LMFDB - Embedded newform 768.2.n.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	768.97
Dual form			768.2.n.b.673.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 + 0.382683i) q^{3} +(1.48656 - 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.923880 + 0.382683i) q^{3} +(1.48656 - 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-2.98911 - 1.23813i) q^{11} +(-1.33971 - 3.23434i) q^{13} +3.88457i q^{15} +5.31367i q^{17} +(-0.339726 - 0.820171i) q^{19} +(1.35649 + 0.561876i) q^{21} +(-4.32186 + 4.32186i) q^{23} +(-7.13463 - 7.13463i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(-5.78209 + 2.39502i) q^{29} +1.42287 q^{31} +3.23539 q^{33} +(-5.26938 + 2.18265i) q^{35} +(-0.646238 + 1.56016i) q^{37} +(2.47546 + 2.47546i) q^{39} +(3.42644 - 3.42644i) q^{41} +(6.50505 + 2.69448i) q^{43} +(-1.48656 - 3.58888i) q^{45} -10.5764i q^{47} -4.84423i q^{49} +(-2.03345 - 4.90919i) q^{51} +(-6.63468 - 2.74817i) q^{53} +(-8.88700 + 8.88700i) q^{55} +(0.627732 + 0.627732i) q^{57} +(-0.185450 + 0.447716i) q^{59} +(3.16624 - 1.31150i) q^{61} -1.46825 q^{63} -13.5992 q^{65} +(-6.09277 + 2.52371i) q^{67} +(2.33898 - 5.64679i) q^{69} +(-2.91549 - 2.91549i) q^{71} +(1.02065 - 1.02065i) q^{73} +(9.32184 + 3.86123i) q^{75} +(1.81789 + 4.38878i) q^{77} -12.8099i q^{79} -1.00000i q^{81} +(-6.41532 - 15.4879i) q^{83} +(19.0701 + 7.89910i) q^{85} +(4.42542 - 4.42542i) q^{87} +(-0.991462 - 0.991462i) q^{89} +(-1.96703 + 4.74883i) q^{91} +(-1.31456 + 0.544508i) q^{93} -3.44851 q^{95} +14.5301 q^{97} +(-2.98911 + 1.23813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$4$		0			0
$5$	1.48656	−	3.58888i	0.664810	−	1.60499i	−0.125364	−	0.992111i	$-0.540010\pi$
$5$	1.48656	−	3.58888i	0.664810	−	1.60499i	0.790174	−	0.612883i	$-0.209990\pi$
$6$		0			0
$7$	−1.03821	−	1.03821i	−0.392407	−	0.392407i	0.483137	−	0.875545i	$-0.339497\pi$
$7$	−1.03821	−	1.03821i	−0.392407	−	0.392407i	−0.875545	+	0.483137i	$0.839497\pi$
$8$		0			0
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	−2.98911	−	1.23813i	−0.901252	−	0.373311i	−0.116550	−	0.993185i	$-0.537184\pi$
$11$	−2.98911	−	1.23813i	−0.901252	−	0.373311i	−0.784701	+	0.619874i	$0.787184\pi$
$12$		0			0
$13$	−1.33971	−	3.23434i	−0.371568	−	0.897045i	−0.993485	−	0.113962i	$-0.963646\pi$
$13$	−1.33971	−	3.23434i	−0.371568	−	0.897045i	0.621917	−	0.783083i	$-0.286354\pi$
$14$		0			0
$15$			3.88457i			1.00299i
$16$		0			0
$17$			5.31367i			1.28876i	0.764708	+	0.644378i	$0.222883\pi$
$17$			5.31367i			1.28876i	−0.764708	+	0.644378i	$0.777117\pi$
$18$		0			0
$19$	−0.339726	−	0.820171i	−0.0779385	−	0.188160i	0.880108	−	0.474774i	$-0.157470\pi$
$19$	−0.339726	−	0.820171i	−0.0779385	−	0.188160i	−0.958046	+	0.286614i	$0.907470\pi$
