.00000i	−0.277017	+	0.195881i
$418$	4.00000	+	4.00000i	0.195646	+	0.195646i
$419$		−	11.3137i		−	0.552711i	−0.961056	−	0.276355i	$-0.910873\pi$
$419$		−	11.3137i		−	0.552711i	0.961056	−	0.276355i	$-0.0891267\pi$
$420$		0			0
$421$	25.0000	−	25.0000i	1.21843	−	1.21843i	0.250242	−	0.968183i	$-0.419490\pi$
$421$	25.0000	−	25.0000i	1.21843	−	1.21843i	0.968183	−	0.250242i	$-0.0805102\pi$
$422$	9.89949	−	9.89949i	0.481900	−	0.481900i
$423$	10.8284	−	5.17157i	0.526496	−	0.251450i
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$		0			0
$426$	5.65685	−	4.00000i	0.274075	−	0.193801i
$427$	−8.00000	+	8.00000i	−0.387147	+	0.387147i
$428$			5.65685i			0.273434i
$429$	−17.1716	+	18.1421i	−0.829051	+	0.875911i
$430$		0			0
$431$	22.6274	+	22.6274i	1.08992	+	1.08992i	0.995535	+	0.0943889i	$0.0300897\pi$
$431$	22.6274	+	22.6274i	1.08992	+	1.08992i	0.0943889	+	0.995535i	$0.469910\pi$
$432$	1.41421	+	5.00000i	0.0680414	+	0.240563i
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$	−7.07107	−	7.07107i	−0.339422	−	0.339422i
$435$		0			0
$436$	−1.00000	−	1.00000i	−0.0478913	−	0.0478913i
$437$	−8.48528	−	8.48528i	−0.405906	−	0.405906i
$438$	1.41421	+	2.00000i	0.0675737	+	0.0955637i
$439$		−	30.0000i		−	1.43182i	−0.698192	−	0.715911i	$-0.746012\pi$
$439$		−	30.0000i		−	1.43182i	0.698192	−	0.715911i	$-0.253988\pi$
$440$		0			0
$441$	14.1421	+	5.00000i	0.673435	+	0.238095i
$442$		0			0
$443$	28.2843			1.34383			0.671913	−	0.740630i	$-0.265473\pi$
$443$	28.2843			1.34383			0.671913	+	0.740630i	$0.265473\pi$
$444$	2.41421	+	0.414214i	0.114574	+	0.0196577i
$445$		0			0
$446$	15.5563			0.736614
$447$	3.41421	+	0.585786i	0.161487	+	0.0277067i
$448$	−7.00000	−	7.00000i	−0.330719	−	0.330719i
$449$	−15.5563	+	15.5563i	−0.734150	+	0.734150i	−0.971439	−	0.237289i	$-0.923741\pi$
$449$	−15.5563	+	15.5563i	−0.734150	+	0.734150i	0.237289	+	0.971439i	$0.423741\pi$
$450$		0			0
$451$	8.00000			0.376705
$452$		−	14.1421i		−	0.665190i
$453$	−2.41421	−	0.414214i	−0.113430	−	0.0194615i
$454$			8.00000i			0.375459i
$455$		0			0
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$	−29.0000	−	29.0000i	−1.35656	−	1.35656i	−0.878117	−	0.478446i	$-0.841200\pi$
$457$	−29.0000	−	29.0000i	−1.35656	−	1.35656i	−0.478446	−	0.878117i	$-0.658800\pi$
$458$	−1.41421			−0.0660819
$459$		0			0
$460$		0			0
$461$	−7.07107	−	7.07107i	−0.329332	−	0.329332i	0.523000	−	0.852333i	$-0.324813\pi$
$461$	−7.07107	−	7.07107i	−0.329332	−	0.329332i	−0.852333	+	0.523000i	$0.824813\pi$
$462$	−9.65685	−	1.65685i	−0.449278	−	0.0770838i
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	−0.981503	−	0.191446i	$-0.938682\pi$
$463$	−17.0000	+	17.0000i	−0.790057	+	0.790057i	0.191446	+	0.981503i	$0.438682\pi$
$464$		−	2.82843i		−	0.131306i
$465$		0			0
$466$	−18.0000	−	18.0000i	−0.833834	−	0.833834i
$467$			25.4558i			1.17796i	0.808149	+	0.588978i	$0.200470\pi$
$467$			25.4558i			1.17796i	−0.808149	+	0.588978i	$0.799530\pi$
$468$	6.48528	+	8.65685i	0.299782	+	0.400163i
$469$	10.0000			0.461757
$470$		0			0
$471$	−14.0000	−	19.7990i	−0.645086	−	0.912289i
$472$	−12.0000			−0.552345
$473$	−16.9706	+	16.9706i	−0.780307	+	0.780307i
$474$	−2.92893	+	17.0711i	−0.134530	+	0.784100i
$475$		0			0
$476$		0			0
$477$	−5.65685	+	16.0000i	−0.259010	+	0.732590i
$478$	−20.0000			−0.914779
$479$	22.6274	−	22.6274i	1.03387	−	1.03387i	0.0344672	−	0.999406i	$-0.489027\pi$
$479$	22.6274	−	22.6274i	1.03387	−	1.03387i	0.999406	−	0.0344672i	$-0.0109734\pi$
$480$		0			0
$481$	−5.00000	+	1.00000i	−0.227980	+	0.0455961i
$482$	−24.0416			−1.09507
$483$	20.4853	+	3.51472i	0.932113	+	0.159925i
$484$	5.00000			0.227273
$485$		0			0
$486$	11.7071	−	10.2929i	0.531045	−	0.466895i
$487$	19.0000	+	19.0000i	0.860972	+	0.860972i	0.991451	−	0.130479i	$-0.0416515\pi$
$487$	19.0000	+	19.0000i	0.860972	+	0.860972i	−0.130479	+	0.991451i	$0.541651\pi$
$488$	16.9706	+	16.9706i	0.768221	+	0.768221i
$489$	−0.414214	+	2.41421i	−0.0187314	+	0.109175i
$490$		0			0
$491$	42.4264			1.91468			0.957338	−	0.288969i	$-0.0933124\pi$
$491$	42.4264			1.91468			0.957338	+	0.288969i	$0.0933124\pi$
$492$	0.585786	−	3.41421i	0.0264093	−	0.153925i
$493$		0			0
$494$	−2.82843	+	4.24264i	−0.127257	+	0.190885i
$495$		0			0
$496$	−5.00000	+	5.00000i	−0.224507	+	0.224507i
$497$	5.65685			0.253745
