LMFDB - Embedded newform 480.2.w.c.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,2,Mod(127,480)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(480, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("480.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	480.w (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:	$3.83281929702$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.2
Root			$2.16053i$ of defining polynomial
Character	$\chi$	$=$	480.223
Dual form			480.2.w.c.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(2.23483 + 0.0743018i) q^{5} +(-3.16053 - 3.16053i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(2.23483 + 0.0743018i) q^{5} +(-3.16053 - 3.16053i) q^{7} -1.00000i q^{9} -4.46967i q^{11} +(-2.51929 - 2.51929i) q^{13} +(-1.63280 + 1.52773i) q^{15} +(-2.30913 + 2.30913i) q^{17} +2.61827 q^{19} +4.46967 q^{21} +(1.64124 - 1.64124i) q^{23} +(4.98896 + 0.332104i) q^{25} +(0.707107 + 0.707107i) q^{27} -8.17246i q^{29} +4.00000i q^{31} +(3.16053 + 3.16053i) q^{33} +(-6.82843 - 7.29809i) q^{35} +(5.80177 - 5.80177i) q^{37} +3.56282 q^{39} -2.61827 q^{41} +(-5.14949 + 5.14949i) q^{43} +(0.0743018 - 2.23483i) q^{45} +(0.679824 + 0.679824i) q^{47} +12.9779i q^{49} -3.26561i q^{51} +(-7.81739 - 7.81739i) q^{53} +(0.332104 - 9.98896i) q^{55} +(-1.85140 + 1.85140i) q^{57} +4.88998 q^{59} +12.2751 q^{61} +(-3.16053 + 3.16053i) q^{63} +(-5.44301 - 5.81739i) q^{65} +(9.44670 + 9.44670i) q^{67} +2.32106i q^{69} -5.65685i q^{71} +(-5.61827 - 5.61827i) q^{73} +(-3.76256 + 3.29289i) q^{75} +(-14.1265 + 14.1265i) q^{77} -3.57969 q^{79} -1.00000 q^{81} +(1.34403 - 1.34403i) q^{83} +(-5.33210 + 4.98896i) q^{85} +(5.77880 + 5.77880i) q^{87} +17.6348i q^{89} +15.9246i q^{91} +(-2.82843 - 2.82843i) q^{93} +(5.85140 + 0.194542i) q^{95} +(-1.32106 + 1.32106i) q^{97} -4.46967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} - 12 q^{13} - 4 q^{15} - 4 q^{17} - 8 q^{19} - 4 q^{25} + 4 q^{33} - 32 q^{35} + 12 q^{37} + 24 q^{39} + 8 q^{41} + 24 q^{43} + 4 q^{45} - 24 q^{47} + 4 q^{53} + 4 q^{55} - 8 q^{57} + 16 q^{59} + 24 q^{61} - 4 q^{63} + 4 q^{65} + 24 q^{67} - 16 q^{73} - 32 q^{77} - 16 q^{79} - 8 q^{81} - 16 q^{83} - 44 q^{85} - 4 q^{87} + 40 q^{95} + 32 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 - 12 * q^13 - 4 * q^15 - 4 * q^17 - 8 * q^19 - 4 * q^25 + 4 * q^33 - 32 * q^35 + 12 * q^37 + 24 * q^39 + 8 * q^41 + 24 * q^43 + 4 * q^45 - 24 * q^47 + 4 * q^53 + 4 * q^55 - 8 * q^57 + 16 * q^59 + 24 * q^61 - 4 * q^63 + 4 * q^65 + 24 * q^67 - 16 * q^73 - 32 * q^77 - 16 * q^79 - 8 * q^81 - 16 * q^83 - 44 * q^85 - 4 * q^87 + 40 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	2.23483	+	0.0743018i	0.999448	+	0.0332288i
$5$	2.23483	+	0.0743018i	0.999448	+	0.0332288i
$6$		0			0
$7$	−3.16053	−	3.16053i	−1.19457	−	1.19457i	−0.975770	−	0.218799i	$-0.929786\pi$
$7$	−3.16053	−	3.16053i	−1.19457	−	1.19457i	−0.218799	−	0.975770i	$-0.570214\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	4.46967i		−	1.34766i	−0.738889	−	0.673828i	$-0.764649\pi$
$11$		−	4.46967i		−	1.34766i	0.738889	−	0.673828i	$-0.235351\pi$
$12$		0			0
$13$	−2.51929	−	2.51929i	−0.698726	−	0.698726i	0.265410	−	0.964136i	$-0.414493\pi$
$13$	−2.51929	−	2.51929i	−0.698726	−	0.698726i	−0.964136	+	0.265410i	$0.914493\pi$
$14$		0			0
$15$	−1.63280	+	1.52773i	−0.421588	+	0.394457i
$16$		0			0
$17$	−2.30913	+	2.30913i	−0.560047	+	0.560047i	−0.929321	−	0.369273i	$-0.879607\pi$
$17$	−2.30913	+	2.30913i	−0.560047	+	0.560047i	0.369273	+	0.929321i	$0.379607\pi$
$18$		0			0
$19$	2.61827			0.600672			0.300336	−	0.953833i	$-0.402901\pi$
$19$	2.61827			0.600672			0.300336	+	0.953833i	$0.402901\pi$
$20$		0			0
$21$	4.46967			0.975361
$22$		0			0
$23$	1.64124	−	1.64124i	0.342222	−	0.342222i	−0.514980	−	0.857202i	$-0.672201\pi$
$23$	1.64124	−	1.64124i	0.342222	−	0.342222i	0.857202	+	0.514980i	$0.172201\pi$
$24$		0			0
$25$	4.98896	+	0.332104i	0.997792	+	0.0664208i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	8.17246i		−	1.51759i	−0.651331	−	0.758794i	$-0.725789\pi$
$29$		−	8.17246i		−	1.51759i	0.651331	−	0.758794i	$-0.274211\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	3.16053	+	3.16053i	0.550178	+	0.550178i
$34$		0			0
$35$	−6.82843	−	7.29809i	−1.15421	−	1.23360i
$36$		0			0
$37$	5.80177	−	5.80177i	0.953805	−	0.953805i	−0.0451739	−	0.998979i	$-0.514384\pi$
$37$	5.80177	−	5.80177i	0.953805	−	0.953805i	0.998979	+	0.0451739i	$0.0143842\pi$
$38$		0			0
$39$	3.56282			0.570507
$40$		0			0
$41$	−2.61827			−0.408905			−0.204453	−	0.978876i	$-0.565541\pi$
$41$	−2.61827			−0.408905			−0.204453	+	0.978876i	$0.565541\pi$
$42$		0			0
$43$	−5.14949	+	5.14949i	−0.785290	+	0.785290i	−0.980718	−	0.195428i	$-0.937390\pi$
$43$	−5.14949	+	5.14949i	−0.785290	+	0.785290i	0.195428	+	0.980718i	$0.437390\pi$
$44$		0			0
$45$	0.0743018	−	2.23483i	0.0110763	−	0.333149i
$46$		0			0
$47$	0.679824	+	0.679824i	0.0991625	+	0.0991625i	0.754948	−	0.655785i	$-0.227662\pi$
$47$	0.679824	+	0.679824i	0.0991625	+	0.0991625i	−0.655785	+	0.754948i	$0.727662\pi$
$48$		0			0
$49$			12.9779i			1.85399i
$50$		0			0
$51$		−	3.26561i		−	0.457277i
$52$		0			0
$53$	−7.81739	−	7.81739i	−1.07380	−	1.07380i	−0.997050	−	0.0767501i	$-0.975546\pi$
$53$	−7.81739	−	7.81739i	−1.07380	−	1.07380i	−0.0767501	−	0.997050i	$-0.524454\pi$
$54$		0			0
$55$	0.332104	−	9.98896i	0.0447809	−	1.34691i
$56$		0			0
$57$	−1.85140	+	1.85140i	−0.245223	+	0.245223i
$58$		0			0
$59$	4.88998			0.636621			0.318311	−	0.947986i	$-0.396885\pi$
$59$	4.88998			0.636621			0.318311	+	0.947986i	$0.396885\pi$
$60$		0			0
$61$	12.2751			1.57167			0.785834	−	0.618437i	$-0.212234\pi$
$61$	12.2751			1.57167			0.785834	+	0.618437i	$0.212234\pi$
$62$		0			0
$63$	−3.16053	+	3.16053i	−0.398190	+	0.398190i
$64$		0			0
$65$	−5.44301	−	5.81739i	−0.675122	−	0.721558i
$66$		0			0
$67$	9.44670	+	9.44670i	1.15410	+	1.15410i	0.985723	+	0.168375i	$0.0538518\pi$
$67$	9.44670	+	9.44670i	1.15410	+	1.15410i	0.168375	+	0.985723i	$0.446148\pi$
$68$		0			0
$69$			2.32106i			0.279423i
$70$		0			0
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$		0			0
$73$	−5.61827	−	5.61827i	−0.657569	−	0.657569i	0.297235	−	0.954804i	$-0.403935\pi$
$73$	−5.61827	−	5.61827i	−0.657569	−	0.657569i	−0.954804	+	0.297235i	$0.903935\pi$
$74$		0			0
$75$	−3.76256	+	3.29289i	−0.434463	+	0.380231i