$20$		0			0
$21$	1.35649	+	0.561876i	0.296010	+	0.122611i
$22$		0			0
$23$	−4.32186	+	4.32186i	−0.901171	+	0.901171i	−0.995537	−	0.0943668i	$-0.969917\pi$
$23$	−4.32186	+	4.32186i	−0.901171	+	0.901171i	0.0943668	+	0.995537i	$0.469917\pi$
$24$		0			0
$25$	−7.13463	−	7.13463i	−1.42693	−	1.42693i
$26$		0			0
$27$	−0.382683	+	0.923880i	−0.0736475	+	0.177801i
$28$		0			0
$29$	−5.78209	+	2.39502i	−1.07371	+	0.444744i	−0.848298	−	0.529520i	$-0.822372\pi$
$29$	−5.78209	+	2.39502i	−1.07371	+	0.444744i	−0.225410	+	0.974264i	$0.572372\pi$
$30$		0			0
$31$	1.42287			0.255555			0.127777	−	0.991803i	$-0.459216\pi$
$31$	1.42287			0.255555			0.127777	+	0.991803i	$0.459216\pi$
$32$		0			0
$33$	3.23539			0.563210
$34$		0			0
$35$	−5.26938	+	2.18265i	−0.890687	+	0.368935i
$36$		0			0
$37$	−0.646238	+	1.56016i	−0.106241	+	0.256488i	−0.968056	−	0.250735i	$-0.919328\pi$
$37$	−0.646238	+	1.56016i	−0.106241	+	0.256488i	0.861815	+	0.507223i	$0.169328\pi$
$38$		0			0
$39$	2.47546	+	2.47546i	0.396390	+	0.396390i
$40$		0			0
$41$	3.42644	−	3.42644i	0.535120	−	0.535120i	−0.386972	−	0.922092i	$-0.626479\pi$
$41$	3.42644	−	3.42644i	0.535120	−	0.535120i	0.922092	+	0.386972i	$0.126479\pi$
$42$		0			0
$43$	6.50505	+	2.69448i	0.992010	+	0.410904i	0.818861	−	0.573991i	$-0.194606\pi$
$43$	6.50505	+	2.69448i	0.992010	+	0.410904i	0.173149	+	0.984896i	$0.444606\pi$
$44$		0			0
$45$	−1.48656	−	3.58888i	−0.221603	−	0.534998i
$46$		0			0
$47$		−	10.5764i		−	1.54273i	−0.636391	−	0.771366i	$-0.719574\pi$
$47$		−	10.5764i		−	1.54273i	0.636391	−	0.771366i	$-0.280426\pi$
$48$		0			0
$49$		−	4.84423i		−	0.692033i
$50$		0			0
$51$	−2.03345	−	4.90919i	−0.284741	−	0.687425i
$52$		0			0
$53$	−6.63468	−	2.74817i	−0.911344	−	0.377491i	−0.122773	−	0.992435i	$-0.539179\pi$
$53$	−6.63468	−	2.74817i	−0.911344	−	0.377491i	−0.788571	+	0.614944i	$0.789179\pi$
$54$		0			0
$55$	−8.88700	+	8.88700i	−1.19832	+	1.19832i
$56$		0			0
$57$	0.627732	+	0.627732i	0.0831451	+	0.0831451i
$58$		0			0
$59$	−0.185450	+	0.447716i	−0.0241435	+	0.0582877i	−0.935492	−	0.353349i	$-0.885043\pi$
$59$	−0.185450	+	0.447716i	−0.0241435	+	0.0582877i	0.911348	+	0.411637i	$0.135043\pi$
$60$		0			0
$61$	3.16624	−	1.31150i	0.405396	−	0.167920i	−0.170662	−	0.985330i	$-0.554590\pi$
$61$	3.16624	−	1.31150i	0.405396	−	0.167920i	0.576057	+	0.817409i	$0.304590\pi$
$62$		0			0
$63$	−1.46825			−0.184983
$64$		0			0
$65$	−13.5992			−1.68677
$66$		0			0
$67$	−6.09277	+	2.52371i	−0.744350	+	0.308320i	−0.722434	−	0.691440i	$-0.756977\pi$
$67$	−6.09277	+	2.52371i	−0.744350	+	0.308320i	−0.0219162	+	0.999760i	$0.506977\pi$
$68$		0			0
$69$	2.33898	−	5.64679i	0.281580	−	0.679793i
$70$		0			0