$498$	8.00000	+	11.3137i	0.358489	+	0.506979i
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	−6.82843	−	1.17157i	−0.305072	−	0.0523420i
$502$	−18.0000	+	18.0000i	−0.803379	+	0.803379i
$503$	−5.65685			−0.252227			−0.126113	−	0.992016i	$-0.540250\pi$
$503$	−5.65685			−0.252227			−0.126113	+	0.992016i	$0.540250\pi$
$504$	−4.24264	+	12.0000i	−0.188982	+	0.534522i
$505$		0			0
$506$	33.9411			1.50887
$507$	−19.0711	−	11.9706i	−0.846976	−	0.531631i
$508$		0			0
$509$	24.0416	+	24.0416i	1.06563	+	1.06563i	0.997690	+	0.0679369i	$0.0216417\pi$
$509$	24.0416	+	24.0416i	1.06563	+	1.06563i	0.0679369	+	0.997690i	$0.478358\pi$
$510$		0			0
$511$			2.00000i			0.0884748i
$512$	−7.77817	+	7.77817i	−0.343750	+	0.343750i
$513$	−6.41421	−	3.58579i	−0.283194	−	0.158316i
$514$	−6.00000	−	6.00000i	−0.264649	−	0.264649i
$515$		0			0
$516$	6.00000	+	8.48528i	0.264135	+	0.373544i
$517$	16.0000			0.703679
$518$	−1.41421	−	1.41421i	−0.0621370	−	0.0621370i
$519$	8.48528	+	12.0000i	0.372463	+	0.526742i
$520$		0			0
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$	−7.65685	+	3.65685i	−0.335131	+	0.160056i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−11.3137			−0.494242
$525$		0			0
$526$	−16.0000	+	16.0000i	−0.697633	+	0.697633i
$527$		0			0
$528$	−1.17157	+	6.82843i	−0.0509862	+	0.297169i
$529$	−49.0000			−2.13043
$530$		0			0
$531$	5.17157	+	10.8284i	0.224427	+	0.469914i
$532$	2.00000			0.0867110
$533$	1.41421	+	7.07107i	0.0612564	+	0.306282i
$534$	14.0000	+	19.7990i	0.605839	+	0.856786i
$535$		0			0
$536$		−	21.2132i		−	0.916271i
$537$		0			0
$538$	−14.0000	−	14.0000i	−0.603583	−	0.603583i
$539$	14.1421	+	14.1421i	0.609145	+	0.609145i
$540$		0			0
$541$	1.00000	+	1.00000i	0.0429934	+	0.0429934i	0.728277	−	0.685283i	$-0.240322\pi$
$541$	1.00000	+	1.00000i	0.0429934	+	0.0429934i	−0.685283	+	0.728277i	$0.740322\pi$
$542$	26.8701			1.15417
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.242641	−	8.82843i	−0.0103841	−	0.377822i
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	9.89949	−	9.89949i	0.422885	−	0.422885i
$549$	8.00000	−	22.6274i	0.341432	−	0.965715i
$550$		0			0
$551$	2.82843	+	2.82843i	0.120495	+	0.120495i
$552$	7.45584	−	43.4558i	0.317342	−	1.84960i
$553$	−10.0000	+	10.0000i	−0.425243	+	0.425243i
$554$	−8.48528	+	8.48528i	−0.360505	+	0.360505i
$555$		0			0
$556$			4.00000i			0.169638i
$557$	−9.89949	−	9.89949i	−0.419455	−	0.419455i	0.465561	−	0.885016i	$-0.345853\pi$
$557$	−9.89949	−	9.89949i	−0.419455	−	0.419455i	−0.885016	+	0.465561i	$0.845853\pi$
$558$	20.0000	+	7.07107i	0.846668	+	0.299342i
$559$	−18.0000	−	12.0000i	−0.761319	−	0.507546i
$560$		0			0
$561$		0			0
$562$			14.0000i			0.590554i
$563$			33.9411i			1.43045i	0.698895	+	0.715224i	$0.253675\pi$
$563$			33.9411i			1.43045i	−0.698895	+	0.715224i	$0.746325\pi$
$564$	1.17157	−	6.82843i	0.0493321	−	0.287529i
$565$		0			0
$566$	−8.48528	+	8.48528i	−0.356663	+	0.356663i
$567$	12.6569	−	1.34315i	0.531538	−	0.0564068i
$568$		−	12.0000i		−	0.503509i
$569$	−8.48528			−0.355722			−0.177861	−	0.984056i	$-0.556918\pi$
$569$	−8.48528			−0.355722			−0.177861	+	0.984056i	$0.556918\pi$
$570$		0			0
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$	2.82843	+	14.1421i	0.118262	+	0.591312i
$573$	−2.82843	−	4.00000i	−0.118159	−	0.167102i
$574$	−2.00000	+	2.00000i	−0.0834784	+	0.0834784i
$575$		0			0
$576$	19.7990	+	7.00000i	0.824958	+	0.291667i
$577$	1.00000	+	1.00000i	0.0416305	+	0.0416305i	0.727616	−	0.685985i	$-0.240628\pi$
$577$	1.00000	+	1.00000i	0.0416305	+	0.0416305i	−0.685985	+	0.727616i	$0.740628\pi$
$578$	12.0208	−	12.0208i	0.500000	−	0.500000i
$579$	−7.87006	+	45.8701i	−0.327068	+	1.90629i
$580$		0			0
$581$			11.3137i			0.469372i
$582$	−14.0000	+	9.89949i	−0.580319	+	0.410347i
$583$	−16.0000	+	16.0000i	−0.662652	+	0.662652i
$584$	4.24264			0.175562
$585$		0			0
$586$	14.0000			0.578335
$587$	−5.65685	+	5.65685i	−0.233483	+	0.233483i	−0.814145	−	0.580662i	$-0.802794\pi$
$587$	−5.65685	+	5.65685i	−0.233483	+	0.233483i	0.580662	+	0.814145i	$0.302794\pi$
$588$	7.07107	−	5.00000i	0.291606	−	0.206197i
$589$		−	10.0000i		−	0.412043i
$590$		0			0
$591$	−6.44365	+	37.5563i	−0.265056	+	1.54486i
$592$	−1.00000	+	1.00000i	−0.0410997	+	0.0410997i
$593$	9.89949	+	9.89949i	0.406524	+	0.406524i	0.880524	−	0.474001i	$-0.157191\pi$