$76$		0			0
$77$	−14.1265	+	14.1265i	−1.60987	+	1.60987i
$78$		0			0
$79$	−3.57969			−0.402746			−0.201373	−	0.979515i	$-0.564540\pi$
$79$	−3.57969			−0.402746			−0.201373	+	0.979515i	$0.564540\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.34403	−	1.34403i	0.147527	−	0.147527i	−0.629486	−	0.777012i	$-0.716734\pi$
$83$	1.34403	−	1.34403i	0.147527	−	0.147527i	0.777012	+	0.629486i	$0.216734\pi$
$84$		0			0
$85$	−5.33210	+	4.98896i	−0.578348	+	0.541129i
$86$		0			0
$87$	5.77880	+	5.77880i	0.619553	+	0.619553i
$88$		0			0
$89$			17.6348i			1.86928i	0.355593	+	0.934641i	$0.384279\pi$
$89$			17.6348i			1.86928i	−0.355593	+	0.934641i	$0.615721\pi$
$90$		0			0
$91$			15.9246i			1.66935i
$92$		0			0
$93$	−2.82843	−	2.82843i	−0.293294	−	0.293294i
$94$		0			0
$95$	5.85140	+	0.194542i	0.600341	+	0.0199596i
$96$		0			0
$97$	−1.32106	+	1.32106i	−0.134134	+	0.134134i	−0.770986	−	0.636852i	$-0.780236\pi$
$97$	−1.32106	+	1.32106i	−0.134134	+	0.134134i	0.636852	+	0.770986i	$0.280236\pi$
$98$		0			0
$99$	−4.46967			−0.449218
$100$		0			0
$101$	−1.47702			−0.146969			−0.0734845	−	0.997296i	$-0.523412\pi$
$101$	−1.47702			−0.146969			−0.0734845	+	0.997296i	$0.523412\pi$
$102$		0			0
$103$	−9.11459	+	9.11459i	−0.898088	+	0.898088i	−0.995267	−	0.0971794i	$-0.969018\pi$
$103$	−9.11459	+	9.11459i	−0.898088	+	0.898088i	0.0971794	+	0.995267i	$0.469018\pi$
$104$		0			0
$105$	9.98896	+	0.332104i	0.974823	+	0.0324101i
$106$		0			0
$107$	2.06155	+	2.06155i	0.199298	+	0.199298i	0.799699	−	0.600401i	$-0.204992\pi$
$107$	2.06155	+	2.06155i	0.199298	+	0.199298i	−0.600401	+	0.799699i	$0.704992\pi$
$108$		0			0
$109$			9.70279i			0.929359i	0.885479	+	0.464679i	$0.153830\pi$
$109$			9.70279i			0.929359i	−0.885479	+	0.464679i	$0.846170\pi$
$110$		0			0
$111$			8.20494i			0.778779i
$112$		0			0
$113$	−4.63020	−	4.63020i	−0.435572	−	0.435572i	0.454946	−	0.890519i	$-0.349658\pi$
$113$	−4.63020	−	4.63020i	−0.435572	−	0.435572i	−0.890519	+	0.454946i	$0.849658\pi$
$114$		0			0
$115$	3.78984	−	3.54595i	0.353405	−	0.330661i
$116$		0			0
$117$	−2.51929	+	2.51929i	−0.232909	+	0.232909i
$118$		0			0
$119$	14.5962			1.33803
$120$		0			0
$121$	−8.97792			−0.816174
$122$		0			0
$123$	1.85140	−	1.85140i	0.166935	−	0.166935i
$124$		0			0
$125$	11.1248	+	1.11289i	0.995034	+	0.0995396i
$126$		0			0
$127$	10.1991	+	10.1991i	0.905025	+	0.905025i	0.995865	−	0.0908403i	$-0.0289553\pi$
$127$	10.1991	+	10.1991i	0.905025	+	0.905025i	−0.0908403	+	0.995865i	$0.528955\pi$
$128$		0			0
$129$		−	7.28248i		−	0.641186i
$130$		0			0
$131$		−	12.4697i		−	1.08948i	−0.838605	−	0.544740i	$-0.816628\pi$
$131$		−	12.4697i		−	1.08948i	0.838605	−	0.544740i	$-0.183372\pi$
$132$		0			0
$133$	−8.27512	−	8.27512i	−0.717544	−	0.717544i
$134$		0			0
$135$	1.52773	+	1.63280i	0.131486	+	0.140529i
$136$		0			0
$137$	4.63020	−	4.63020i	0.395584	−	0.395584i	−0.481088	−	0.876672i	$-0.659758\pi$
$137$	4.63020	−	4.63020i	0.395584	−	0.395584i	0.876672	+	0.481088i	$0.159758\pi$
$138$		0			0
$139$	−3.00735			−0.255080			−0.127540	−	0.991833i	$-0.540708\pi$
$139$	−3.00735			−0.255080			−0.127540	+	0.991833i	$0.540708\pi$
$140$		0			0
$141$	−0.961416			−0.0809658
$142$		0			0
$143$	−11.2604	+	11.2604i	−0.941642	+	0.941642i
$144$		0			0
$145$	0.607228	−	18.2641i	0.0504276	−	1.51675i
$146$		0			0
$147$	−9.17677	−	9.17677i	−0.756887	−	0.756887i
$148$		0			0
$149$		−	0.148604i		−	0.0121741i	−0.999981	−	0.00608704i	$-0.998062\pi$
$149$		−	0.148604i		−	0.0121741i	0.999981	−	0.00608704i	$-0.00193758\pi$
$150$		0			0
$151$		−	20.6200i		−	1.67804i	−0.544104	−	0.839018i	$-0.683130\pi$
$151$		−	20.6200i		−	1.67804i	0.544104	−	0.839018i	$-0.316870\pi$
$152$		0			0
$153$	2.30913	+	2.30913i	0.186682	+	0.186682i
$154$		0			0
$155$	−0.297207	+	8.93933i	−0.0238723	+	0.718024i
$156$		0			0
$157$	−9.77969	+	9.77969i	−0.780504	+	0.780504i	−0.979916	−	0.199412i	$-0.936097\pi$
$157$	−9.77969	+	9.77969i	−0.780504	+	0.780504i	0.199412	+	0.979916i	$0.436097\pi$
$158$		0			0
$159$	11.0555			0.876754
$160$		0			0
$161$	−10.3744			−0.817615
$162$		0			0
$163$	10.4081	−	10.4081i	0.815226	−	0.815226i	−0.170186	−	0.985412i	$-0.554437\pi$
$163$	10.4081	−	10.4081i	0.815226	−	0.815226i	0.985412	+	0.170186i	$0.0544368\pi$
$164$		0			0
$165$	6.82843	+	7.29809i	0.531592	+	0.568156i
$166$		0			0
$167$	−6.06155	−	6.06155i	−0.469057	−	0.469057i	0.432552	−	0.901609i	$-0.357613\pi$
$167$	−6.06155	−	6.06155i	−0.469057	−	0.469057i	−0.901609	+	0.432552i	$0.857613\pi$
$168$		0			0
$169$		−	0.306334i		−	0.0235641i
$170$		0			0
$171$		−	2.61827i		−	0.200224i
$172$		0			0
$173$	0.355074	+	0.355074i	0.0269957	+	0.0269957i	0.720476	−	0.693480i	$-0.243923\pi$
$173$	0.355074	+	0.355074i	0.0269957	+	0.0269957i	−0.693480	+	0.720476i	$0.743923\pi$
$174$		0			0
$175$	−14.7181	−	16.8174i	−1.11259	−	1.27127i
$176$		0			0
$177$	−3.45774	+	3.45774i	−0.259900	+	0.259900i
$178$		0			0
$179$	15.7521			1.17737			0.588685	−	0.808362i	$-0.299646\pi$
$179$	15.7521			1.17737			0.588685	+	0.808362i	$0.299646\pi$
$180$		0			0
$181$	7.77996			0.578280			0.289140	−	0.957287i	$-0.406631\pi$
$181$	7.77996			0.578280			0.289140	+	0.957287i	$0.406631\pi$
$182$		0			0
$183$	−8.67982	+	8.67982i	−0.641631	+	0.641631i
$184$		0			0
$185$	13.3971	−	12.5349i	0.984972	−	0.921585i
$186$		0			0
$187$	10.3211	+	10.3211i	0.754751	+	0.754751i
$188$		0			0
$189$		−	4.46967i		−	0.325120i
$190$		0			0
$191$			9.35965i			0.677240i	0.940923	+	0.338620i	$0.109960\pi$
$191$			9.35965i			0.677240i	−0.940923	+	0.338620i	$0.890040\pi$
$192$		0			0
$193$	17.1759	+	17.1759i	1.23635	+	1.23635i	0.961483	+	0.274863i	$0.0886325\pi$
$193$	17.1759	+	17.1759i	1.23635	+	1.23635i	0.274863	+	0.961483i	$0.411368\pi$
$194$		0			0
$195$	7.96230	+	0.264724i	0.570192	+	0.0189573i
$196$		0			0
$197$	1.83947	−	1.83947i	0.131057	−	0.131057i	−0.638536	−	0.769592i	$-0.720459\pi$
$197$	1.83947	−	1.83947i	0.131057	−	0.131057i	0.769592	+	0.638536i	$0.220459\pi$
$198$		0			0
$199$	−0.442397			−0.0313607			−0.0156804	−	0.999877i	$-0.504991\pi$
$199$	−0.442397			−0.0313607			−0.0156804	+	0.999877i	$0.504991\pi$
$200$		0			0
$201$	−13.3596			−0.942317
$202$		0			0
$203$	−25.8293	+	25.8293i	−1.81286	+	1.81286i
$204$		0			0
$205$	−5.85140	−	0.194542i	−0.408679	−	0.0135874i
$206$		0			0
$207$	−1.64124	−	1.64124i	−0.114074	−	0.114074i
$208$		0			0
$209$		−	11.7028i		−	0.809499i