$71$	−2.91549	−	2.91549i	−0.346005	−	0.346005i	0.512614	−	0.858619i	$-0.328677\pi$
$71$	−2.91549	−	2.91549i	−0.346005	−	0.346005i	−0.858619	+	0.512614i	$0.828677\pi$
$72$		0			0
$73$	1.02065	−	1.02065i	0.119458	−	0.119458i	−0.644851	−	0.764309i	$-0.723080\pi$
$73$	1.02065	−	1.02065i	0.119458	−	0.119458i	0.764309	+	0.644851i	$0.223080\pi$
$74$		0			0
$75$	9.32184	+	3.86123i	1.07639	+	0.445857i
$76$		0			0
$77$	1.81789	+	4.38878i	0.207168	+	0.500147i
$78$		0			0
$79$		−	12.8099i		−	1.44122i	−0.693338	−	0.720612i	$-0.743861\pi$
$79$		−	12.8099i		−	1.44122i	0.693338	−	0.720612i	$-0.256139\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−6.41532	−	15.4879i	−0.704173	−	1.70002i	−0.714072	−	0.700072i	$-0.753151\pi$
$83$	−6.41532	−	15.4879i	−0.704173	−	1.70002i	0.00989955	−	0.999951i	$-0.496849\pi$
$84$		0			0
$85$	19.0701	+	7.89910i	2.06844	+	0.856778i
$86$		0			0
$87$	4.42542	−	4.42542i	0.474455	−	0.474455i
$88$		0			0
$89$	−0.991462	−	0.991462i	−0.105095	−	0.105095i	0.652604	−	0.757699i	$-0.273676\pi$
$89$	−0.991462	−	0.991462i	−0.105095	−	0.105095i	−0.757699	+	0.652604i	$0.773676\pi$
$90$		0			0
$91$	−1.96703	+	4.74883i	−0.206201	+	0.497813i
$92$		0			0
$93$	−1.31456	+	0.544508i	−0.136313	+	0.0564628i
$94$		0			0
$95$	−3.44851			−0.353810
$96$		0			0
$97$	14.5301			1.47530			0.737652	−	0.675182i	$-0.235935\pi$
$97$	14.5301			1.47530			0.737652	+	0.675182i	$0.235935\pi$
$98$		0			0
$99$	−2.98911	+	1.23813i	−0.300417	+	0.124437i
$100$		0			0
$101$	−0.742560	+	1.79270i	−0.0738875	+	0.178380i	−0.956508	−	0.291706i	$-0.905777\pi$
$101$	−0.742560	+	1.79270i	−0.0738875	+	0.178380i	0.882621	+	0.470086i	$0.155777\pi$
$102$		0			0
$103$	2.11500	+	2.11500i	0.208397	+	0.208397i	0.803586	−	0.595189i	$-0.202923\pi$
$103$	2.11500	+	2.11500i	0.208397	+	0.208397i	−0.595189	+	0.803586i	$0.702923\pi$
$104$		0			0
$105$	4.03301	−	4.03301i	0.393581	−	0.393581i
$106$		0			0
$107$	4.62290	+	1.91487i	0.446913	+	0.185117i	0.594778	−	0.803890i	$-0.297240\pi$
$107$	4.62290	+	1.91487i	0.446913	+	0.185117i	−0.147865	+	0.989008i	$0.547240\pi$
$108$		0			0
$109$	−0.135885	−	0.328056i	−0.0130155	−	0.0314221i	0.917238	−	0.398339i	$-0.130413\pi$
$109$	−0.135885	−	0.328056i	−0.0130155	−	0.0314221i	−0.930254	+	0.366917i	$0.880413\pi$
$110$		0			0
$111$		−	1.68870i		−	0.160284i
$112$		0			0
$113$			2.38693i			0.224543i	0.993678	+	0.112272i	$0.0358127\pi$
$113$			2.38693i			0.224543i	−0.993678	+	0.112272i	$0.964187\pi$
$114$		0			0
$115$	9.08591	+	21.9353i	0.847266	+	2.04548i
$116$		0			0
$117$	−3.23434	−	1.33971i	−0.299015	−	0.123856i
$118$		0			0
$119$	5.51672	−	5.51672i	0.505717	−	0.505717i
$120$		0			0
$121$	−0.376343	−	0.376343i	−0.0342130	−	0.0342130i
$122$		0			0
$123$	−1.85438	+	4.47686i	−0.167203	+	0.403665i
