LMFDB - Embedded newform 960.2.w.f.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(127,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, 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("960.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.w (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:	$7.66563859404$
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:	no (minimal twist has level 480)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$-3.16053i$ of defining polynomial
Character	$\chi$	$=$	960.127
Dual form			960.2.w.f.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-2.23483 + 0.0743018i) q^{5} +(3.16053 - 3.16053i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.23483 + 0.0743018i) q^{5} +(3.16053 - 3.16053i) q^{7} +1.00000i q^{9} +4.46967i q^{11} +(2.51929 - 2.51929i) q^{13} +(1.63280 + 1.52773i) q^{15} +(-2.30913 - 2.30913i) q^{17} +2.61827 q^{19} -4.46967 q^{21} +(-1.64124 - 1.64124i) q^{23} +(4.98896 - 0.332104i) q^{25} +(0.707107 - 0.707107i) q^{27} -8.17246i q^{29} +4.00000i q^{31} +(3.16053 - 3.16053i) q^{33} +(-6.82843 + 7.29809i) q^{35} +(-5.80177 - 5.80177i) q^{37} -3.56282 q^{39} -2.61827 q^{41} +(-5.14949 - 5.14949i) q^{43} +(-0.0743018 - 2.23483i) q^{45} +(-0.679824 + 0.679824i) q^{47} -12.9779i q^{49} +3.26561i q^{51} +(7.81739 - 7.81739i) q^{53} +(-0.332104 - 9.98896i) q^{55} +(-1.85140 - 1.85140i) q^{57} +4.88998 q^{59} -12.2751 q^{61} +(3.16053 + 3.16053i) q^{63} +(-5.44301 + 5.81739i) q^{65} +(9.44670 - 9.44670i) q^{67} +2.32106i q^{69} -5.65685i q^{71} +(-5.61827 + 5.61827i) q^{73} +(-3.76256 - 3.29289i) q^{75} +(14.1265 + 14.1265i) q^{77} +3.57969 q^{79} -1.00000 q^{81} +(1.34403 + 1.34403i) q^{83} +(5.33210 + 4.98896i) q^{85} +(-5.77880 + 5.77880i) q^{87} -17.6348i q^{89} -15.9246i q^{91} +(2.82843 - 2.82843i) q^{93} +(-5.85140 + 0.194542i) q^{95} +(-1.32106 - 1.32106i) q^{97} -4.46967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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	0.218799	−	0.975770i	$-0.429786\pi$
$7$	3.16053	−	3.16053i	1.19457	−	1.19457i	0.975770	−	0.218799i	$-0.0702137\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			4.46967i			1.34766i	0.738889	+	0.673828i	$0.235351\pi$
$11$			4.46967i			1.34766i	−0.738889	+	0.673828i	$0.764649\pi$
$12$		0			0
$13$	2.51929	−	2.51929i	0.698726	−	0.698726i	−0.265410	−	0.964136i	$-0.585507\pi$
$13$	2.51929	−	2.51929i	0.698726	−	0.698726i	0.964136	+	0.265410i	$0.0855072\pi$
$14$		0			0
$15$	1.63280	+	1.52773i	0.421588	+	0.394457i
$16$		0			0
$17$	−2.30913	−	2.30913i	−0.560047	−	0.560047i	0.369273	−	0.929321i	$-0.379607\pi$
$17$	−2.30913	−	2.30913i	−0.560047	−	0.560047i	−0.929321	+	0.369273i	$0.879607\pi$
$18$		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	$-0.327799\pi$
$23$	−1.64124	−	1.64124i	−0.342222	−	0.342222i	−0.857202	+	0.514980i	$0.827799\pi$
$24$		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	$-0.485616\pi$
$37$	−5.80177	−	5.80177i	−0.953805	−	0.953805i	−0.998979	+	0.0451739i	$0.985616\pi$
$38$		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	0.195428	−	0.980718i	$-0.437390\pi$
$43$	−5.14949	−	5.14949i	−0.785290	−	0.785290i	−0.980718	+	0.195428i	$0.937390\pi$
$44$		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	$-0.772338\pi$
$47$	−0.679824	+	0.679824i	−0.0991625	+	0.0991625i	0.655785	+	0.754948i	$0.272338\pi$
$48$		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	0.0767501	−	0.997050i	$-0.475546\pi$