$210$		0			0
$211$		−	5.30633i		−	0.365303i	−0.983178	−	0.182652i	$-0.941532\pi$
$211$		−	5.30633i		−	0.365303i	0.983178	−	0.182652i	$-0.0584680\pi$
$212$		0			0
$213$	4.00000	+	4.00000i	0.274075	+	0.274075i
$214$		0			0
$215$	−11.8909	+	11.1256i	−0.810950	+	0.758762i
$216$		0			0
$217$	12.6421	−	12.6421i	0.858203	−	0.858203i
$218$		0			0
$219$	7.94543			0.536903
$220$		0			0
$221$	11.6348			0.782639
$222$		0			0
$223$	5.48159	−	5.48159i	0.367075	−	0.367075i	−0.499335	−	0.866409i	$-0.666422\pi$
$223$	5.48159	−	5.48159i	0.367075	−	0.367075i	0.866409	+	0.499335i	$0.166422\pi$
$224$		0			0
$225$	0.332104	−	4.98896i	0.0221403	−	0.332597i
$226$		0			0
$227$	−9.51649	−	9.51649i	−0.631632	−	0.631632i	0.316845	−	0.948477i	$-0.397376\pi$
$227$	−9.51649	−	9.51649i	−0.631632	−	0.631632i	−0.948477	+	0.316845i	$0.897376\pi$
$228$		0			0
$229$			5.25862i			0.347500i	0.984790	+	0.173750i	$0.0555884\pi$
$229$			5.25862i			0.347500i	−0.984790	+	0.173750i	$0.944412\pi$
$230$		0			0
$231$		−	19.9779i		−	1.31445i
$232$		0			0
$233$	2.92740	+	2.92740i	0.191781	+	0.191781i	0.796465	−	0.604684i	$-0.206701\pi$
$233$	2.92740	+	2.92740i	0.191781	+	0.191781i	−0.604684	+	0.796465i	$0.706701\pi$
$234$		0			0
$235$	1.46878	+	1.56980i	0.0958126	+	0.102403i
$236$		0			0
$237$	2.53122	−	2.53122i	0.164420	−	0.164420i
$238$		0			0
$239$	−12.6421			−0.817751			−0.408876	−	0.912590i	$-0.634079\pi$
$239$	−12.6421			−0.817751			−0.408876	+	0.912590i	$0.634079\pi$
$240$		0			0
$241$	14.5650			0.938211			0.469106	−	0.883142i	$-0.344576\pi$
$241$	14.5650			0.938211			0.469106	+	0.883142i	$0.344576\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.964283	+	29.0035i	−0.0616058	+	1.85296i
$246$		0			0
$247$	−6.59619	−	6.59619i	−0.419705	−	0.419705i
$248$		0			0
$249$			1.90075i			0.120455i
$250$		0			0
$251$		−	18.5468i		−	1.17067i	−0.810793	−	0.585333i	$-0.800964\pi$
$251$		−	18.5468i		−	1.17067i	0.810793	−	0.585333i	$-0.199036\pi$
$252$		0			0
$253$	−7.33579	−	7.33579i	−0.461197	−	0.461197i
$254$		0			0
$255$	0.242641	−	7.29809i	0.0151947	−	0.457024i
$256$		0			0
$257$	13.2485	−	13.2485i	0.826417	−	0.826417i	−0.160602	−	0.987019i	$-0.551344\pi$
$257$	13.2485	−	13.2485i	0.826417	−	0.826417i	0.987019	+	0.160602i	$0.0513437\pi$
$258$		0			0
$259$	−36.6734			−2.27877
$260$		0			0
$261$	−8.17246			−0.505863
$262$		0			0
$263$	22.5806	−	22.5806i	1.39238	−	1.39238i	0.572411	−	0.819967i	$-0.306008\pi$
$263$	22.5806	−	22.5806i	1.39238	−	1.39238i	0.819967	−	0.572411i	$-0.193992\pi$
$264$		0			0
$265$	−16.8897	−	18.0514i	−1.03753	−	1.10889i
$266$		0			0
$267$	−12.4697	−	12.4697i	−0.763131	−	0.763131i
$268$		0			0
$269$		−	6.82019i		−	0.415834i	−0.978146	−	0.207917i	$-0.933332\pi$
$269$		−	6.82019i		−	0.415834i	0.978146	−	0.207917i	$-0.0666684\pi$
$270$		0			0
$271$			2.74138i			0.166527i	0.996528	+	0.0832634i	$0.0265343\pi$
$271$			2.74138i			0.166527i	−0.996528	+	0.0832634i	$0.973466\pi$
$272$		0			0
$273$	−11.2604	−	11.2604i	−0.681510	−	0.681510i
$274$		0			0
$275$	1.48440	−	22.2990i	0.0895124	−	1.34468i
$276$		0			0
$277$	−7.75583	+	7.75583i	−0.466003	+	0.466003i	−0.900617	−	0.434614i	$-0.856885\pi$
$277$	−7.75583	+	7.75583i	−0.466003	+	0.466003i	0.434614	+	0.900617i	$0.356885\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	4.54110			0.270899			0.135450	−	0.990784i	$-0.456752\pi$
$281$	4.54110			0.270899			0.135450	+	0.990784i	$0.456752\pi$
$282$		0			0
$283$	7.91295	−	7.91295i	0.470376	−	0.470376i	−0.431660	−	0.902036i	$-0.642072\pi$
$283$	7.91295	−	7.91295i	0.470376	−	0.470376i	0.902036	+	0.431660i	$0.142072\pi$
$284$		0			0
$285$	−4.27512	+	4.00000i	−0.253236	+	0.236940i
$286$		0			0
$287$	8.27512	+	8.27512i	0.488465	+	0.488465i
$288$		0			0
$289$			6.33579i			0.372694i
$290$		0			0
$291$		−	1.86826i		−	0.109520i
$292$		0			0
$293$	15.0999	+	15.0999i	0.882143	+	0.882143i	0.993752	−	0.111609i	$-0.0356003\pi$
$293$	15.0999	+	15.0999i	0.882143	+	0.882143i	−0.111609	+	0.993752i	$0.535600\pi$
$294$		0			0
$295$	10.9283	+	0.363334i	0.636270	+	0.0211541i
$296$		0			0
$297$	3.16053	−	3.16053i	0.183393	−	0.183393i
$298$		0			0
$299$	−8.26952			−0.478239
$300$		0			0
$301$	32.5502			1.87617
$302$		0			0
$303$	1.04441	−	1.04441i	0.0599999	−	0.0599999i
$304$		0			0
$305$	27.4329	+	0.912064i	1.57080	+	0.0522246i
$306$		0			0
$307$	4.43197	+	4.43197i	0.252946	+	0.252946i	0.822177	−	0.569232i	$-0.192759\pi$
$307$	4.43197	+	4.43197i	0.252946	+	0.252946i	−0.569232	+	0.822177i	$0.692759\pi$
$308$		0			0
$309$		−	12.8900i		−	0.733285i
$310$		0			0
$311$			23.5355i			1.33458i	0.744799	+	0.667288i	$0.232545\pi$
$311$			23.5355i			1.33458i	−0.744799	+	0.667288i	$0.767455\pi$
$312$		0			0
$313$	−18.6035	−	18.6035i	−1.05153	−	1.05153i	−0.998598	−	0.0529364i	$-0.983142\pi$
$313$	−18.6035	−	18.6035i	−1.05153	−	1.05153i	−0.0529364	−	0.998598i	$-0.516858\pi$
$314$		0			0
$315$	−7.29809	+	6.82843i	−0.411201	+	0.384738i
$316$		0			0
$317$	7.56953	−	7.56953i	0.425147	−	0.425147i	−0.461824	−	0.886971i	$-0.652805\pi$
$317$	7.56953	−	7.56953i	0.425147	−	0.425147i	0.886971	+	0.461824i	$0.152805\pi$
$318$		0			0
$319$	−36.5282			−2.04518
$320$		0			0
$321$	−2.91548			−0.162726
$322$		0			0
$323$	−6.04594	+	6.04594i	−0.336405	+	0.336405i
$324$		0			0
$325$	−11.7320	−	13.4053i	−0.650773	−	0.743593i
$326$		0			0
$327$	−6.86091	−	6.86091i	−0.379409	−	0.379409i
$328$		0			0
$329$		−	4.29721i		−	0.236913i
$330$		0			0
$331$			13.8020i			0.758629i	0.925268	+	0.379314i	$0.123840\pi$
$331$			13.8020i			0.758629i	−0.925268	+	0.379314i	$0.876160\pi$
$332$		0			0
$333$	−5.80177	−	5.80177i	−0.317935	−	0.317935i
$334$		0			0
$335$	20.4099	+	21.8137i	1.11511	+	1.19181i
$336$		0			0
$337$	10.9541	−	10.9541i	0.596706	−	0.596706i	−0.342729	−	0.939434i	$-0.611351\pi$
$337$	10.9541	−	10.9541i	0.596706	−	0.596706i	0.939434	+	0.342729i	$0.111351\pi$
$338$		0			0
$339$	6.54809			0.355643
$340$		0			0
$341$	17.8787			0.968184
$342$		0			0
$343$	18.8934	−	18.8934i	1.02015	−	1.02015i
$344$		0			0
$345$	−0.172459	+	5.18719i	−0.00928489	+	0.279269i
$346$		0			0
$347$	13.3934	+	13.3934i	0.718995	+	0.718995i	0.968399	−	0.249405i	$-0.0802350\pi$
$347$	13.3934	+	13.3934i	0.718995	+	0.718995i	−0.249405	+	0.968399i	$0.580235\pi$
$348$		0			0
$349$			21.6035i			1.15641i	0.815891	+	0.578206i	$0.196247\pi$
$349$			21.6035i			1.15641i	−0.815891	+	0.578206i	$0.803753\pi$