$593$	9.89949	+	9.89949i	0.406524	+	0.406524i	−0.474001	+	0.880524i	$0.657191\pi$
$594$	20.0000	−	5.65685i	0.820610	−	0.232104i
$595$		0			0
$596$	1.41421	−	1.41421i	0.0579284	−	0.0579284i
$597$		0			0
$598$	6.00000	+	30.0000i	0.245358	+	1.22679i
$599$		−	11.3137i		−	0.462266i	−0.972922	−	0.231133i	$-0.925757\pi$
$599$		−	11.3137i		−	0.462266i	0.972922	−	0.231133i	$-0.0742432\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		−	8.48528i		−	0.345834i
$603$	−19.1421	+	9.14214i	−0.779528	+	0.372297i
$604$	−1.00000	+	1.00000i	−0.0406894	+	0.0406894i
$605$		0			0
$606$	−2.48528	+	14.4853i	−0.100958	+	0.588424i
$607$		−	40.0000i		−	1.62355i	−0.583970	−	0.811775i	$-0.698502\pi$
$607$		−	40.0000i		−	1.62355i	0.583970	−	0.811775i	$-0.301498\pi$
$608$		−	7.07107i		−	0.286770i
$609$	−6.82843	−	1.17157i	−0.276702	−	0.0474745i
$610$		0			0
$611$	2.82843	+	14.1421i	0.114426	+	0.572130i
$612$		0			0
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	0.686624	−	0.727013i	$-0.259092\pi$
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	−0.727013	+	0.686624i	$0.759092\pi$
$614$		−	24.0416i		−	0.970241i
$615$		0			0
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.0854011	+	0.996347i	$0.527217\pi$
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.996347	+	0.0854011i	$0.972783\pi$
$618$	−1.75736	+	10.2426i	−0.0706914	+	0.412019i
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	0.686724	−	0.726918i	$-0.259048\pi$
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	−0.726918	+	0.686724i	$0.759048\pi$
$620$		0			0
$621$	−42.4264	+	12.0000i	−1.70251	+	0.481543i
$622$	−6.00000	+	6.00000i	−0.240578	+	0.240578i
$623$			19.7990i			0.793230i
$624$	−6.24264	+	0.171573i	−0.249906	+	0.00686841i
$625$		0			0
$626$	−5.65685	−	5.65685i	−0.226093	−	0.226093i
$627$	−5.65685	−	8.00000i	−0.225913	−	0.319489i
$628$	−14.0000			−0.558661
$629$		0			0
$630$		0			0
$631$	19.0000	+	19.0000i	0.756378	+	0.756378i	0.975661	−	0.219283i	$-0.0703719\pi$
$631$	19.0000	+	19.0000i	0.756378	+	0.756378i	−0.219283	+	0.975661i	$0.570372\pi$
$632$	21.2132	+	21.2132i	0.843816	+	0.843816i
$633$	−19.7990	+	14.0000i	−0.786939	+	0.556450i
$634$		−	10.0000i		−	0.397151i
$635$		0			0
$636$	5.65685	+	8.00000i	0.224309	+	0.317221i
$637$	−10.0000	+	15.0000i	−0.396214	+	0.594322i
$638$	−11.3137			−0.447914
$639$	−10.8284	+	5.17157i	−0.428366	+	0.204584i
$640$		0			0
$641$	−16.9706			−0.670297			−0.335148	−	0.942165i	$-0.608786\pi$
$641$	−16.9706			−0.670297			−0.335148	+	0.942165i	$0.608786\pi$
$642$	−1.65685	+	9.65685i	−0.0653908	+	0.381126i
$643$	5.00000	+	5.00000i	0.197181	+	0.197181i	0.798790	−	0.601610i	$-0.205474\pi$
$643$	5.00000	+	5.00000i	0.197181	+	0.197181i	−0.601610	+	0.798790i	$0.705474\pi$
$644$	8.48528	−	8.48528i	0.334367	−	0.334367i
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−2.84924	−	26.8492i	−0.111929	−	1.05474i
$649$			16.0000i			0.628055i
$650$		0			0
$651$	10.0000	+	14.1421i	0.391931	+	0.554274i
$652$	1.00000	+	1.00000i	0.0391630	+	0.0391630i
$653$	−14.1421			−0.553425			−0.276712	−	0.960953i	$-0.589245\pi$
$653$	−14.1421			−0.553425			−0.276712	+	0.960953i	$0.589245\pi$
$654$	−1.41421	−	2.00000i	−0.0553001	−	0.0782062i
$655$		0			0
$656$	1.41421	+	1.41421i	0.0552158	+	0.0552158i
$657$	−1.82843	−	3.82843i	−0.0713337	−	0.149361i
$658$	−4.00000	+	4.00000i	−0.155936	+	0.155936i
$659$		−	2.82843i		−	0.110180i	−0.998481	−	0.0550899i	$-0.982455\pi$
$659$		−	2.82843i		−	0.110180i	0.998481	−	0.0550899i	$-0.0175446\pi$
$660$		0			0
$661$	1.00000	+	1.00000i	0.0388955	+	0.0388955i	0.726287	−	0.687392i	$-0.241244\pi$
$661$	1.00000	+	1.00000i	0.0388955	+	0.0388955i	−0.687392	+	0.726287i	$0.741244\pi$
$662$		−	9.89949i		−	0.384755i
$663$		0			0
$664$	24.0000			0.931381
$665$		0			0
$666$	4.00000	+	1.41421i	0.154997	+	0.0547997i
$667$	24.0000			0.929284
$668$	−2.82843	+	2.82843i	−0.109435	+	0.109435i
$669$	−26.5563	−	4.55635i	−1.02673	−	0.176159i
$670$		0			0
$671$	22.6274	−	22.6274i	0.873522	−	0.873522i
$672$	7.07107	+	10.0000i	0.272772	+	0.385758i
$673$	12.0000			0.462566			0.231283	−	0.972887i	$-0.425708\pi$
$673$	12.0000			0.462566			0.231283	+	0.972887i	$0.425708\pi$
$674$	−4.24264	+	4.24264i	−0.163420	+	0.163420i
$675$		0			0