$53$	7.81739	−	7.81739i	1.07380	−	1.07380i	0.997050	−	0.0767501i	$-0.0244544\pi$
$54$		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	$-0.787766\pi$
$61$	−12.2751			−1.57167			−0.785834	+	0.618437i	$0.787766\pi$
$62$		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	0.168375	−	0.985723i	$-0.446148\pi$
$67$	9.44670	−	9.44670i	1.15410	−	1.15410i	0.985723	−	0.168375i	$-0.0538518\pi$
$68$		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	−0.954804	−	0.297235i	$-0.903935\pi$
$73$	−5.61827	+	5.61827i	−0.657569	+	0.657569i	0.297235	+	0.954804i	$0.403935\pi$
$74$		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	$-0.435460\pi$
$79$	3.57969			0.402746			0.201373	+	0.979515i	$0.435460\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.34403	+	1.34403i	0.147527	+	0.147527i	0.777012	−	0.629486i	$-0.216734\pi$
$83$	1.34403	+	1.34403i	0.147527	+	0.147527i	−0.629486	+	0.777012i	$0.716734\pi$
$84$		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	$-0.615721\pi$
$89$		−	17.6348i		−	1.86928i	0.355593	−	0.934641i	$-0.384279\pi$
$90$		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	0.636852	−	0.770986i	$-0.280236\pi$
$97$	−1.32106	−	1.32106i	−0.134134	−	0.134134i	−0.770986	+	0.636852i	$0.780236\pi$
$98$		0			0
$99$	−4.46967			−0.449218
$100$		0			0
$101$	1.47702			0.146969			0.0734845	−	0.997296i	$-0.476588\pi$
$101$	1.47702			0.146969			0.0734845	+	0.997296i	$0.476588\pi$
$102$		0			0
$103$	9.11459	+	9.11459i	0.898088	+	0.898088i	0.995267	−	0.0971794i	$-0.0309821\pi$
$103$	9.11459	+	9.11459i	0.898088	+	0.898088i	−0.0971794	+	0.995267i	$0.530982\pi$
$104$		0			0
$105$	9.98896	−	0.332104i	0.974823	−	0.0324101i
$106$		0			0
$107$	2.06155	−	2.06155i	0.199298	−	0.199298i	−0.600401	−	0.799699i	$-0.704992\pi$
$107$	2.06155	−	2.06155i	0.199298	−	0.199298i	0.799699	+	0.600401i	$0.204992\pi$
$108$		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	−0.890519	−	0.454946i	$-0.849658\pi$
$113$	−4.63020	+	4.63020i	−0.435572	+	0.435572i	0.454946	+	0.890519i	$0.349658\pi$
$114$		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	$-0.971045\pi$
$127$	−10.1991	+	10.1991i	−0.905025	+	0.905025i	0.0908403	+	0.995865i	$0.471045\pi$
$128$		0			0
$129$			7.28248i			0.641186i
$130$		0			0
$131$			12.4697i			1.08948i	0.838605	+	0.544740i	$0.183372\pi$
$131$			12.4697i			1.08948i	−0.838605	+	0.544740i	$0.816628\pi$
$132$		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	0.876672	−	0.481088i	$-0.159758\pi$
$137$	4.63020	+	4.63020i	0.395584	+	0.395584i	−0.481088	+	0.876672i	$0.659758\pi$
$138$		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	$-0.0639031\pi$
$157$	9.77969	+	9.77969i	0.780504	+	0.780504i	−0.199412	+	0.979916i	$0.563903\pi$
$158$		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	0.985412	−	0.170186i	$-0.0544368\pi$
$163$	10.4081	+	10.4081i	0.815226	+	0.815226i	−0.170186	+	0.985412i	$0.554437\pi$
$164$		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	$-0.642387\pi$
$167$	6.06155	−	6.06155i	0.469057	−	0.469057i	0.901609	+	0.432552i	$0.142387\pi$
$168$		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	$-0.756077\pi$
$173$	−0.355074	+	0.355074i	−0.0269957	+	0.0269957i	0.693480	+	0.720476i	$0.256077\pi$
$174$		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	$-0.593369\pi$
$181$	−7.77996			−0.578280			−0.289140	+	0.957287i	$0.593369\pi$
$182$		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	0.274863	−	0.961483i	$-0.411368\pi$
$193$	17.1759	−	17.1759i	1.23635	−	1.23635i	0.961483	−	0.274863i	$-0.0886325\pi$