$350$		0			0
$351$		−	3.56282i		−	0.190169i
$352$		0			0
$353$	25.9678	+	25.9678i	1.38212	+	1.38212i	0.840839	+	0.541286i	$0.182062\pi$
$353$	25.9678	+	25.9678i	1.38212	+	1.38212i	0.541286	+	0.840839i	$0.317938\pi$
$354$		0			0
$355$	0.420314	−	12.6421i	0.0223080	−	0.670974i
$356$		0			0
$357$	−10.3211	+	10.3211i	−0.546249	+	0.546249i
$358$		0			0
$359$	−8.93933			−0.471800			−0.235900	−	0.971777i	$-0.575804\pi$
$359$	−8.93933			−0.471800			−0.235900	+	0.971777i	$0.575804\pi$
$360$		0			0
$361$	−12.1447			−0.639193
$362$		0			0
$363$	6.34835	−	6.34835i	0.333202	−	0.333202i
$364$		0			0
$365$	−12.1384	−	12.9733i	−0.635355	−	0.679056i
$366$		0			0
$367$	13.7788	+	13.7788i	0.719248	+	0.719248i	0.968451	−	0.249204i	$-0.0801688\pi$
$367$	13.7788	+	13.7788i	0.719248	+	0.719248i	−0.249204	+	0.968451i	$0.580169\pi$
$368$		0			0
$369$			2.61827i			0.136302i
$370$		0			0
$371$			49.4142i			2.56546i
$372$		0			0
$373$	−12.4439	−	12.4439i	−0.644321	−	0.644321i	0.307294	−	0.951615i	$-0.400576\pi$
$373$	−12.4439	−	12.4439i	−0.644321	−	0.644321i	−0.951615	+	0.307294i	$0.900576\pi$
$374$		0			0
$375$	−8.65336	+	7.07950i	−0.446858	+	0.365584i
$376$		0			0
$377$	−20.5888	+	20.5888i	−1.06038	+	1.06038i
$378$		0			0
$379$	34.9190			1.79367			0.896835	−	0.442366i	$-0.145861\pi$
$379$	34.9190			1.79367			0.896835	+	0.442366i	$0.145861\pi$
$380$		0			0
$381$	−14.4237			−0.738950
$382$		0			0
$383$	5.69455	−	5.69455i	0.290978	−	0.290978i	−0.546489	−	0.837467i	$-0.684036\pi$
$383$	5.69455	−	5.69455i	0.290978	−	0.290978i	0.837467	+	0.546489i	$0.184036\pi$
$384$		0			0
$385$	−32.6200	+	30.5208i	−1.66247	+	1.55548i
$386$		0			0
$387$	5.14949	+	5.14949i	0.261763	+	0.261763i
$388$		0			0
$389$		−	8.44581i		−	0.428220i	−0.976810	−	0.214110i	$-0.931315\pi$
$389$		−	8.44581i		−	0.428220i	0.976810	−	0.214110i	$-0.0686850\pi$
$390$		0			0
$391$			7.57969i			0.383321i
$392$		0			0
$393$	8.81739	+	8.81739i	0.444778	+	0.444778i
$394$		0			0
$395$	−8.00000	−	0.265977i	−0.402524	−	0.0133828i
$396$		0			0
$397$	18.0769	−	18.0769i	0.907253	−	0.907253i	−0.0887965	−	0.996050i	$-0.528302\pi$
$397$	18.0769	−	18.0769i	0.907253	−	0.907253i	0.996050	+	0.0887965i	$0.0283021\pi$
$398$		0			0
$399$	11.7028			0.585872
$400$		0			0
$401$	−31.8787			−1.59194			−0.795972	−	0.605333i	$-0.793040\pi$
$401$	−31.8787			−1.59194			−0.795972	+	0.605333i	$0.793040\pi$
$402$		0			0
$403$	10.0772	−	10.0772i	0.501980	−	0.501980i
$404$		0			0
$405$	−2.23483	−	0.0743018i	−0.111050	−	0.00369209i
$406$		0			0
$407$	−25.9320	−	25.9320i	−1.28540	−	1.28540i
$408$		0			0
$409$			27.3063i			1.35021i	0.737721	+	0.675106i	$0.235902\pi$
$409$			27.3063i			1.35021i	−0.737721	+	0.675106i	$0.764098\pi$
$410$		0			0
$411$			6.54809i			0.322993i
$412$		0			0
$413$	−15.4549	−	15.4549i	−0.760488	−	0.760488i
$414$		0			0
$415$	3.10355	−	2.90382i	0.152347	−	0.142543i
$416$		0			0
$417$	2.12652	−	2.12652i	0.104136	−	0.104136i
$418$		0			0
$419$	16.1412			0.788551			0.394275	−	0.918992i	$-0.370996\pi$
$419$	16.1412			0.788551			0.394275	+	0.918992i	$0.370996\pi$
$420$		0			0
$421$	−20.6200			−1.00496			−0.502480	−	0.864589i	$-0.667579\pi$
$421$	−20.6200			−1.00496			−0.502480	+	0.864589i	$0.667579\pi$
$422$		0			0
$423$	0.679824	−	0.679824i	0.0330542	−	0.0330542i
$424$		0			0
$425$	−12.2871	+	10.7533i	−0.596010	+	0.521612i
$426$		0			0
$427$	−38.7959	−	38.7959i	−1.87747	−	1.87747i
$428$		0			0
$429$		−	15.9246i		−	0.768847i
$430$		0			0
$431$			2.54848i			0.122756i	0.998115	+	0.0613779i	$0.0195495\pi$
$431$			2.54848i			0.122756i	−0.998115	+	0.0613779i	$0.980451\pi$
$432$		0			0
$433$	6.77996	+	6.77996i	0.325824	+	0.325824i	0.850996	−	0.525172i	$-0.175999\pi$
$433$	6.77996	+	6.77996i	0.325824	+	0.325824i	−0.525172	+	0.850996i	$0.675999\pi$
$434$		0			0
$435$	12.4853	+	13.3440i	0.598623	+	0.639797i
$436$		0			0
$437$	4.29721	−	4.29721i	0.205563	−	0.205563i
$438$		0			0
$439$	15.0698			0.719243			0.359622	−	0.933098i	$-0.382906\pi$
$439$	15.0698			0.719243			0.359622	+	0.933098i	$0.382906\pi$
$440$		0			0
$441$	12.9779			0.617996
$442$		0			0
$443$	−9.69059	+	9.69059i	−0.460414	+	0.460414i	−0.898791	−	0.438377i	$-0.855553\pi$
$443$	−9.69059	+	9.69059i	−0.460414	+	0.460414i	0.438377	+	0.898791i	$0.355553\pi$
$444$		0			0
$445$	−1.31030	+	39.4108i	−0.0621139	+	1.86825i
$446$		0			0
$447$	0.105079	+	0.105079i	0.00497005	+	0.00497005i
$448$		0			0
$449$		−	20.1759i		−	0.952158i	−0.879402	−	0.476079i	$-0.842058\pi$
$449$		−	20.1759i		−	0.952158i	0.879402	−	0.476079i	$-0.157942\pi$
$450$		0			0
$451$			11.7028i			0.551063i
$452$		0			0
$453$	14.5806	+	14.5806i	0.685055	+	0.685055i
$454$		0			0
$455$	−1.18323	+	35.5888i	−0.0554705	+	1.66843i
$456$		0			0
$457$	−0.579686	+	0.579686i	−0.0271165	+	0.0271165i	−0.720535	−	0.693419i	$-0.756104\pi$
$457$	−0.579686	+	0.579686i	−0.0271165	+	0.0271165i	0.693419	+	0.720535i	$0.256104\pi$
$458$		0			0
$459$	−3.26561			−0.152426
$460$		0			0
$461$	−4.40164			−0.205005			−0.102503	−	0.994733i	$-0.532685\pi$
$461$	−4.40164			−0.205005			−0.102503	+	0.994733i	$0.532685\pi$
$462$		0			0
$463$	−0.786155	+	0.786155i	−0.0365357	+	0.0365357i	−0.725139	−	0.688603i	$-0.758224\pi$
$463$	−0.786155	+	0.786155i	−0.0365357	+	0.0365357i	0.688603	+	0.725139i	$0.258224\pi$
$464$		0			0
$465$	−6.11091	−	6.53122i	−0.283386	−	0.302878i
$466$		0			0
$467$	19.6430	+	19.6430i	0.908970	+	0.908970i	0.996189	−	0.0872190i	$-0.0277980\pi$
$467$	19.6430	+	19.6430i	0.908970	+	0.908970i	−0.0872190	+	0.996189i	$0.527798\pi$
$468$		0			0
$469$		−	59.7132i		−	2.75730i
$470$		0			0
$471$		−	13.8306i		−	0.637279i
$472$		0			0
$473$	23.0165	+	23.0165i	1.05830	+	1.05830i
$474$		0			0
$475$	13.0624	+	0.869539i	0.599346	+	0.0398972i
$476$		0			0
$477$	−7.81739	+	7.81739i	−0.357933	+	0.357933i
$478$		0			0
$479$	−30.6274			−1.39940			−0.699701	−	0.714436i	$-0.746684\pi$
$479$	−30.6274			−1.39940			−0.699701	+	0.714436i	$0.746684\pi$
$480$		0			0
$481$	−29.2327			−1.33290
$482$		0			0
$483$	7.33579	−	7.33579i	0.333790	−	0.333790i
$484$		0			0
$485$	−3.05051	+	2.85420i	−0.138517	+	0.129602i
$486$		0			0
$487$	24.7641	+	24.7641i	1.12217	+	1.12217i	0.991415	+	0.130752i	$0.0417392\pi$
$487$	24.7641	+	24.7641i	1.12217	+	1.12217i	0.130752	+	0.991415i	$0.458261\pi$
$488$		0			0
$489$			14.7193i			0.665629i
$490$		0			0