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$	22.6274			0.869642			0.434821	−	0.900517i	$-0.356812\pi$
$677$	22.6274			0.869642			0.434821	+	0.900517i	$0.356812\pi$
$678$	4.14214	−	24.1421i	0.159078	−	0.927173i
$679$	−14.0000			−0.537271
$680$		0			0
$681$	2.34315	−	13.6569i	0.0897895	−	0.523332i
$682$	20.0000	+	20.0000i	0.765840	+	0.765840i
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	0.650920	−	0.759147i	$-0.274383\pi$
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	−0.759147	+	0.650920i	$0.774383\pi$
$684$	−3.82843	+	1.82843i	−0.146384	+	0.0699117i
$685$		0			0
$686$	−16.9706			−0.647939
$687$	2.41421	+	0.414214i	0.0921080	+	0.0158032i
$688$	−6.00000			−0.228748
$689$	−16.9706	−	11.3137i	−0.646527	−	0.431018i
$690$		0			0
$691$	−11.0000	+	11.0000i	−0.418460	+	0.418460i	−0.884673	−	0.466213i	$-0.845618\pi$
$691$	−11.0000	+	11.0000i	−0.418460	+	0.418460i	0.466213	+	0.884673i	$0.345618\pi$
$692$	8.48528			0.322562
$693$	16.0000	+	5.65685i	0.607790	+	0.214886i
$694$	10.0000	−	10.0000i	0.379595	−	0.379595i
$695$		0			0
$696$	−2.48528	+	14.4853i	−0.0942043	+	0.549063i
$697$		0			0
$698$	24.0416			0.909989
$699$	25.4558	+	36.0000i	0.962828	+	1.36165i
$700$		0			0
$701$	−50.9117			−1.92291			−0.961454	−	0.274966i	$-0.911333\pi$
$701$	−50.9117			−1.92291			−0.961454	+	0.274966i	$0.911333\pi$
$702$	8.53553	+	16.6777i	0.322153	+	0.629458i
$703$		−	2.00000i		−	0.0754314i
$704$	19.7990	+	19.7990i	0.746203	+	0.746203i
$705$		0			0
$706$		−	26.0000i		−	0.978523i
$707$	−8.48528	+	8.48528i	−0.319122	+	0.319122i
$708$	6.82843	+	1.17157i	0.256628	+	0.0440304i
$709$	−19.0000	−	19.0000i	−0.713560	−	0.713560i	0.253718	−	0.967278i	$-0.418346\pi$
$709$	−19.0000	−	19.0000i	−0.713560	−	0.713560i	−0.967278	+	0.253718i	$0.918346\pi$
$710$		0			0
$711$	10.0000	−	28.2843i	0.375029	−	1.06074i
$712$	42.0000			1.57402
$713$	−42.4264	−	42.4264i	−1.58888	−	1.58888i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	34.1421	+	5.85786i	1.27506	+	0.218766i
$718$			4.00000i			0.149279i
$719$	−25.4558			−0.949343			−0.474671	−	0.880163i	$-0.657433\pi$
$719$	−25.4558			−0.949343			−0.474671	+	0.880163i	$0.657433\pi$
$720$		0			0
$721$	−6.00000	+	6.00000i	−0.223452	+	0.223452i
$722$	12.0208	+	12.0208i	0.447368	+	0.447368i
$723$	41.0416	+	7.04163i	1.52635	+	0.261881i
$724$		0			0
$725$		0			0
$726$	8.53553	+	1.46447i	0.316783	+	0.0543514i
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$	−12.7279	−	8.48528i	−0.471728	−	0.314485i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		0			0
$731$		0			0
$732$	−8.00000	−	11.3137i	−0.295689	−	0.418167i
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	0.793391	−	0.608712i	$-0.208314\pi$
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	−0.608712	+	0.793391i	$0.708314\pi$
$734$	5.65685	+	5.65685i	0.208798	+	0.208798i
$735$		0			0
$736$	−30.0000	−	30.0000i	−1.10581	−	1.10581i
$737$	−28.2843			−1.04186
$738$	2.00000	−	5.65685i	0.0736210	−	0.208232i
$739$	−1.00000	−	1.00000i	−0.0367856	−	0.0367856i	0.688475	−	0.725260i	$-0.258281\pi$
$739$	−1.00000	−	1.00000i	−0.0367856	−	0.0367856i	−0.725260	+	0.688475i	$0.758281\pi$
$740$		0			0
$741$	6.07107	−	6.41421i	0.223026	−	0.235632i
$742$		−	8.00000i		−	0.293689i
$743$	−11.3137	+	11.3137i	−0.415060	+	0.415060i	−0.883497	−	0.468437i	$-0.844817\pi$
$743$	−11.3137	+	11.3137i	−0.415060	+	0.415060i	0.468437	+	0.883497i	$0.344817\pi$
$744$	30.0000	−	21.2132i	1.09985	−	0.777714i
$745$		0			0
$746$	2.82843	+	2.82843i	0.103556	+	0.103556i
$747$	−10.3431	−	21.6569i	−0.378436	−	0.792383i
$748$		0			0
$749$	−5.65685	+	5.65685i	−0.206697	+	0.206697i
$750$		0			0
$751$		−	30.0000i		−	1.09472i	−0.836899	−	0.547358i	$-0.815634\pi$
$751$		−	30.0000i		−	1.09472i	0.836899	−	0.547358i	$-0.184366\pi$
$752$	2.82843	+	2.82843i	0.103142	+	0.103142i
$753$	36.0000	−	25.4558i	1.31191	−	0.927663i
$754$	−2.00000	−	10.0000i	−0.0728357	−	0.364179i
$755$		0			0
$756$	3.58579	−	6.41421i	0.130414	−	0.233283i
$757$		−	16.0000i		−	0.581530i	−0.956795	−	0.290765i	$-0.906090\pi$
$757$		−	16.0000i		−	0.581530i	0.956795	−	0.290765i	$-0.0939098\pi$
$758$			26.8701i			0.975964i
$759$	−57.9411	−	9.94113i	−2.10313	−	0.360840i
$760$		0			0
$761$	−35.3553	+	35.3553i	−1.28163	+	1.28163i	−0.341890	+	0.939740i	$0.611067\pi$
$761$	−35.3553	+	35.3553i	−1.28163	+	1.28163i	−0.939740	+	0.341890i	$0.888933\pi$