$194$		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	$-0.279541\pi$
$197$	−1.83947	−	1.83947i	−0.131057	−	0.131057i	−0.769592	+	0.638536i	$0.779541\pi$
$198$		0			0
$199$	0.442397			0.0313607			0.0156804	−	0.999877i	$-0.495009\pi$
$199$	0.442397			0.0313607			0.0156804	+	0.999877i	$0.495009\pi$
$200$		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	$0.0584680\pi$
$211$			5.30633i			0.365303i	−0.983178	+	0.182652i	$0.941532\pi$
$212$		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	$-0.333578\pi$
$223$	−5.48159	−	5.48159i	−0.367075	−	0.367075i	−0.866409	+	0.499335i	$0.833578\pi$
$224$		0			0
$225$	0.332104	+	4.98896i	0.0221403	+	0.332597i
$226$		0			0
$227$	−9.51649	+	9.51649i	−0.631632	+	0.631632i	−0.948477	−	0.316845i	$-0.897376\pi$
$227$	−9.51649	+	9.51649i	−0.631632	+	0.631632i	0.316845	+	0.948477i	$0.397376\pi$
$228$		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	−0.604684	−	0.796465i	$-0.706701\pi$
$233$	2.92740	−	2.92740i	0.191781	−	0.191781i	0.796465	+	0.604684i	$0.206701\pi$
$234$		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	$-0.365921\pi$
$239$	12.6421			0.817751			0.408876	+	0.912590i	$0.365921\pi$
$240$		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	$0.199036\pi$
$251$			18.5468i			1.17067i	−0.810793	+	0.585333i	$0.800964\pi$
$252$		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	0.987019	−	0.160602i	$-0.0513437\pi$
$257$	13.2485	+	13.2485i	0.826417	+	0.826417i	−0.160602	+	0.987019i	$0.551344\pi$
$258$		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	−0.819967	−	0.572411i	$-0.806008\pi$
$263$	−22.5806	−	22.5806i	−1.39238	−	1.39238i	−0.572411	−	0.819967i	$-0.693992\pi$
$264$		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	$-0.143115\pi$
$277$	7.75583	+	7.75583i	0.466003	+	0.466003i	−0.434614	+	0.900617i	$0.643115\pi$
$278$		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	0.902036	−	0.431660i	$-0.142072\pi$
$283$	7.91295	+	7.91295i	0.470376	+	0.470376i	−0.431660	+	0.902036i	$0.642072\pi$
$284$		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	$-0.964400\pi$
$293$	−15.0999	+	15.0999i	−0.882143	+	0.882143i	0.111609	+	0.993752i	$0.464400\pi$
$294$		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	−0.569232	−	0.822177i	$-0.692759\pi$
$307$	4.43197	−	4.43197i	0.252946	−	0.252946i	0.822177	+	0.569232i	$0.192759\pi$
$308$		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	−0.0529364	+	0.998598i	$0.516858\pi$
$313$	−18.6035	+	18.6035i	−1.05153	+	1.05153i	−0.998598	+	0.0529364i	$0.983142\pi$
$314$		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	$-0.347195\pi$
$317$	−7.56953	−	7.56953i	−0.425147	−	0.425147i	−0.886971	+	0.461824i	$0.847195\pi$
$318$		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	$-0.876160\pi$
$331$		−	13.8020i		−	0.758629i	0.925268	−	0.379314i	$-0.123840\pi$
$332$		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	0.939434	−	0.342729i	$-0.111351\pi$
$337$	10.9541	+	10.9541i	0.596706	+	0.596706i	−0.342729	+	0.939434i	$0.611351\pi$
$338$		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	−0.249405	−	0.968399i	$-0.580235\pi$
$347$	13.3934	−	13.3934i	0.718995	−	0.718995i	0.968399	+	0.249405i	$0.0802350\pi$
$348$		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	0.541286	−	0.840839i	$-0.317938\pi$
$353$	25.9678	−	25.9678i	1.38212	−	1.38212i	0.840839	−	0.541286i	$-0.182062\pi$
$354$		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	$-0.424196\pi$