$491$		−	23.3318i		−	1.05295i	−0.850190	−	0.526475i	$-0.823513\pi$
$491$		−	23.3318i		−	1.05295i	0.850190	−	0.526475i	$-0.176487\pi$
$492$		0			0
$493$	18.8713	+	18.8713i	0.849921	+	0.849921i
$494$		0			0
$495$	−9.98896	−	0.332104i	−0.448970	−	0.0149270i
$496$		0			0
$497$	−17.8787	+	17.8787i	−0.801968	+	0.801968i
$498$		0			0
$499$	−40.4051			−1.80878			−0.904389	−	0.426708i	$-0.859673\pi$
$499$	−40.4051			−1.80878			−0.904389	+	0.426708i	$0.859673\pi$
$500$		0			0
$501$	8.57233			0.382984
$502$		0			0
$503$	0.160805	−	0.160805i	0.00716996	−	0.00716996i	−0.703513	−	0.710683i	$-0.748386\pi$
$503$	0.160805	−	0.160805i	0.00716996	−	0.00716996i	0.710683	+	0.703513i	$0.248386\pi$
$504$		0			0
$505$	−3.30089	−	0.109745i	−0.146888	−	0.00488360i
$506$		0			0
$507$	0.216611	+	0.216611i	0.00962002	+	0.00962002i
$508$		0			0
$509$		−	11.4862i		−	0.509115i	−0.967058	−	0.254558i	$-0.918070\pi$
$509$		−	11.4862i		−	0.509115i	0.967058	−	0.254558i	$-0.0819299\pi$
$510$		0			0
$511$			35.5134i			1.57102i
$512$		0			0
$513$	1.85140	+	1.85140i	0.0817411	+	0.0817411i
$514$		0			0
$515$	−21.0468	+	19.6924i	−0.927434	+	0.867749i
$516$		0			0
$517$	3.03858	−	3.03858i	0.133637	−	0.133637i
$518$		0			0
$519$	−0.502150			−0.0220419
$520$		0			0
$521$	16.3744			0.717374			0.358687	−	0.933458i	$-0.383224\pi$
$521$	16.3744			0.717374			0.358687	+	0.933458i	$0.383224\pi$
$522$		0			0
$523$	5.02638	−	5.02638i	0.219788	−	0.219788i	−0.588621	−	0.808409i	$-0.700329\pi$
$523$	5.02638	−	5.02638i	0.219788	−	0.219788i	0.808409	+	0.588621i	$0.200329\pi$
$524$		0			0
$525$	22.2990	+	1.48440i	0.973207	+	0.0647843i
$526$		0			0
$527$	−9.23654	−	9.23654i	−0.402350	−	0.402350i
$528$		0			0
$529$			17.6127i			0.765768i
$530$		0			0
$531$		−	4.88998i		−	0.212207i
$532$		0			0
$533$	6.59619	+	6.59619i	0.285713	+	0.285713i
$534$		0			0
$535$	4.45405	+	4.76041i	0.192565	+	0.205810i
$536$		0			0
$537$	−11.1384	+	11.1384i	−0.480660	+	0.480660i
$538$		0			0
$539$	58.0070			2.49854
$540$		0			0
$541$	−32.3302			−1.38998			−0.694992	−	0.719017i	$-0.744592\pi$
$541$	−32.3302			−1.38998			−0.694992	+	0.719017i	$0.744592\pi$
$542$		0			0
$543$	−5.50126	+	5.50126i	−0.236082	+	0.236082i
$544$		0			0
$545$	−0.720935	+	21.6841i	−0.0308815	+	0.928846i
$546$		0			0
$547$	−8.01165	−	8.01165i	−0.342554	−	0.342554i	0.514773	−	0.857327i	$-0.327876\pi$
$547$	−8.01165	−	8.01165i	−0.342554	−	0.342554i	−0.857327	+	0.514773i	$0.827876\pi$
$548$		0			0
$549$		−	12.2751i		−	0.523890i
$550$		0			0
$551$		−	21.3977i		−	0.911573i
$552$		0			0
$553$	11.3137	+	11.3137i	0.481108	+	0.481108i
$554$		0			0
$555$	−0.609642	+	18.3367i	−0.0258779	+	0.778349i
$556$		0			0
$557$	0.138448	−	0.138448i	0.00586624	−	0.00586624i	−0.704168	−	0.710034i	$-0.748680\pi$
$557$	0.138448	−	0.138448i	0.00586624	−	0.00586624i	0.710034	+	0.704168i	$0.248680\pi$
$558$		0			0
$559$	25.9461			1.09740
$560$		0			0
$561$	−14.5962			−0.616251
$562$		0			0
$563$	14.7843	−	14.7843i	0.623082	−	0.623082i	−0.323236	−	0.946318i	$-0.604771\pi$
$563$	14.7843	−	14.7843i	0.623082	−	0.623082i	0.946318	+	0.323236i	$0.104771\pi$
$564$		0			0
$565$	−10.0037	−	10.6918i	−0.420858	−	0.449805i
$566$		0			0
$567$	3.16053	+	3.16053i	0.132730	+	0.132730i
$568$		0			0
$569$		−	29.9558i		−	1.25581i	−0.778288	−	0.627907i	$-0.783912\pi$
$569$		−	29.9558i		−	1.25581i	0.778288	−	0.627907i	$-0.216088\pi$
$570$		0			0
$571$		−	8.52134i		−	0.356607i	−0.983976	−	0.178303i	$-0.942939\pi$
$571$		−	8.52134i		−	0.356607i	0.983976	−	0.178303i	$-0.0570609\pi$
$572$		0			0
$573$	−6.61827	−	6.61827i	−0.276482	−	0.276482i
$574$		0			0
$575$	8.73314	−	7.64301i	0.364197	−	0.318736i
$576$		0			0
$577$	10.9779	−	10.9779i	0.457017	−	0.457017i	−0.440658	−	0.897675i	$-0.645255\pi$
$577$	10.9779	−	10.9779i	0.457017	−	0.457017i	0.897675	+	0.440658i	$0.145255\pi$
$578$		0			0
$579$	−24.2904			−1.00947
$580$		0			0
$581$	−8.49571			−0.352461
$582$		0			0
$583$	−34.9411	+	34.9411i	−1.44711	+	1.44711i
$584$		0			0
$585$	−5.81739	+	5.44301i	−0.240519	+	0.225041i
$586$		0			0
$587$	−18.0174	−	18.0174i	−0.743657	−	0.743657i	0.229623	−	0.973280i	$-0.426251\pi$
$587$	−18.0174	−	18.0174i	−0.743657	−	0.743657i	−0.973280	+	0.229623i	$0.926251\pi$
$588$		0			0
$589$			10.4731i			0.431536i
$590$		0			0
$591$			2.60140i			0.107007i
$592$		0			0
$593$	−25.8906	−	25.8906i	−1.06320	−	1.06320i	−0.997863	−	0.0653359i	$-0.979188\pi$
$593$	−25.8906	−	25.8906i	−1.06320	−	1.06320i	−0.0653359	−	0.997863i	$-0.520812\pi$
$594$		0			0
$595$	32.6200	+	1.08452i	1.33729	+	0.0444611i
$596$		0			0
$597$	0.312822	−	0.312822i	0.0128030	−	0.0128030i
$598$		0			0
$599$	8.89517			0.363447			0.181723	−	0.983350i	$-0.441832\pi$
$599$	8.89517			0.363447			0.181723	+	0.983350i	$0.441832\pi$
$600$		0			0
$601$	35.3393			1.44152			0.720761	−	0.693184i	$-0.243793\pi$
$601$	35.3393			1.44152			0.720761	+	0.693184i	$0.243793\pi$
$602$		0			0
$603$	9.44670	−	9.44670i	0.384699	−	0.384699i
$604$		0			0
$605$	−20.0641	−	0.667075i	−0.815724	−	0.0271205i
$606$		0			0
$607$	−4.90926	−	4.90926i	−0.199261	−	0.199261i	0.600422	−	0.799683i	$-0.294999\pi$
$607$	−4.90926	−	4.90926i	−0.199261	−	0.199261i	−0.799683	+	0.600422i	$0.794999\pi$
$608$		0			0
$609$		−	36.5282i		−	1.48020i
$610$		0			0
$611$		−	3.42535i		−	0.138575i
$612$		0			0
$613$	1.87894	+	1.87894i	0.0758896	+	0.0758896i	0.744033	−	0.668143i	$-0.232911\pi$
$613$	1.87894	+	1.87894i	0.0758896	+	0.0758896i	−0.668143	+	0.744033i	$0.732911\pi$
$614$		0			0
$615$	4.27512	−	4.00000i	0.172390	−	0.161296i
$616$		0			0
$617$	−5.07260	+	5.07260i	−0.204215	+	0.204215i	−0.801803	−	0.597588i	$-0.796126\pi$
$617$	−5.07260	+	5.07260i	−0.204215	+	0.204215i	0.597588	+	0.801803i	$0.296126\pi$
$618$		0			0
$619$	−46.2769			−1.86003			−0.930013	−	0.367527i	$-0.880204\pi$
$619$	−46.2769			−1.86003			−0.930013	+	0.367527i	$0.880204\pi$
$620$		0			0
$621$	2.32106			0.0931410
$622$		0			0
$623$	55.7352	−	55.7352i	2.23299	−	2.23299i
$624$		0			0
$625$	24.7794	+	3.31371i	0.991177	+	0.132548i
$626$		0			0
$627$	8.27512	+	8.27512i	0.330477	+	0.330477i
$628$		0			0
$629$			26.7941i			1.06835i
$630$		0			0
$631$			36.6457i			1.45884i	0.684066	+	0.729421i	$0.260210\pi$
$631$			36.6457i			1.45884i	−0.684066	+	0.729421i	$0.739790\pi$
$632$		0			0
$633$	3.75214	+	3.75214i	0.149134	+	0.149134i
$634$		0			0
$635$	22.0355	+	23.5511i	0.874453	+	0.934598i
$636$		0			0