$124$		0			0
$125$	−18.2670	+	7.56643i	−1.63385	+	0.676762i
$126$		0			0
$127$	13.4220			1.19101			0.595507	−	0.803350i	$-0.296951\pi$
$127$	13.4220			1.19101			0.595507	+	0.803350i	$0.296951\pi$
$128$		0			0
$129$	−7.04101			−0.619927
$130$		0			0
$131$	7.38818	−	3.06028i	0.645508	−	0.267378i	−0.0358180	−	0.999358i	$-0.511404\pi$
$131$	7.38818	−	3.06028i	0.645508	−	0.267378i	0.681326	+	0.731980i	$0.261404\pi$
$132$		0			0
$133$	−0.498804	+	1.20422i	−0.0432518	+	0.104419i
$134$		0			0
$135$	2.74681	+	2.74681i	0.236407	+	0.236407i
$136$		0			0
$137$	−10.6802	+	10.6802i	−0.912474	+	0.912474i	−0.996466	−	0.0839927i	$-0.973233\pi$
$137$	−10.6802	+	10.6802i	−0.912474	+	0.912474i	0.0839927	+	0.996466i	$0.473233\pi$
$138$		0			0
$139$	−4.00214	−	1.65774i	−0.339457	−	0.140608i	0.206441	−	0.978459i	$-0.433812\pi$
$139$	−4.00214	−	1.65774i	−0.339457	−	0.140608i	−0.545899	+	0.837851i	$0.683812\pi$
$140$		0			0
$141$	4.04743	+	9.77136i	0.340855	+	0.822897i
$142$		0			0
$143$			11.3265i			0.947173i
$144$		0			0
$145$			24.3116i			2.01896i
$146$		0			0
$147$	1.85381	+	4.47549i	0.152899	+	0.369132i
$148$		0			0
$149$	17.5080	+	7.25206i	1.43431	+	0.594112i	0.958412	−	0.285387i	$-0.0921222\pi$
$149$	17.5080	+	7.25206i	1.43431	+	0.594112i	0.475901	+	0.879499i	$0.342122\pi$
$150$		0			0
$151$	−1.13128	+	1.13128i	−0.0920621	+	0.0920621i	−0.751638	−	0.659576i	$-0.770736\pi$
$151$	−1.13128	+	1.13128i	−0.0920621	+	0.0920621i	0.659576	+	0.751638i	$0.270736\pi$
$152$		0			0
$153$	3.75733	+	3.75733i	0.303762	+	0.303762i
$154$		0			0
$155$	2.11518	−	5.10649i	0.169895	−	0.410163i
$156$		0			0
$157$	−1.69192	+	0.700815i	−0.135030	+	0.0559311i	−0.449175	−	0.893444i	$-0.648282\pi$
$157$	−1.69192	+	0.700815i	−0.135030	+	0.0559311i	0.314145	+	0.949375i	$0.398282\pi$
$158$		0			0
$159$	7.18133			0.569516
$160$		0			0
$161$	8.97402			0.707252
$162$		0			0
$163$	20.1880	−	8.36212i	1.58124	−	0.654972i	0.592632	−	0.805473i	$-0.298089\pi$
$163$	20.1880	−	8.36212i	1.58124	−	0.654972i	0.988610	+	0.150501i	$0.0480887\pi$
$164$		0			0
$165$	4.80961	−	11.6114i	0.374428	−	0.903948i
$166$		0			0
$167$	2.40472	+	2.40472i	0.186083	+	0.186083i	0.794000	−	0.607917i	$-0.207995\pi$
$167$	2.40472	+	2.40472i	0.186083	+	0.186083i	−0.607917	+	0.794000i	$0.707995\pi$
$168$		0			0
$169$	0.526247	−	0.526247i	0.0404805	−	0.0404805i
$170$		0			0
$171$	−0.820171	−	0.339726i	−0.0627200	−	0.0259795i
$172$		0			0
$173$	3.78491	+	9.13758i	0.287761	+	0.694717i	0.999974	−	0.00724669i	$-0.00230671\pi$
$173$	3.78491	+	9.13758i	0.287761	+	0.694717i	−0.712212	+	0.701964i	$0.752307\pi$
$174$		0			0
$175$			14.8145i			1.11987i
$176$		0			0
$177$		−	0.484604i		−	0.0364251i
$178$		0			0