$359$	8.93933			0.471800			0.235900	+	0.971777i	$0.424196\pi$
$360$		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	$-0.919831\pi$
$367$	−13.7788	+	13.7788i	−0.719248	+	0.719248i	0.249204	+	0.968451i	$0.419831\pi$
$368$		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	$-0.599424\pi$
$373$	12.4439	−	12.4439i	0.644321	−	0.644321i	0.951615	+	0.307294i	$0.0994235\pi$
$374$		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	$-0.315964\pi$
$383$	−5.69455	−	5.69455i	−0.290978	−	0.290978i	−0.837467	+	0.546489i	$0.815964\pi$
$384$		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	$-0.471698\pi$
$397$	−18.0769	−	18.0769i	−0.907253	−	0.907253i	−0.996050	+	0.0887965i	$0.971698\pi$
$398$		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	$-0.764098\pi$
$409$		−	27.3063i		−	1.35021i	0.737721	−	0.675106i	$-0.235902\pi$
$410$		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	$-0.332421\pi$
$421$	20.6200			1.00496			0.502480	+	0.864589i	$0.332421\pi$
$422$		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	−0.525172	−	0.850996i	$-0.675999\pi$
$433$	6.77996	−	6.77996i	0.325824	−	0.325824i	0.850996	+	0.525172i	$0.175999\pi$
$434$		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	$-0.617094\pi$
$439$	−15.0698			−0.719243			−0.359622	+	0.933098i	$0.617094\pi$
$440$		0			0
$441$	12.9779			0.617996
$442$		0			0
$443$	−9.69059	−	9.69059i	−0.460414	−	0.460414i	0.438377	−	0.898791i	$-0.355553\pi$
$443$	−9.69059	−	9.69059i	−0.460414	−	0.460414i	−0.898791	+	0.438377i	$0.855553\pi$
$444$		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	$0.157942\pi$
$449$			20.1759i			0.952158i	−0.879402	+	0.476079i	$0.842058\pi$
$450$		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	0.693419	−	0.720535i	$-0.256104\pi$
$457$	−0.579686	−	0.579686i	−0.0271165	−	0.0271165i	−0.720535	+	0.693419i	$0.756104\pi$
$458$		0			0
$459$	−3.26561			−0.152426
$460$		0			0
$461$	4.40164			0.205005			0.102503	−	0.994733i	$-0.467315\pi$
$461$	4.40164			0.205005			0.102503	+	0.994733i	$0.467315\pi$
$462$		0			0
$463$	0.786155	+	0.786155i	0.0365357	+	0.0365357i	0.725139	−	0.688603i	$-0.241776\pi$
$463$	0.786155	+	0.786155i	0.0365357	+	0.0365357i	−0.688603	+	0.725139i	$0.741776\pi$
$464$		0			0
$465$	−6.11091	+	6.53122i	−0.283386	+	0.302878i
$466$		0			0
$467$	19.6430	−	19.6430i	0.908970	−	0.908970i	−0.0872190	−	0.996189i	$-0.527798\pi$
$467$	19.6430	−	19.6430i	0.908970	−	0.908970i	0.996189	+	0.0872190i	$0.0277980\pi$
$468$		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	$-0.253316\pi$
$479$	30.6274			1.39940			0.699701	+	0.714436i	$0.253316\pi$
$480$		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	−0.130752	+	0.991415i	$0.541739\pi$
$487$	−24.7641	+	24.7641i	−1.12217	+	1.12217i	−0.991415	+	0.130752i	$0.958261\pi$
$488$		0			0
$489$		−	14.7193i		−	0.665629i
$490$		0			0
$491$			23.3318i			1.05295i	0.850190	+	0.526475i	$0.176487\pi$
$491$			23.3318i			1.05295i	−0.850190	+	0.526475i	$0.823513\pi$
$492$		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	$-0.251614\pi$
$503$	−0.160805	−	0.160805i	−0.00716996	−	0.00716996i	−0.710683	+	0.703513i	$0.751614\pi$
$504$		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	0.808409	−	0.588621i	$-0.200329\pi$
$523$	5.02638	+	5.02638i	0.219788	+	0.219788i	−0.588621	+	0.808409i	$0.700329\pi$
$524$		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	$-0.255408\pi$
$541$	32.3302			1.38998			0.694992	+	0.719017i	$0.255408\pi$