$637$	32.6952	−	32.6952i	1.29543	−	1.29543i
$638$		0			0
$639$	−5.65685			−0.223782
$640$		0			0
$641$	−12.1520			−0.479976			−0.239988	−	0.970776i	$-0.577143\pi$
$641$	−12.1520			−0.479976			−0.239988	+	0.970776i	$0.577143\pi$
$642$		0			0
$643$	6.53122	−	6.53122i	0.257566	−	0.257566i	−0.566497	−	0.824064i	$-0.691702\pi$
$643$	6.53122	−	6.53122i	0.257566	−	0.257566i	0.824064	+	0.566497i	$0.191702\pi$
$644$		0			0
$645$	0.541101	−	16.2751i	0.0213058	−	0.640832i
$646$		0			0
$647$	−17.6192	−	17.6192i	−0.692681	−	0.692681i	0.270140	−	0.962821i	$-0.412930\pi$
$647$	−17.6192	−	17.6192i	−0.692681	−	0.692681i	−0.962821	+	0.270140i	$0.912930\pi$
$648$		0			0
$649$		−	21.8566i		−	0.857946i
$650$		0			0
$651$			17.8787i			0.700720i
$652$		0			0
$653$	0.727677	+	0.727677i	0.0284762	+	0.0284762i	0.721202	−	0.692725i	$-0.243590\pi$
$653$	0.727677	+	0.727677i	0.0284762	+	0.0284762i	−0.692725	+	0.721202i	$0.743590\pi$
$654$		0			0
$655$	0.926519	−	27.8676i	0.0362021	−	1.08888i
$656$		0			0
$657$	−5.61827	+	5.61827i	−0.219190	+	0.219190i
$658$		0			0
$659$	−44.9004			−1.74907			−0.874535	−	0.484963i	$-0.838833\pi$
$659$	−44.9004			−1.74907			−0.874535	+	0.484963i	$0.838833\pi$
$660$		0			0
$661$	14.9320			0.580786			0.290393	−	0.956907i	$-0.406214\pi$
$661$	14.9320			0.580786			0.290393	+	0.956907i	$0.406214\pi$
$662$		0			0
$663$	−8.22703	+	8.22703i	−0.319511	+	0.319511i
$664$		0			0
$665$	−17.8787	−	19.1084i	−0.693305	−	0.740991i
$666$		0			0
$667$	−13.4130	−	13.4130i	−0.519352	−	0.519352i
$668$		0			0
$669$			7.75214i			0.299715i
$670$		0			0
$671$		−	54.8657i		−	2.11807i
$672$		0			0
$673$	2.55583	+	2.55583i	0.0985200	+	0.0985200i	0.754649	−	0.656129i	$-0.227807\pi$
$673$	2.55583	+	2.55583i	0.0985200	+	0.0985200i	−0.656129	+	0.754649i	$0.727807\pi$
$674$		0			0
$675$	3.29289	+	3.76256i	0.126744	+	0.144821i
$676$		0			0
$677$	17.7147	−	17.7147i	0.680832	−	0.680832i	−0.279356	−	0.960188i	$-0.590121\pi$
$677$	17.7147	−	17.7147i	0.680832	−	0.680832i	0.960188	+	0.279356i	$0.0901209\pi$
$678$		0			0
$679$	8.35052			0.320464
$680$		0			0
$681$	13.4584			0.515725
$682$		0			0
$683$	11.3968	−	11.3968i	0.436086	−	0.436086i	−0.454606	−	0.890693i	$-0.650220\pi$
$683$	11.3968	−	11.3968i	0.436086	−	0.436086i	0.890693	+	0.454606i	$0.150220\pi$
$684$		0			0
$685$	10.6918	−	10.0037i	0.408511	−	0.382221i
$686$		0			0
$687$	−3.71841	−	3.71841i	−0.141866	−	0.141866i
$688$		0			0
$689$			39.3886i			1.50058i
$690$		0			0
$691$			6.94671i			0.264265i	0.991232	+	0.132133i	$0.0421825\pi$
$691$			6.94671i			0.264265i	−0.991232	+	0.132133i	$0.957818\pi$
$692$		0			0
$693$	14.1265	+	14.1265i	0.536622	+	0.536622i
$694$		0			0
$695$	−6.72093	−	0.223452i	−0.254940	−	0.00847601i
$696$		0			0
$697$	6.04594	−	6.04594i	0.229006	−	0.229006i
$698$		0			0
$699$	−4.13998			−0.156588
$700$		0			0
$701$	−9.70621			−0.366598			−0.183299	−	0.983057i	$-0.558678\pi$
$701$	−9.70621			−0.366598			−0.183299	+	0.983057i	$0.558678\pi$
$702$		0			0
$703$	15.1906	−	15.1906i	0.572924	−	0.572924i
$704$		0			0
$705$	−2.14860	−	0.0714349i	−0.0809211	−	0.00269039i
$706$		0			0
$707$	4.66817	+	4.66817i	0.175565	+	0.175565i
$708$		0			0
$709$			10.7414i			0.403401i	0.979447	+	0.201700i	$0.0646467\pi$
$709$			10.7414i			0.403401i	−0.979447	+	0.201700i	$0.935353\pi$
$710$		0			0
$711$			3.57969i			0.134249i
$712$		0			0
$713$	6.56496	+	6.56496i	0.245860	+	0.245860i
$714$		0			0
$715$	−26.0018	+	24.3284i	−0.972411	+	0.909832i
$716$		0			0
$717$	8.93933	−	8.93933i	0.333845	−	0.333845i
$718$		0			0
$719$	−43.8640			−1.63585			−0.817925	−	0.575325i	$-0.804876\pi$
$719$	−43.8640			−1.63585			−0.817925	+	0.575325i	$0.804876\pi$
$720$		0			0
$721$	57.6139			2.14565
$722$		0			0
$723$	−10.2990	+	10.2990i	−0.383023	+	0.383023i
$724$		0			0
$725$	2.71411	−	40.7721i	0.100799	−	1.51424i
$726$		0			0
$727$	−9.95522	−	9.95522i	−0.369219	−	0.369219i	0.497974	−	0.867192i	$-0.334078\pi$
$727$	−9.95522	−	9.95522i	−0.369219	−	0.369219i	−0.867192	+	0.497974i	$0.834078\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	23.7817i		−	0.879599i
$732$		0			0
$733$	16.9924	+	16.9924i	0.627628	+	0.627628i	0.947471	−	0.319843i	$-0.103630\pi$
$733$	16.9924	+	16.9924i	0.627628	+	0.627628i	−0.319843	+	0.947471i	$0.603630\pi$
$734$		0			0
$735$	−19.8267	−	21.1904i	−0.731319	−	0.781620i
$736$		0			0
$737$	42.2236	−	42.2236i	1.55533	−	1.55533i
$738$		0			0
$739$	−27.9025			−1.02641			−0.513205	−	0.858266i	$-0.671542\pi$
$739$	−27.9025			−1.02641			−0.513205	+	0.858266i	$0.671542\pi$
$740$		0			0
$741$	9.32842			0.342688
$742$		0			0
$743$	−20.2907	+	20.2907i	−0.744395	+	0.744395i	−0.973420	−	0.229025i	$-0.926446\pi$
$743$	−20.2907	+	20.2907i	−0.744395	+	0.744395i	0.229025	+	0.973420i	$0.426446\pi$
$744$		0			0
$745$	0.0110415	−	0.332104i	0.000404530	−	0.0121674i
$746$		0			0
$747$	−1.34403	−	1.34403i	−0.0491756	−	0.0491756i
$748$		0			0
$749$		−	13.0312i		−	0.476150i
$750$		0			0
$751$		−	1.97054i		−	0.0719061i	−0.999353	−	0.0359531i	$-0.988553\pi$
$751$		−	1.97054i		−	0.0719061i	0.999353	−	0.0359531i	$-0.0114467\pi$
$752$		0			0
$753$	13.1146	+	13.1146i	0.477922	+	0.477922i
$754$		0			0
$755$	1.53211	−	46.0824i	0.0557591	−	1.67711i
$756$		0			0
$757$	9.13933	−	9.13933i	0.332175	−	0.332175i	−0.521237	−	0.853412i	$-0.674529\pi$
$757$	9.13933	−	9.13933i	0.332175	−	0.332175i	0.853412	+	0.521237i	$0.174529\pi$
$758$		0			0
$759$	10.3744			0.376566
$760$		0			0
$761$	−23.7800			−0.862023			−0.431011	−	0.902346i	$-0.641843\pi$
$761$	−23.7800			−0.862023			−0.431011	+	0.902346i	$0.641843\pi$
$762$		0			0
$763$	30.6660	−	30.6660i	1.11018	−	1.11018i
$764$		0			0
$765$	4.98896	+	5.33210i	0.180376	+	0.192783i
$766$		0			0
$767$	−12.3193	−	12.3193i	−0.444824	−	0.444824i
$768$		0			0
$769$			17.7022i			0.638359i	0.947694	+	0.319180i	$0.103407\pi$
$769$			17.7022i			0.638359i	−0.947694	+	0.319180i	$0.896593\pi$
$770$		0			0
$771$			18.7362i			0.674766i
$772$		0			0
$773$	9.30178	+	9.30178i	0.334562	+	0.334562i	0.854316	−	0.519754i	$-0.173976\pi$
$773$	9.30178	+	9.30178i	0.334562	+	0.334562i	−0.519754	+	0.854316i	$0.673976\pi$
$774$		0			0
$775$	−1.32842	+	19.9558i	−0.0477181	+	0.716835i
$776$		0			0
$777$	25.9320	−	25.9320i	0.930305	−	0.930305i
$778$		0			0
$779$	−6.85534			−0.245618
$780$		0			0
$781$	−25.2843			−0.904742
$782$		0			0
$783$	5.77880	−	5.77880i	0.206518	−	0.206518i