$179$	−7.05680	−	17.0366i	−0.527450	−	1.27338i	−0.933188	−	0.359388i	$-0.882985\pi$
$179$	−7.05680	−	17.0366i	−0.527450	−	1.27338i	0.405738	−	0.913989i	$-0.367015\pi$
$180$		0			0
$181$	−17.3885	−	7.20257i	−1.29248	−	0.535363i	−0.372757	−	0.927929i	$-0.621587\pi$
$181$	−17.3885	−	7.20257i	−1.29248	−	0.535363i	−0.919724	+	0.392566i	$0.871587\pi$
$182$		0			0
$183$	−2.42334	+	2.42334i	−0.179138	+	0.179138i
$184$		0			0
$185$	4.63854	+	4.63854i	0.341032	+	0.341032i
$186$		0			0
$187$	6.57903	−	15.8832i	0.481106	−	1.16149i
$188$		0			0
$189$	1.35649	−	0.561876i	0.0986701	−	0.0408705i
$190$		0			0
$191$	−9.91467			−0.717400			−0.358700	−	0.933453i	$-0.616780\pi$
$191$	−9.91467			−0.717400			−0.358700	+	0.933453i	$0.616780\pi$
$192$		0			0
$193$	9.84834			0.708899			0.354450	−	0.935075i	$-0.384668\pi$
$193$	9.84834			0.708899			0.354450	+	0.935075i	$0.384668\pi$
$194$		0			0
$195$	12.5640	−	5.20419i	0.899728	−	0.372680i
$196$		0			0
$197$	−5.46439	+	13.1922i	−0.389322	+	0.939905i	0.600762	+	0.799428i	$0.294864\pi$
$197$	−5.46439	+	13.1922i	−0.389322	+	0.939905i	−0.990084	+	0.140478i	$0.955136\pi$
$198$		0			0
$199$	6.14473	+	6.14473i	0.435588	+	0.435588i	0.890524	−	0.454936i	$-0.150338\pi$
$199$	6.14473	+	6.14473i	0.435588	+	0.435588i	−0.454936	+	0.890524i	$0.650338\pi$
$200$		0			0
$201$	4.66320	−	4.66320i	0.328917	−	0.328917i
$202$		0			0
$203$	8.48958	+	3.51650i	0.595852	+	0.246810i
$204$		0			0
$205$	−7.20345	−	17.3907i	−0.503111	−	1.21462i
$206$		0			0
$207$			6.11204i			0.424816i
$208$		0			0
$209$			2.87221i			0.198675i
$210$		0			0
$211$	−4.14085	−	9.99689i	−0.285068	−	0.688214i	0.714871	−	0.699256i	$-0.246485\pi$
$211$	−4.14085	−	9.99689i	−0.285068	−	0.688214i	−0.999939	+	0.0110418i	$0.996485\pi$
$212$		0			0
$213$	3.80927	+	1.57785i	0.261007	+	0.108113i
$214$		0			0
$215$	19.3403	−	19.3403i	1.31900	−	1.31900i
$216$		0			0
$217$	−1.47724	−	1.47724i	−0.100281	−	0.100281i
$218$		0			0
$219$	−0.552372	+	1.33355i	−0.0373259	+	0.0901126i
$220$		0			0
$221$	17.1862	−	7.11877i	1.15607	−	0.478860i
$222$		0			0
$223$	14.1199			0.945540			0.472770	−	0.881186i	$-0.343254\pi$
$223$	14.1199			0.945540			0.472770	+	0.881186i	$0.343254\pi$
$224$		0			0
$225$	−10.0899			−0.672659
$226$		0			0
$227$	−16.8836	+	6.99343i	−1.12061	+	0.464170i	−0.864578	−	0.502499i	$-0.832414\pi$
$227$	−16.8836	+	6.99343i	−1.12061	+	0.464170i	−0.256029	+	0.966669i	$0.582414\pi$
$228$		0			0
$229$	−3.92011	+	9.46398i	−0.259048	+	0.625397i	−0.998876	−	0.0473987i	$-0.984907\pi$
$229$	−3.92011	+	9.46398i	−0.259048	+	0.625397i	0.739828	+	0.672796i	$0.234907\pi$
$230$		0			0
$231$	−3.35902	−	3.35902i	−0.221008	−	0.221008i
$232$		0			0
$233$	3.06027	−	3.06027i	0.200485	−	0.200485i	−0.599723	−	0.800208i	$-0.704722\pi$