$542$		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	−0.857327	−	0.514773i	$-0.827876\pi$
$547$	−8.01165	+	8.01165i	−0.342554	+	0.342554i	0.514773	+	0.857327i	$0.327876\pi$
$548$		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	$-0.251320\pi$
$557$	−0.138448	−	0.138448i	−0.00586624	−	0.00586624i	−0.710034	+	0.704168i	$0.751320\pi$
$558$		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	0.946318	−	0.323236i	$-0.104771\pi$
$563$	14.7843	+	14.7843i	0.623082	+	0.623082i	−0.323236	+	0.946318i	$0.604771\pi$
$564$		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	$0.216088\pi$
$569$			29.9558i			1.25581i	−0.778288	+	0.627907i	$0.783912\pi$
$570$		0			0
$571$			8.52134i			0.356607i	0.983976	+	0.178303i	$0.0570609\pi$
$571$			8.52134i			0.356607i	−0.983976	+	0.178303i	$0.942939\pi$
$572$		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	0.897675	−	0.440658i	$-0.145255\pi$
$577$	10.9779	+	10.9779i	0.457017	+	0.457017i	−0.440658	+	0.897675i	$0.645255\pi$
$578$		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	−0.973280	−	0.229623i	$-0.926251\pi$
$587$	−18.0174	+	18.0174i	−0.743657	+	0.743657i	0.229623	+	0.973280i	$0.426251\pi$
$588$		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	−0.0653359	+	0.997863i	$0.520812\pi$
$593$	−25.8906	+	25.8906i	−1.06320	+	1.06320i	−0.997863	+	0.0653359i	$0.979188\pi$
$594$		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	$-0.558168\pi$
$599$	−8.89517			−0.363447			−0.181723	+	0.983350i	$0.558168\pi$
$600$		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	$-0.705001\pi$
$607$	4.90926	−	4.90926i	0.199261	−	0.199261i	0.799683	+	0.600422i	$0.205001\pi$
$608$		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	$-0.767089\pi$
$613$	−1.87894	+	1.87894i	−0.0758896	+	0.0758896i	0.668143	+	0.744033i	$0.267089\pi$
$614$		0			0
$615$	−4.27512	−	4.00000i	−0.172390	−	0.161296i
$616$		0			0
$617$	−5.07260	−	5.07260i	−0.204215	−	0.204215i	0.597588	−	0.801803i	$-0.296126\pi$
$617$	−5.07260	−	5.07260i	−0.204215	−	0.204215i	−0.801803	+	0.597588i	$0.796126\pi$
$618$		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	0.824064	−	0.566497i	$-0.191702\pi$
$643$	6.53122	+	6.53122i	0.257566	+	0.257566i	−0.566497	+	0.824064i	$0.691702\pi$
$644$		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	$-0.587070\pi$
$647$	17.6192	−	17.6192i	0.692681	−	0.692681i	0.962821	+	0.270140i	$0.0870701\pi$
$648$		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	$-0.756410\pi$
$653$	−0.727677	+	0.727677i	−0.0284762	+	0.0284762i	0.692725	+	0.721202i	$0.256410\pi$
$654$		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	$-0.593786\pi$
$661$	−14.9320			−0.580786			−0.290393	+	0.956907i	$0.593786\pi$
$662$		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	−0.656129	−	0.754649i	$-0.727807\pi$
$673$	2.55583	−	2.55583i	0.0985200	−	0.0985200i	0.754649	+	0.656129i	$0.227807\pi$
$674$		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	$-0.409879\pi$
$677$	−17.7147	−	17.7147i	−0.680832	−	0.680832i	−0.960188	+	0.279356i	$0.909879\pi$
$678$		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	0.890693	−	0.454606i	$-0.150220\pi$
$683$	11.3968	+	11.3968i	0.436086	+	0.436086i	−0.454606	+	0.890693i	$0.650220\pi$
$684$		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	$-0.957818\pi$
$691$		−	6.94671i		−	0.264265i	0.991232	−	0.132133i	$-0.0421825\pi$
$692$		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	$-0.441322\pi$
$701$	9.70621			0.366598			0.183299	+	0.983057i	$0.441322\pi$