$784$		0			0
$785$	−22.5826	+	21.1293i	−0.806008	+	0.754138i
$786$		0			0
$787$	18.1642	+	18.1642i	0.647484	+	0.647484i	0.952384	−	0.304900i	$-0.0986230\pi$
$787$	18.1642	+	18.1642i	0.647484	+	0.647484i	−0.304900	+	0.952384i	$0.598623\pi$
$788$		0			0
$789$			31.9338i			1.13687i
$790$		0			0
$791$			29.2678i			1.04064i
$792$		0			0
$793$	−30.9246	−	30.9246i	−1.09817	−	1.09817i
$794$		0			0
$795$	24.7071	+	0.821440i	0.876270	+	0.0291335i
$796$		0			0
$797$	−4.75098	+	4.75098i	−0.168289	+	0.168289i	−0.786227	−	0.617938i	$-0.787968\pi$
$797$	−4.75098	+	4.75098i	−0.168289	+	0.168289i	0.617938	+	0.786227i	$0.287968\pi$
$798$		0			0
$799$	−3.13961			−0.111071
$800$		0			0
$801$	17.6348			0.623094
$802$		0			0
$803$	−25.1118	+	25.1118i	−0.886176	+	0.886176i
$804$		0			0
$805$	−23.1850	−	0.770835i	−0.817164	−	0.0271684i
$806$		0			0
$807$	4.82260	+	4.82260i	0.169764	+	0.169764i
$808$		0			0
$809$		−	37.7891i		−	1.32859i	−0.747469	−	0.664297i	$-0.768731\pi$
$809$		−	37.7891i		−	1.32859i	0.747469	−	0.664297i	$-0.231269\pi$
$810$		0			0
$811$		−	44.4215i		−	1.55985i	−0.625872	−	0.779926i	$-0.715257\pi$
$811$		−	44.4215i		−	1.55985i	0.625872	−	0.779926i	$-0.284743\pi$
$812$		0			0
$813$	−1.93845	−	1.93845i	−0.0679843	−	0.0679843i
$814$		0			0
$815$	24.0337	−	22.4871i	0.841865	−	0.787687i
$816$		0			0
$817$	−13.4828	+	13.4828i	−0.471702	+	0.471702i
$818$		0			0
$819$	15.9246			0.556451
$820$		0			0
$821$	−29.3648			−1.02484			−0.512420	−	0.858735i	$-0.671251\pi$
$821$	−29.3648			−1.02484			−0.512420	+	0.858735i	$0.671251\pi$
$822$		0			0
$823$	−22.7402	+	22.7402i	−0.792674	+	0.792674i	−0.981928	−	0.189254i	$-0.939393\pi$
$823$	−22.7402	+	22.7402i	−0.792674	+	0.792674i	0.189254	+	0.981928i	$0.439393\pi$
$824$		0			0
$825$	14.7181	+	16.8174i	0.512420	+	0.585506i
$826$		0			0
$827$	−1.50001	−	1.50001i	−0.0521605	−	0.0521605i	0.680545	−	0.732706i	$-0.261743\pi$
$827$	−1.50001	−	1.50001i	−0.0521605	−	0.0521605i	−0.732706	+	0.680545i	$0.761743\pi$
$828$		0			0
$829$			29.0642i			1.00944i	0.863283	+	0.504721i	$0.168405\pi$
$829$			29.0642i			1.00944i	−0.863283	+	0.504721i	$0.831595\pi$
$830$		0			0
$831$		−	10.9684i		−	0.380490i
$832$		0			0
$833$	−29.9678	−	29.9678i	−1.03832	−	1.03832i
$834$		0			0
$835$	−13.0962	−	13.9969i	−0.453212	−	0.484384i
$836$		0			0
$837$	−2.82843	+	2.82843i	−0.0977647	+	0.0977647i
$838$		0			0
$839$	38.3779			1.32495			0.662476	−	0.749083i	$-0.269505\pi$
$839$	38.3779			1.32495			0.662476	+	0.749083i	$0.269505\pi$
$840$		0			0
$841$	−37.7891			−1.30307
$842$		0			0
$843$	−3.21104	+	3.21104i	−0.110594	+	0.110594i
$844$		0			0
$845$	0.0227612	−	0.684605i	0.000783008	−	0.0235511i
$846$		0			0
$847$	28.3750	+	28.3750i	0.974976	+	0.974976i
$848$		0			0
$849$			11.1906i			0.384060i
$850$		0			0
$851$		−	19.0442i		−	0.652826i
$852$		0			0
$853$	28.1467	+	28.1467i	0.963724	+	0.963724i	0.999365	−	0.0356404i	$-0.0113471\pi$
$853$	28.1467	+	28.1467i	0.963724	+	0.963724i	−0.0356404	+	0.999365i	$0.511347\pi$
$854$		0			0
$855$	0.194542	−	5.85140i	0.00665320	−	0.200114i
$856$		0			0
$857$	−13.5990	+	13.5990i	−0.464533	+	0.464533i	−0.900138	−	0.435605i	$-0.856534\pi$
$857$	−13.5990	+	13.5990i	−0.464533	+	0.464533i	0.435605	+	0.900138i	$0.356534\pi$
$858$		0			0
$859$	−14.9155			−0.508910			−0.254455	−	0.967085i	$-0.581896\pi$
$859$	−14.9155			−0.508910			−0.254455	+	0.967085i	$0.581896\pi$
$860$		0			0
$861$	−11.7028			−0.398830
$862$		0			0
$863$	−8.95495	+	8.95495i	−0.304830	+	0.304830i	−0.842900	−	0.538070i	$-0.819154\pi$
$863$	−8.95495	+	8.95495i	−0.304830	+	0.304830i	0.538070	+	0.842900i	$0.319154\pi$
$864$		0			0
$865$	0.767147	+	0.819913i	0.0260838	+	0.0278779i
$866$		0			0
$867$	−4.48008	−	4.48008i	−0.152152	−	0.152152i
$868$		0			0
$869$			16.0000i			0.542763i
$870$		0			0
$871$		−	47.5980i		−	1.61280i
$872$		0			0
$873$	1.32106	+	1.32106i	0.0447112	+	0.0447112i
$874$		0			0
$875$	−31.6430	−	38.6776i	−1.06973	−	1.30754i
$876$		0			0
$877$	−37.8274	+	37.8274i	−1.27734	+	1.27734i	−0.335190	+	0.942151i	$0.608800\pi$
$877$	−37.8274	+	37.8274i	−1.27734	+	1.27734i	−0.942151	+	0.335190i	$0.891200\pi$
$878$		0			0
$879$	−21.3544			−0.720267
$880$		0			0
$881$	23.7119			0.798876			0.399438	−	0.916760i	$-0.369205\pi$
$881$	23.7119			0.798876			0.399438	+	0.916760i	$0.369205\pi$
$882$		0			0
$883$	−9.39338	+	9.39338i	−0.316113	+	0.316113i	−0.847272	−	0.531159i	$-0.821757\pi$
$883$	−9.39338	+	9.39338i	−0.316113	+	0.316113i	0.531159	+	0.847272i	$0.321757\pi$
$884$		0			0
$885$	−7.98438	+	7.47055i	−0.268392	+	0.251120i
$886$		0			0
$887$	0.825014	+	0.825014i	0.0277013	+	0.0277013i	0.720822	−	0.693120i	$-0.243765\pi$
$887$	0.825014	+	0.825014i	0.0277013	+	0.0277013i	−0.693120	+	0.720822i	$0.743765\pi$
$888$		0			0
$889$		−	64.4693i		−	2.16223i
$890$		0			0
$891$			4.46967i			0.149739i
$892$		0			0
$893$	1.77996	+	1.77996i	0.0595641	+	0.0595641i
$894$		0			0
$895$	35.2034	+	1.17041i	1.17672	+	0.0391226i
$896$		0			0
$897$	5.84744	−	5.84744i	0.195240	−	0.195240i
$898$		0			0
$899$	32.6898			1.09027
$900$		0			0
$901$	36.1028			1.20276
$902$		0			0
$903$	−23.0165	+	23.0165i	−0.765941	+	0.765941i
$904$		0			0
$905$	17.3869	+	0.578065i	0.577961	+	0.0192155i
$906$		0			0
$907$	−1.59189	−	1.59189i	−0.0528578	−	0.0528578i	0.680184	−	0.733042i	$-0.261900\pi$
$907$	−1.59189	−	1.59189i	−0.0528578	−	0.0528578i	−0.733042	+	0.680184i	$0.761900\pi$
$908$		0			0
$909$			1.47702i			0.0489897i
$910$		0			0
$911$			55.3926i			1.83524i	0.397458	+	0.917620i	$0.369892\pi$
$911$			55.3926i			1.83524i	−0.397458	+	0.917620i	$0.630108\pi$
$912$		0			0
$913$	−6.00737	−	6.00737i	−0.198815	−	0.198815i
$914$		0			0
$915$	−20.0429	+	18.7530i	−0.662597	+	0.619956i
$916$		0			0
$917$	−39.4108	+	39.4108i	−1.30146	+	1.30146i
$918$		0			0
$919$	−4.31369			−0.142295			−0.0711477	−	0.997466i	$-0.522666\pi$
$919$	−4.31369			−0.142295			−0.0711477	+	0.997466i	$0.522666\pi$
$920$		0			0
$921$	−6.26775			−0.206529
$922$		0			0
$923$	−14.2513	+	14.2513i	−0.469086	+	0.469086i
$924$		0			0
$925$	30.8716	−	27.0180i	1.01505	−	0.888346i
$926$		0			0
$927$	9.11459	+	9.11459i	0.299363	+	0.299363i
$928$		0			0
$929$		−	19.9774i		−	0.655436i	−0.944776	−	0.327718i	$-0.893720\pi$
$929$		−	19.9774i		−	0.655436i	0.944776	−	0.327718i	$-0.106280\pi$
$930$		0			0
$931$			33.9797i			1.11364i
$932$		0			0