$762$		0			0
$763$		−	2.00000i		−	0.0724049i
$764$	−2.82843			−0.102329
$765$		0			0
$766$			16.0000i			0.578103i
$767$	−14.1421	+	2.82843i	−0.510643	+	0.102129i
$768$	24.0416	−	17.0000i	0.867528	−	0.613435i
$769$	−13.0000	+	13.0000i	−0.468792	+	0.468792i	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−13.0000	+	13.0000i	−0.468792	+	0.468792i	0.432731	+	0.901523i	$0.357550\pi$
$770$		0			0
$771$	8.48528	+	12.0000i	0.305590	+	0.432169i
$772$	19.0000	+	19.0000i	0.683825	+	0.683825i
$773$	9.89949	−	9.89949i	0.356060	−	0.356060i	−0.506298	−	0.862358i	$-0.668987\pi$
$773$	9.89949	−	9.89949i	0.356060	−	0.356060i	0.862358	+	0.506298i	$0.168987\pi$
$774$	7.75736	+	16.2426i	0.278833	+	0.583830i
$775$		0			0
$776$			29.6985i			1.06611i
$777$	2.00000	+	2.82843i	0.0717496	+	0.101469i
$778$	12.0000	−	12.0000i	0.430221	−	0.430221i
$779$	−2.82843			−0.101339
$780$		0			0
$781$	−16.0000			−0.572525
$782$		0			0
$783$	14.1421	−	4.00000i	0.505399	−	0.142948i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	−19.3137	−	3.31371i	−0.688897	−	0.118196i
$787$	−19.0000	+	19.0000i	−0.677277	+	0.677277i	−0.959383	−	0.282106i	$-0.908967\pi$
$787$	−19.0000	+	19.0000i	−0.677277	+	0.677277i	0.282106	+	0.959383i	$0.408967\pi$
$788$	15.5563	+	15.5563i	0.554172	+	0.554172i
$789$	32.0000	−	22.6274i	1.13923	−	0.805557i
$790$		0			0
$791$	14.1421	−	14.1421i	0.502836	−	0.502836i
$792$	12.0000	−	33.9411i	0.426401	−	1.20605i
$793$	24.0000	+	16.0000i	0.852265	+	0.568177i
$794$		−	24.0416i		−	0.853206i
$795$		0			0
$796$		0			0
$797$			16.9706i			0.601128i	0.953762	+	0.300564i	$0.0971749\pi$
$797$			16.9706i			0.601128i	−0.953762	+	0.300564i	$0.902825\pi$
$798$	3.41421	+	0.585786i	0.120862	+	0.0207366i
$799$		0			0
$800$		0			0
$801$	−18.1005	−	37.8995i	−0.639550	−	1.33911i
$802$		−	22.0000i		−	0.776847i
$803$		−	5.65685i		−	0.199626i
$804$	−2.07107	+	12.0711i	−0.0730409	+	0.425714i
$805$		0			0
$806$	−14.1421	+	21.2132i	−0.498135	+	0.747203i
$807$	19.7990	+	28.0000i	0.696957	+	0.985647i
$808$	18.0000	+	18.0000i	0.633238	+	0.633238i
$809$			31.1127i			1.09386i	0.837177	+	0.546932i	$0.184204\pi$
$809$			31.1127i			1.09386i	−0.837177	+	0.546932i	$0.815796\pi$
$810$		0			0
$811$	1.00000	−	1.00000i	0.0351147	−	0.0351147i	−0.689331	−	0.724446i	$-0.742096\pi$
$811$	1.00000	−	1.00000i	0.0351147	−	0.0351147i	0.724446	+	0.689331i	$0.242096\pi$
$812$	−2.82843	+	2.82843i	−0.0992583	+	0.0992583i
$813$	−45.8701	−	7.87006i	−1.60873	−	0.276015i
$814$	4.00000	+	4.00000i	0.140200	+	0.140200i
$815$		0			0
$816$		0			0
$817$	6.00000	−	6.00000i	0.209913	−	0.209913i
$818$		−	32.5269i		−	1.13728i
$819$	−2.17157	+	15.1421i	−0.0758809	+	0.529109i
$820$		0			0
$821$	−7.07107	−	7.07107i	−0.246782	−	0.246782i	0.572867	−	0.819649i	$-0.305831\pi$
$821$	−7.07107	−	7.07107i	−0.246782	−	0.246782i	−0.819649	+	0.572867i	$0.805831\pi$
$822$	19.7990	−	14.0000i	0.690569	−	0.488306i
$823$	−30.0000			−1.04573			−0.522867	−	0.852414i	$-0.675138\pi$
$823$	−30.0000			−1.04573			−0.522867	+	0.852414i	$0.675138\pi$
$824$	12.7279	+	12.7279i	0.443398	+	0.443398i
$825$		0			0
$826$	−4.00000	−	4.00000i	−0.139178	−	0.139178i
$827$	−22.6274	−	22.6274i	−0.786832	−	0.786832i	0.194141	−	0.980974i	$-0.437808\pi$
$827$	−22.6274	−	22.6274i	−0.786832	−	0.786832i	−0.980974	+	0.194141i	$0.937808\pi$
$828$	−8.48528	+	24.0000i	−0.294884	+	0.834058i
$829$			18.0000i			0.625166i	0.949890	+	0.312583i	$0.101194\pi$
$829$			18.0000i			0.625166i	−0.949890	+	0.312583i	$0.898806\pi$
$830$		0			0
$831$	16.9706	−	12.0000i	0.588702	−	0.416275i
$832$	−14.0000	+	21.0000i	−0.485363	+	0.728044i
$833$		0			0
$834$	−1.17157	+	6.82843i	−0.0405683	+	0.236449i
$835$		0			0
$836$	−5.65685			−0.195646
$837$	−32.0711	−	17.9289i	−1.10854	−	0.619715i
$838$	−8.00000	−	8.00000i	−0.276355	−	0.276355i
$839$	−2.82843	+	2.82843i	−0.0976481	+	0.0976481i	−0.754243	−	0.656595i	$-0.771996\pi$
$839$	−2.82843	+	2.82843i	−0.0976481	+	0.0976481i	0.656595	+	0.754243i	$0.271996\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$		−	35.3553i		−	1.21843i
$843$	4.10051	−	23.8995i	0.141229	−	0.823142i
$844$			14.0000i			0.481900i
$845$		0			0
$846$	4.00000	−	11.3137i	0.137523	−	0.388973i
$847$	5.00000	+	5.00000i	0.171802	+	0.171802i
$848$	−5.65685			−0.194257
$849$	16.9706	−	12.0000i	0.582428	−	0.411839i