$702$		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	$-0.195124\pi$
$719$	43.8640			1.63585			0.817925	+	0.575325i	$0.195124\pi$
$720$		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	$-0.665922\pi$
$727$	9.95522	−	9.95522i	0.369219	−	0.369219i	0.867192	+	0.497974i	$0.165922\pi$
$728$		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	$-0.896370\pi$
$733$	−16.9924	+	16.9924i	−0.627628	+	0.627628i	0.319843	+	0.947471i	$0.396370\pi$
$734$		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	$-0.0735539\pi$
$743$	20.2907	+	20.2907i	0.744395	+	0.744395i	−0.229025	+	0.973420i	$0.573554\pi$
$744$		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	$-0.325471\pi$
$757$	−9.13933	−	9.13933i	−0.332175	−	0.332175i	−0.853412	+	0.521237i	$0.825471\pi$
$758$		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	$-0.896593\pi$
$769$		−	17.7022i		−	0.638359i	0.947694	−	0.319180i	$-0.103407\pi$
$770$		0			0
$771$		−	18.7362i		−	0.674766i
$772$		0			0
$773$	−9.30178	+	9.30178i	−0.334562	+	0.334562i	−0.854316	−	0.519754i	$-0.826024\pi$
$773$	−9.30178	+	9.30178i	−0.334562	+	0.334562i	0.519754	+	0.854316i	$0.326024\pi$
$774$		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	−0.304900	−	0.952384i	$-0.598623\pi$
$787$	18.1642	−	18.1642i	0.647484	−	0.647484i	0.952384	+	0.304900i	$0.0986230\pi$
$788$		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	$-0.212032\pi$
$797$	4.75098	+	4.75098i	0.168289	+	0.168289i	−0.617938	+	0.786227i	$0.712032\pi$
$798$		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	$0.231269\pi$
$809$			37.7891i			1.32859i	−0.747469	+	0.664297i	$0.768731\pi$
$810$		0			0
$811$			44.4215i			1.55985i	0.625872	+	0.779926i	$0.284743\pi$
$811$			44.4215i			1.55985i	−0.625872	+	0.779926i	$0.715257\pi$
$812$		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	$-0.328749\pi$
$821$	29.3648			1.02484			0.512420	+	0.858735i	$0.328749\pi$
$822$		0			0
$823$	22.7402	+	22.7402i	0.792674	+	0.792674i	0.981928	−	0.189254i	$-0.0606070\pi$
$823$	22.7402	+	22.7402i	0.792674	+	0.792674i	−0.189254	+	0.981928i	$0.560607\pi$
$824$		0			0
$825$	14.7181	−	16.8174i	0.512420	−	0.585506i
$826$		0			0
$827$	−1.50001	+	1.50001i	−0.0521605	+	0.0521605i	−0.732706	−	0.680545i	$-0.761743\pi$
$827$	−1.50001	+	1.50001i	−0.0521605	+	0.0521605i	0.680545	+	0.732706i	$0.261743\pi$
$828$		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	$-0.730495\pi$
$839$	−38.3779			−1.32495			−0.662476	+	0.749083i	$0.730495\pi$
$840$		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	$-0.988653\pi$
$853$	−28.1467	+	28.1467i	−0.963724	+	0.963724i	0.0356404	+	0.999365i	$0.488653\pi$
$854$		0			0
$855$	−0.194542	−	5.85140i	−0.00665320	−	0.200114i
$856$		0			0
$857$	−13.5990	−	13.5990i	−0.464533	−	0.464533i	0.435605	−	0.900138i	$-0.356534\pi$
$857$	−13.5990	−	13.5990i	−0.464533	−	0.464533i	−0.900138	+	0.435605i	$0.856534\pi$
$858$		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	$-0.180846\pi$
$863$	8.95495	+	8.95495i	0.304830	+	0.304830i	−0.538070	+	0.842900i	$0.680846\pi$
$864$		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	0.942151	+	0.335190i	$0.108800\pi$
$877$	37.8274	+	37.8274i	1.27734	+	1.27734i	0.335190	+	0.942151i	$0.391200\pi$
$878$		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	0.531159	−	0.847272i	$-0.321757\pi$
$883$	−9.39338	−	9.39338i	−0.316113	−	0.316113i	−0.847272	+	0.531159i	$0.821757\pi$
$884$		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	$-0.756235\pi$