$933$	−16.6421	−	16.6421i	−0.544839	−	0.544839i
$934$		0			0
$935$	22.2990	+	23.8327i	0.729255	+	0.779414i
$936$		0			0
$937$	−8.97792	+	8.97792i	−0.293296	+	0.293296i	−0.838381	−	0.545085i	$-0.816497\pi$
$937$	−8.97792	+	8.97792i	−0.293296	+	0.293296i	0.545085	+	0.838381i	$0.316497\pi$
$938$		0			0
$939$	26.3094			0.858574
$940$		0			0
$941$	−37.9831			−1.23821			−0.619107	−	0.785307i	$-0.712505\pi$
$941$	−37.9831			−1.23821			−0.619107	+	0.785307i	$0.712505\pi$
$942$		0			0
$943$	−4.29721	+	4.29721i	−0.139936	+	0.139936i
$944$		0			0
$945$	0.332104	−	9.98896i	0.0108034	−	0.324941i
$946$		0			0
$947$	39.0815	+	39.0815i	1.26998	+	1.26998i	0.946099	+	0.323878i	$0.104987\pi$
$947$	39.0815	+	39.0815i	1.26998	+	1.26998i	0.323878	+	0.946099i	$0.395013\pi$
$948$		0			0
$949$			28.3081i			0.918921i
$950$		0			0
$951$			10.7049i			0.347131i
$952$		0			0
$953$	−1.27232	−	1.27232i	−0.0412146	−	0.0412146i	0.686199	−	0.727414i	$-0.259278\pi$
$953$	−1.27232	−	1.27232i	−0.0412146	−	0.0412146i	−0.727414	+	0.686199i	$0.759278\pi$
$954$		0			0
$955$	−0.695439	+	20.9172i	−0.0225039	+	0.676866i
$956$		0			0
$957$	25.8293	−	25.8293i	0.834943	−	0.834943i
$958$		0			0
$959$	−29.2678			−0.945106
$960$		0			0
$961$	15.0000			0.483871
$962$		0			0
$963$	2.06155	−	2.06155i	0.0664326	−	0.0664326i
$964$		0			0
$965$	37.1090	+	39.6614i	1.19458	+	1.27675i
$966$		0			0
$967$	−1.67778	−	1.67778i	−0.0539537	−	0.0539537i	0.679615	−	0.733569i	$-0.262147\pi$
$967$	−1.67778	−	1.67778i	−0.0539537	−	0.0539537i	−0.733569	+	0.679615i	$0.762147\pi$
$968$		0			0
$969$		−	8.55025i		−	0.274674i
$970$		0			0
$971$		−	15.9887i		−	0.513102i	−0.966531	−	0.256551i	$-0.917414\pi$
$971$		−	15.9887i		−	0.513102i	0.966531	−	0.256551i	$-0.0825862\pi$
$972$		0			0
$973$	9.50484	+	9.50484i	0.304711	+	0.304711i
$974$		0			0
$975$	17.7747	+	1.18323i	0.569247	+	0.0378936i
$976$		0			0
$977$	16.7754	−	16.7754i	0.536692	−	0.536692i	−0.385864	−	0.922556i	$-0.626096\pi$
$977$	16.7754	−	16.7754i	0.536692	−	0.536692i	0.922556	+	0.385864i	$0.126096\pi$
$978$		0			0
$979$	78.8215			2.51915
$980$		0			0
$981$	9.70279			0.309786
$982$		0			0
$983$	34.3367	−	34.3367i	1.09517	−	1.09517i	0.100203	−	0.994967i	$-0.468051\pi$
$983$	34.3367	−	34.3367i	1.09517	−	1.09517i	0.994967	−	0.100203i	$-0.0319492\pi$
$984$		0			0
$985$	4.24758	−	3.97423i	0.135339	−	0.126629i
$986$		0			0
$987$	3.03858	+	3.03858i	0.0967192	+	0.0967192i
$988$		0			0
$989$			16.9031i			0.537487i
$990$		0			0
$991$		−	26.7414i		−	0.849468i	−0.905318	−	0.424734i	$-0.860368\pi$
$991$		−	26.7414i		−	0.849468i	0.905318	−	0.424734i	$-0.139632\pi$
$992$		0			0
$993$	−9.75952	−	9.75952i	−0.309709	−	0.309709i
$994$		0			0
$995$	−0.988685	−	0.0328709i	−0.0313434	−	0.00104208i
$996$		0			0
$997$	−9.80177	+	9.80177i	−0.310425	+	0.310425i	−0.845074	−	0.534649i	$-0.820444\pi$
$997$	−9.80177	+	9.80177i	−0.310425	+	0.310425i	0.534649	+	0.845074i	$0.320444\pi$
$998$		0			0
$999$	8.20494			0.259593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.2.w.c.223.2	yes	8
3.2	odd	2		1440.2.x.q.703.1		8
4.3	odd	2		480.2.w.d.223.4	yes	8
5.2	odd	4		480.2.w.d.127.4	yes	8
5.3	odd	4		2400.2.w.i.607.1		8
5.4	even	2		2400.2.w.j.2143.4		8
8.3	odd	2		960.2.w.f.703.1		8
8.5	even	2		960.2.w.e.703.3		8
12.11	even	2		1440.2.x.r.703.1		8
15.2	even	4		1440.2.x.r.127.1		8
20.3	even	4		2400.2.w.j.607.4		8
20.7	even	4	inner	480.2.w.c.127.2	✓	8
20.19	odd	2		2400.2.w.i.2143.1		8
40.27	even	4		960.2.w.e.127.3		8
40.37	odd	4		960.2.w.f.127.1		8
60.47	odd	4		1440.2.x.q.127.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.w.c.127.2	✓	8	20.7	even	4	inner
480.2.w.c.223.2	yes	8	1.1	even	1	trivial
480.2.w.d.127.4	yes	8	5.2	odd	4
480.2.w.d.223.4	yes	8	4.3	odd	2
960.2.w.e.127.3		8	40.27	even	4
960.2.w.e.703.3		8	8.5	even	2
960.2.w.f.127.1		8	40.37	odd	4
960.2.w.f.703.1		8	8.3	odd	2
1440.2.x.q.127.1		8	60.47	odd	4
1440.2.x.q.703.1		8	3.2	odd	2
1440.2.x.r.127.1		8	15.2	even	4
1440.2.x.r.703.1		8	12.11	even	2
2400.2.w.i.607.1		8	5.3	odd	4
2400.2.w.i.2143.1		8	20.19	odd	2
2400.2.w.j.607.4		8	20.3	even	4
2400.2.w.j.2143.4		8	5.4	even	2

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:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(2.23483 + 0.0743018i) q^{5} +(-3.16053 - 3.16053i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(2.23483 + 0.0743018i) q^{5} +(-3.16053 - 3.16053i) q^{7} -1.00000i q^{9} -4.46967i q^{11} +(-2.51929 - 2.51929i) q^{13} +(-1.63280 + 1.52773i) q^{15} +(-2.30913 + 2.30913i) q^{17} +2.61827 q^{19} +4.46967 q^{21} +(1.64124 - 1.64124i) q^{23} +(4.98896 + 0.332104i) q^{25} +(0.707107 + 0.707107i) q^{27} -8.17246i q^{29} +4.00000i q^{31} +(3.16053 + 3.16053i) q^{33} +(-6.82843 - 7.29809i) q^{35} +(5.80177 - 5.80177i) q^{37} +3.56282 q^{39} -2.61827 q^{41} +(-5.14949 + 5.14949i) q^{43} +(0.0743018 - 2.23483i) q^{45} +(0.679824 + 0.679824i) q^{47} +12.9779i q^{49} -3.26561i q^{51} +(-7.81739 - 7.81739i) q^{53} +(0.332104 - 9.98896i) q^{55} +(-1.85140 + 1.85140i) q^{57} +4.88998 q^{59} +12.2751 q^{61} +(-3.16053 + 3.16053i) q^{63} +(-5.44301 - 5.81739i) q^{65} +(9.44670 + 9.44670i) q^{67} +2.32106i q^{69} -5.65685i q^{71} +(-5.61827 - 5.61827i) q^{73} +(-3.76256 + 3.29289i) q^{75} +(-14.1265 + 14.1265i) q^{77} -3.57969 q^{79} -1.00000 q^{81} +(1.34403 - 1.34403i) q^{83} +(-5.33210 + 4.98896i) q^{85} +(5.77880 + 5.77880i) q^{87} +17.6348i q^{89} +15.9246i q^{91} +(-2.82843 - 2.82843i) q^{93} +(5.85140 + 0.194542i) q^{95} +(-1.32106 + 1.32106i) q^{97} -4.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} - 12 q^{13} - 4 q^{15} - 4 q^{17} - 8 q^{19} - 4 q^{25} + 4 q^{33} - 32 q^{35} + 12 q^{37} + 24 q^{39} + 8 q^{41} + 24 q^{43} + 4 q^{45} - 24 q^{47} + 4 q^{53} + 4 q^{55} - 8 q^{57} + 16 q^{59} + 24 q^{61} - 4 q^{63} + 4 q^{65} + 24 q^{67} - 16 q^{73} - 32 q^{77} - 16 q^{79} - 8 q^{81} - 16 q^{83} - 44 q^{85} - 4 q^{87} + 40 q^{95} + 32 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 - 12 * q^13 - 4 * q^15 - 4 * q^17 - 8 * q^19 - 4 * q^25 + 4 * q^33 - 32 * q^35 + 12 * q^37 + 24 * q^39 + 8 * q^41 + 24 * q^43 + 4 * q^45 - 24 * q^47 + 4 * q^53 + 4 * q^55 - 8 * q^57 + 16 * q^59 + 24 * q^61 - 4 * q^63 + 4 * q^65 + 24 * q^67 - 16 * q^73 - 32 * q^77 - 16 * q^79 - 8 * q^81 - 16 * q^83 - 44 * q^85 - 4 * q^87 + 40 * q^95 + 32 * q^97

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