$850$		0			0
$851$	−8.48528	−	8.48528i	−0.290872	−	0.290872i
$852$	−1.17157	+	6.82843i	−0.0401374	+	0.233938i
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.319152	−	0.947703i	$-0.396602\pi$
$853$	37.0000	−	37.0000i	1.26686	−	1.26686i	0.947703	−	0.319152i	$-0.103398\pi$
$854$			11.3137i			0.387147i
$855$		0			0
$856$	12.0000	+	12.0000i	0.410152	+	0.410152i
$857$			8.48528i			0.289852i	0.989443	+	0.144926i	$0.0462944\pi$
$857$			8.48528i			0.289852i	−0.989443	+	0.144926i	$0.953706\pi$
$858$	0.686292	+	24.9706i	0.0234296	+	0.852481i
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$		0			0
$861$	4.00000	−	2.82843i	0.136320	−	0.0963925i
$862$	32.0000			1.08992
$863$	−2.82843	+	2.82843i	−0.0962808	+	0.0962808i	−0.753607	−	0.657326i	$-0.771688\pi$
$863$	−2.82843	+	2.82843i	−0.0962808	+	0.0962808i	0.657326	+	0.753607i	$0.271688\pi$
$864$	−22.6777	−	12.6777i	−0.771510	−	0.431303i
$865$		0			0
$866$	−12.7279	+	12.7279i	−0.432512	+	0.432512i
$867$	−24.0416	+	17.0000i	−0.816497	+	0.577350i
$868$	10.0000			0.339422
$869$	28.2843	−	28.2843i	0.959478	−	0.959478i
$870$		0			0
$871$	−5.00000	−	25.0000i	−0.169419	−	0.847093i
$872$	−4.24264			−0.143674
$873$	26.7990	−	12.7990i	0.907008	−	0.433180i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	−2.41421	−	0.414214i	−0.0815687	−	0.0139950i
$877$	13.0000	+	13.0000i	0.438979	+	0.438979i	0.891668	−	0.452689i	$-0.149535\pi$
$877$	13.0000	+	13.0000i	0.438979	+	0.438979i	−0.452689	+	0.891668i	$0.649535\pi$
$878$	−21.2132	−	21.2132i	−0.715911	−	0.715911i
$879$	−23.8995	−	4.10051i	−0.806110	−	0.138307i
$880$		0			0
$881$	−25.4558			−0.857629			−0.428815	−	0.903393i	$-0.641069\pi$
$881$	−25.4558			−0.857629			−0.428815	+	0.903393i	$0.641069\pi$
$882$	13.5355	−	6.46447i	0.455765	−	0.217670i
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$		0			0
$886$	20.0000	−	20.0000i	0.671913	−	0.671913i
$887$	14.1421			0.474846			0.237423	−	0.971406i	$-0.423697\pi$
$887$	14.1421			0.474846			0.237423	+	0.971406i	$0.423697\pi$
$888$	6.00000	−	4.24264i	0.201347	−	0.142374i
$889$		0			0
$890$		0			0
$891$	−35.7990	+	3.79899i	−1.19931	+	0.127271i
$892$	−11.0000	+	11.0000i	−0.368307	+	0.368307i
$893$	−5.65685			−0.189299
$894$	2.82843	−	2.00000i	0.0945968	−	0.0668900i
$895$		0			0
$896$	4.24264			0.141737
$897$	−1.45584	−	52.9706i	−0.0486092	−	1.76864i
$898$			22.0000i			0.734150i
$899$	14.1421	+	14.1421i	0.471667	+	0.471667i
$900$		0			0
$901$		0			0
$902$	5.65685	−	5.65685i	0.188353	−	0.188353i
$903$	−2.48528	+	14.4853i	−0.0827050	+	0.482040i
$904$	−30.0000	−	30.0000i	−0.997785	−	0.997785i
$905$		0			0
$906$	−2.00000	+	1.41421i	−0.0664455	+	0.0469841i
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$	−5.65685	−	5.65685i	−0.187729	−	0.187729i
$909$	8.48528	−	24.0000i	0.281439	−	0.796030i
$910$		0			0
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$	0.414214	−	2.41421i	0.0137160	−	0.0799426i
$913$		−	32.0000i		−	1.05905i
$914$	−41.0122			−1.35656
$915$		0			0
$916$	1.00000	−	1.00000i	0.0330409	−	0.0330409i
$917$	−11.3137	−	11.3137i	−0.373612	−	0.373612i
$918$		0			0
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$		0			0
$921$	−7.04163	+	41.0416i	−0.232030	+	1.35237i
$922$	−10.0000			−0.329332
$923$	−2.82843	−	14.1421i	−0.0930988	−	0.465494i
$924$	8.00000	−	5.65685i	0.263181	−	0.186097i
$925$		0			0
$926$			24.0416i			0.790057i
$927$	6.00000	−	16.9706i	0.197066	−	0.557386i
$928$	10.0000	+	10.0000i	0.328266	+	0.328266i
$929$	32.5269	+	32.5269i	1.06717	+	1.06717i	0.997575	+	0.0695983i	$0.0221717\pi$
$929$	32.5269	+	32.5269i	1.06717	+	1.06717i	0.0695983	+	0.997575i	$0.477828\pi$
$930$		0			0
$931$	−5.00000	−	5.00000i	−0.163868	−	0.163868i
$932$	25.4558			0.833834
$933$	12.0000	−	8.48528i	0.392862	−	0.277796i
$934$	18.0000	+	18.0000i	0.588978	+	0.588978i
$935$		0			0
$936$	32.1213	+	4.60660i	1.04992	+	0.150571i
$937$		−	52.0000i		−	1.69877i	−0.527777	−	0.849383i	$-0.676974\pi$
$937$		−	52.0000i		−	1.69877i	0.527777	−	0.849383i	$-0.323026\pi$
$938$	7.07107	−	7.07107i	0.230879	−	0.230879i
$939$	8.00000	+	11.3137i	0.261070	+	0.369209i
$940$		0			0
$941$	26.8701	+	26.8701i	0.875939	+	0.875939i	0.993112	−	0.117173i	$-0.0373831\pi$
$941$	26.8701	+	26.8701i	0.875939	+	0.875939i	−0.117173	+	0.993112i	$0.537383\pi$