$887$	−0.825014	+	0.825014i	−0.0277013	+	0.0277013i	0.693120	+	0.720822i	$0.256235\pi$
$888$		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	−0.733042	−	0.680184i	$-0.761900\pi$
$907$	−1.59189	+	1.59189i	−0.0528578	+	0.0528578i	0.680184	+	0.733042i	$0.261900\pi$
$908$		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	$-0.477334\pi$
$919$	4.31369			0.142295			0.0711477	+	0.997466i	$0.477334\pi$
$920$		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	$0.106280\pi$
$929$			19.9774i			0.655436i	−0.944776	+	0.327718i	$0.893720\pi$
$930$		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	0.545085	−	0.838381i	$-0.316497\pi$
$937$	−8.97792	−	8.97792i	−0.293296	−	0.293296i	−0.838381	+	0.545085i	$0.816497\pi$
$938$		0			0
$939$	26.3094			0.858574
$940$		0			0
$941$	37.9831			1.23821			0.619107	−	0.785307i	$-0.287495\pi$
$941$	37.9831			1.23821			0.619107	+	0.785307i	$0.287495\pi$
$942$		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	0.323878	−	0.946099i	$-0.395013\pi$
$947$	39.0815	−	39.0815i	1.26998	−	1.26998i	0.946099	−	0.323878i	$-0.104987\pi$
$948$		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	−0.727414	−	0.686199i	$-0.759278\pi$
$953$	−1.27232	+	1.27232i	−0.0412146	+	0.0412146i	0.686199	+	0.727414i	$0.259278\pi$
$954$		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	$-0.737853\pi$
$967$	1.67778	−	1.67778i	0.0539537	−	0.0539537i	0.733569	+	0.679615i	$0.237853\pi$
$968$		0			0
$969$			8.55025i			0.274674i
$970$		0			0
$971$			15.9887i			0.513102i	0.966531	+	0.256551i	$0.0825862\pi$
$971$			15.9887i			0.513102i	−0.966531	+	0.256551i	$0.917414\pi$
$972$		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	0.922556	−	0.385864i	$-0.126096\pi$
$977$	16.7754	+	16.7754i	0.536692	+	0.536692i	−0.385864	+	0.922556i	$0.626096\pi$
$978$		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	−0.994967	−	0.100203i	$-0.968051\pi$
$983$	−34.3367	−	34.3367i	−1.09517	−	1.09517i	−0.100203	−	0.994967i	$-0.531949\pi$
$984$		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	$-0.179556\pi$
$997$	9.80177	+	9.80177i	0.310425	+	0.310425i	−0.534649	+	0.845074i	$0.679556\pi$
$998$		0			0
$999$	−8.20494			−0.259593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.w.f.127.1		8
4.3	odd	2		960.2.w.e.127.3		8
5.3	odd	4		960.2.w.e.703.3		8
8.3	odd	2		480.2.w.c.127.2	✓	8
8.5	even	2		480.2.w.d.127.4	yes	8
20.3	even	4	inner	960.2.w.f.703.1		8
24.5	odd	2		1440.2.x.r.127.1		8
24.11	even	2		1440.2.x.q.127.1		8
40.3	even	4		480.2.w.d.223.4	yes	8
40.13	odd	4		480.2.w.c.223.2	yes	8
40.19	odd	2		2400.2.w.j.607.4		8
40.27	even	4		2400.2.w.i.2143.1		8
40.29	even	2		2400.2.w.i.607.1		8
40.37	odd	4		2400.2.w.j.2143.4		8
120.53	even	4		1440.2.x.q.703.1		8
120.83	odd	4		1440.2.x.r.703.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.w.c.127.2	✓	8	8.3	odd	2
480.2.w.c.223.2	yes	8	40.13	odd	4
480.2.w.d.127.4	yes	8	8.5	even	2
480.2.w.d.223.4	yes	8	40.3	even	4
960.2.w.e.127.3		8	4.3	odd	2
960.2.w.e.703.3		8	5.3	odd	4
960.2.w.f.127.1		8	1.1	even	1	trivial
960.2.w.f.703.1		8	20.3	even	4	inner
1440.2.x.q.127.1		8	24.11	even	2
1440.2.x.q.703.1		8	120.53	even	4
1440.2.x.r.127.1		8	24.5	odd	2
1440.2.x.r.703.1		8	120.83	odd	4
2400.2.w.i.607.1		8	40.29	even	2
2400.2.w.i.2143.1		8	40.27	even	4
2400.2.w.j.607.4		8	40.19	odd	2
2400.2.w.j.2143.4		8	40.37	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.w (of order \(4\), degree \(2\), not 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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