$942$	−23.8995	−	4.10051i	−0.778688	−	0.133602i
$943$	−12.0000	+	12.0000i	−0.390774	+	0.390774i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$		0			0
$946$			24.0000i			0.780307i
$947$	−22.6274	−	22.6274i	−0.735292	−	0.735292i	0.236371	−	0.971663i	$-0.424042\pi$
$947$	−22.6274	−	22.6274i	−0.735292	−	0.735292i	−0.971663	+	0.236371i	$0.924042\pi$
$948$	−10.0000	−	14.1421i	−0.324785	−	0.459315i
$949$	5.00000	−	1.00000i	0.162307	−	0.0324614i
$950$		0			0
$951$	−2.92893	+	17.0711i	−0.0949771	+	0.553567i
$952$		0			0
$953$			25.4558i			0.824596i	0.911049	+	0.412298i	$0.135274\pi$
$953$			25.4558i			0.824596i	−0.911049	+	0.412298i	$0.864726\pi$
$954$	7.31371	+	15.3137i	0.236790	+	0.495800i
$955$		0			0
$956$	14.1421	−	14.1421i	0.457389	−	0.457389i
$957$	19.3137	+	3.31371i	0.624324	+	0.107117i
$958$		−	32.0000i		−	1.03387i
$959$	19.7990			0.639343
$960$		0			0
$961$		−	19.0000i		−	0.612903i
$962$	−2.82843	+	4.24264i	−0.0911922	+	0.136788i
$963$	5.65685	−	16.0000i	0.182290	−	0.515593i
$964$	17.0000	−	17.0000i	0.547533	−	0.547533i
$965$		0			0
$966$	16.9706	−	12.0000i	0.546019	−	0.386094i
$967$	−23.0000	−	23.0000i	−0.739630	−	0.739630i	0.232876	−	0.972506i	$-0.425186\pi$
$967$	−23.0000	−	23.0000i	−0.739630	−	0.739630i	−0.972506	+	0.232876i	$0.925186\pi$
$968$	10.6066	−	10.6066i	0.340909	−	0.340909i
$969$		0			0
$970$		0			0
$971$		−	31.1127i		−	0.998454i	−0.866471	−	0.499227i	$-0.833617\pi$
$971$		−	31.1127i		−	0.998454i	0.866471	−	0.499227i	$-0.166383\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	−4.00000	+	4.00000i	−0.128234	+	0.128234i
$974$	26.8701			0.860972
$975$		0			0
$976$	8.00000			0.256074
$977$	−26.8701	+	26.8701i	−0.859649	+	0.859649i	−0.991297	−	0.131647i	$-0.957973\pi$
$977$	−26.8701	+	26.8701i	−0.859649	+	0.859649i	0.131647	+	0.991297i	$0.457973\pi$
$978$	1.41421	+	2.00000i	0.0452216	+	0.0639529i
$979$		−	56.0000i		−	1.78977i
$980$		0			0
$981$	1.82843	+	3.82843i	0.0583772	+	0.122232i
$982$	30.0000	−	30.0000i	0.957338	−	0.957338i
$983$	−2.82843	−	2.82843i	−0.0902128	−	0.0902128i	0.660560	−	0.750773i	$-0.270319\pi$
$983$	−2.82843	−	2.82843i	−0.0902128	−	0.0902128i	−0.750773	+	0.660560i	$0.770319\pi$
$984$	−6.00000	−	8.48528i	−0.191273	−	0.270501i
$985$		0			0
$986$		0			0
$987$	8.00000	−	5.65685i	0.254643	−	0.180060i
$988$	−1.00000	−	5.00000i	−0.0318142	−	0.159071i
$989$		−	50.9117i		−	1.61890i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		−	35.3553i		−	1.12253i
$993$	−2.89949	+	16.8995i	−0.0920127	+	0.536289i
$994$	4.00000	−	4.00000i	0.126872	−	0.126872i
$995$		0			0
$996$	−13.6569	−	2.34315i	−0.432734	−	0.0742454i
$997$			26.0000i			0.823428i	0.911313	+	0.411714i	$0.135070\pi$
$997$			26.0000i			0.823428i	−0.911313	+	0.411714i	$0.864930\pi$
$998$		−	32.5269i		−	1.02962i
$999$	−6.41421	−	3.58579i	−0.202937	−	0.113449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.c.824.2		4
3.2	odd	2	inner	975.2.n.c.824.1		4
5.2	odd	4		975.2.o.j.551.2		4
5.3	odd	4		39.2.f.a.5.1	✓	4
5.4	even	2		975.2.n.d.824.1		4
13.8	odd	4		975.2.n.d.749.2		4
15.2	even	4		975.2.o.j.551.1		4
15.8	even	4		39.2.f.a.5.2	yes	4
15.14	odd	2		975.2.n.d.824.2		4
20.3	even	4		624.2.bf.d.161.2		4
39.8	even	4		975.2.n.d.749.1		4
60.23	odd	4		624.2.bf.d.161.1		4
65.3	odd	12		507.2.k.j.188.2		8
65.8	even	4		39.2.f.a.8.2	yes	4
65.18	even	4		507.2.f.a.437.1		4
65.23	odd	12		507.2.k.i.188.1		8
65.28	even	12		507.2.k.i.488.1		8
65.33	even	12		507.2.k.j.89.1		8
65.34	odd	4	inner	975.2.n.c.749.1		4
65.38	odd	4		507.2.f.a.239.2		4
65.43	odd	12		507.2.k.i.80.2		8
65.47	even	4		975.2.o.j.476.1		4
65.48	odd	12		507.2.k.j.80.1		8
65.58	even	12		507.2.k.i.89.2		8
65.63	even	12		507.2.k.j.488.2		8
195.8	odd	4		39.2.f.a.8.1	yes	4
195.23	even	12		507.2.k.i.188.2		8
195.38	even	4		507.2.f.a.239.1		4
195.47	odd	4		975.2.o.j.476.2		4
195.68	even	12		507.2.k.j.188.1		8
195.83	odd	4		507.2.f.a.437.2		4
195.98	odd	12		507.2.k.j.89.2		8
195.113	even	12		507.2.k.j.80.2		8
195.128	odd	12		507.2.k.j.488.1		8
195.158	odd	12		507.2.k.i.488.2		8
195.164	even	4	inner	975.2.n.c.749.2		4
195.173	even	12		507.2.k.i.80.1		8
195.188	odd	12		507.2.k.i.89.1		8
260.203	odd	4		624.2.bf.d.593.2		4
780.203	even	4		624.2.bf.d.593.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.f.a.5.1	✓	4	5.3	odd	4
39.2.f.a.5.2	yes	4	15.8	even	4
39.2.f.a.8.1	yes	4	195.8	odd	4
39.2.f.a.8.2	yes	4	65.8	even	4
507.2.f.a.239.1		4	195.38	even	4
507.2.f.a.239.2		4	65.38	odd	4
507.2.f.a.437.1		4	65.18	even	4
507.2.f.a.437.2		4	195.83	odd	4
507.2.k.i.80.1		8	195.173	even	12
507.2.k.i.80.2		8	65.43	odd	12
507.2.k.i.89.1		8	195.188	odd	12
507.2.k.i.89.2		8	65.58	even	12
507.2.k.i.188.1		8	65.23	odd	12
507.2.k.i.188.2		8	195.23	even	12
507.2.k.i.488.1		8	65.28	even	12
507.2.k.i.488.2		8	195.158	odd	12
507.2.k.j.80.1		8	65.48	odd	12
507.2.k.j.80.2		8	195.113	even	12
507.2.k.j.89.1		8	65.33	even	12
507.2.k.j.89.2		8	195.98	odd	12
507.2.k.j.188.1		8	195.68	even	12
507.2.k.j.188.2		8	65.3	odd	12
507.2.k.j.488.1		8	195.128	odd	12
507.2.k.j.488.2		8	65.63	even	12
624.2.bf.d.161.1		4	60.23	odd	4
624.2.bf.d.161.2		4	20.3	even	4
624.2.bf.d.593.1		4	780.203	even	4
624.2.bf.d.593.2		4	260.203	odd	4
975.2.n.c.749.1		4	65.34	odd	4	inner
975.2.n.c.749.2		4	195.164	even	4	inner
975.2.n.c.824.1		4	3.2	odd	2	inner
975.2.n.c.824.2		4	1.1	even	1	trivial
975.2.n.d.749.1		4	39.8	even	4
975.2.n.d.749.2		4	13.8	odd	4
975.2.n.d.824.1		4	5.4	even	2
975.2.n.d.824.2		4	15.14	odd	2
975.2.o.j.476.1		4	65.47	even	4
975.2.o.j.476.2		4	195.47	odd	4
975.2.o.j.551.1		4	15.2	even	4
975.2.o.j.551.2		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.292893 + 1.70711i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.292893 + 1.70711i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +(2.82843 - 2.82843i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(3.00000 + 2.00000i) q^{13} +1.41421i q^{14} +1.00000 q^{16} +(-1.29289 - 2.70711i) q^{18} +(-1.00000 + 1.00000i) q^{19} +(0.414214 - 2.41421i) q^{21} -4.00000i q^{22} +8.48528i q^{23} +(-5.12132 - 0.878680i) q^{24} +(3.53553 - 0.707107i) q^{26} +(1.41421 + 5.00000i) q^{27} +(-1.00000 - 1.00000i) q^{28} -2.82843i q^{29} +(-5.00000 + 5.00000i) q^{31} +(-3.53553 + 3.53553i) q^{32} +(-1.17157 + 6.82843i) q^{33} +(2.82843 + 1.00000i) q^{36} +(-1.00000 + 1.00000i) q^{37} +1.41421i q^{38} +(-6.24264 + 0.171573i) q^{39} +(1.41421 + 1.41421i) q^{41} +(-1.41421 - 2.00000i) q^{42} -6.00000 q^{43} +(2.82843 + 2.82843i) q^{44} +(6.00000 + 6.00000i) q^{46} +(2.82843 + 2.82843i) q^{47} +(-1.41421 + 1.00000i) q^{48} +5.00000i q^{49} +(-2.00000 + 3.00000i) q^{52} -5.65685 q^{53} +(4.53553 + 2.53553i) q^{54} -4.24264 q^{56} +(0.414214 - 2.41421i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-2.82843 + 2.82843i) q^{59} +8.00000 q^{61} +7.07107i q^{62} +(1.82843 + 3.82843i) q^{63} +7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-5.00000 - 5.00000i) q^{67} +(-8.48528 - 12.0000i) q^{69} +(-2.82843 - 2.82843i) q^{71} +(8.12132 - 3.87868i) q^{72} +(1.00000 - 1.00000i) q^{73} +1.41421i q^{74} +(-1.00000 - 1.00000i) q^{76} +5.65685i q^{77} +(-4.29289 + 4.53553i) q^{78} +10.0000 q^{79} +(-7.00000 - 5.65685i) q^{81} +2.00000 q^{82} +(5.65685 - 5.65685i) q^{83} +(2.41421 + 0.414214i) q^{84} +(-4.24264 + 4.24264i) q^{86} +(2.82843 + 4.00000i) q^{87} +12.0000 q^{88} +(9.89949 - 9.89949i) q^{89} +(-5.00000 + 1.00000i) q^{91} -8.48528 q^{92} +(2.07107 - 12.0711i) q^{93} +4.00000 q^{94} +(1.46447 - 8.53553i) q^{96} +(7.00000 + 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^6 - 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{6} - 4 q^{7} + 4 q^{9} - 4 q^{12} + 12 q^{13} + 4 q^{16} - 8 q^{18} - 4 q^{19} - 4 q^{21} - 12 q^{24} - 4 q^{28} - 20 q^{31} - 16 q^{33} - 4 q^{37} - 8 q^{39} - 24 q^{43} + 24 q^{46} - 8 q^{52} + 4 q^{54} - 4 q^{57} - 8 q^{58} + 32 q^{61} - 4 q^{63} + 16 q^{66} - 20 q^{67} + 24 q^{72} + 4 q^{73} - 4 q^{76} - 20 q^{78} + 40 q^{79} - 28 q^{81} + 8 q^{82} + 4 q^{84} + 48 q^{88} - 20 q^{91} - 20 q^{93} + 16 q^{94} + 20 q^{96} + 28 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^6 - 4 * q^7 + 4 * q^9 - 4 * q^12 + 12 * q^13 + 4 * q^16 - 8 * q^18 - 4 * q^19 - 4 * q^21 - 12 * q^24 - 4 * q^28 - 20 * q^31 - 16 * q^33 - 4 * q^37 - 8 * q^39 - 24 * q^43 + 24 * q^46 - 8 * q^52 + 4 * q^54 - 4 * q^57 - 8 * q^58 + 32 * q^61 - 4 * q^63 + 16 * q^66 - 20 * q^67 + 24 * q^72 + 4 * q^73 - 4 * q^76 - 20 * q^78 + 40 * q^79 - 28 * q^81 + 8 * q^82 + 4 * q^84 + 48 * q^88 - 20 * q^91 - 20 * q^93 + 16 * q^94 + 20 * q^96 + 28 * q^97 - 32 * q^99

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