$233$	3.06027	−	3.06027i	0.200485	−	0.200485i	0.800208	+	0.599723i	$0.204722\pi$
$234$		0			0
$235$	−37.9575	−	15.7225i	−2.47608	−	1.02562i
$236$		0			0
$237$	4.90213	+	11.8348i	0.318428	+	0.768752i
$238$		0			0
$239$		−	0.210325i		−	0.0136048i	−0.999977	−	0.00680240i	$-0.997835\pi$
$239$		−	0.210325i		−	0.0136048i	0.999977	−	0.00680240i	$-0.00216529\pi$
$240$		0			0
$241$		−	13.0724i		−	0.842068i	−0.907045	−	0.421034i	$-0.861667\pi$
$241$		−	13.0724i		−	0.842068i	0.907045	−	0.421034i	$-0.138333\pi$
$242$		0			0
$243$	0.382683	+	0.923880i	0.0245492	+	0.0592669i
$244$		0			0
$245$	−17.3853	−	7.20125i	−1.11071	−	0.460071i
$246$		0			0
$247$	−2.19758	+	2.19758i	−0.139829	+	0.139829i
$248$		0			0
$249$	11.8540	+	11.8540i	0.751214	+	0.751214i
$250$		0			0
$251$	−1.21528	+	2.93395i	−0.0767079	+	0.185189i	−0.957582	−	0.288162i	$-0.906956\pi$
$251$	−1.21528	+	2.93395i	−0.0767079	+	0.185189i	0.880874	+	0.473351i	$0.156956\pi$
$252$		0			0
$253$	18.2696	−	7.56751i	1.14860	−	0.475765i
$254$		0			0
$255$	−20.6413			−1.29261
$256$		0			0
$257$	2.57305			0.160502			0.0802512	−	0.996775i	$-0.474428\pi$
$257$	2.57305			0.160502			0.0802512	+	0.996775i	$0.474428\pi$
$258$		0			0
$259$	2.29071	−	0.948841i	0.142338	−	0.0589581i
$260$		0			0
$261$	−2.39502	+	5.78209i	−0.148248	+	0.357903i
$262$		0			0
$263$	−12.8467	−	12.8467i	−0.792159	−	0.792159i	0.189686	−	0.981845i	$-0.439253\pi$
$263$	−12.8467	−	12.8467i	−0.792159	−	0.792159i	−0.981845	+	0.189686i	$0.939253\pi$
$264$		0			0
$265$	−19.7257	+	19.7257i	−1.21174	+	1.21174i
$266$		0			0
$267$	1.29541	+	0.536575i	0.0792776	+	0.0328379i
$268$		0			0
$269$	−3.18478	−	7.68874i	−0.194180	−	0.468791i	0.796561	−	0.604558i	$-0.206650\pi$
$269$	−3.18478	−	7.68874i	−0.194180	−	0.468791i	−0.990741	+	0.135767i	$0.956650\pi$
$270$		0			0
$271$		−	29.7589i		−	1.80772i	−0.427823	−	0.903862i	$-0.640719\pi$
$271$		−	29.7589i		−	1.80772i	0.427823	−	0.903862i	$-0.359281\pi$
$272$		0			0
$273$		−	5.14010i		−	0.311093i
$274$		0			0
$275$	12.4926	+	30.1598i	0.753333	+	1.81871i
$276$		0			0
$277$	−13.4191	−	5.55836i	−0.806274	−	0.333970i	−0.0588078	−	0.998269i	$-0.518730\pi$
$277$	−13.4191	−	5.55836i	−0.806274	−	0.333970i	−0.747466	+	0.664300i	$0.768730\pi$
$278$		0			0
$279$	1.00612	−	1.00612i	0.0602348	−	0.0602348i
$280$		0			0
$281$	0.428981	+	0.428981i	0.0255909	+	0.0255909i	0.719786	−	0.694196i	$-0.244240\pi$
$281$	0.428981	+	0.428981i	0.0255909	+	0.0255909i	−0.694196	+	0.719786i	$0.744240\pi$
$282$		0			0
$283$	10.2786	−	24.8146i	0.610997	−	1.47508i	−0.250910	−	0.968010i	$-0.580730\pi$
$283$	10.2786	−	24.8146i	0.610997	−	1.47508i	0.861907	−	0.507067i	$-0.169270\pi$
$284$		0			0
$285$	3.18601	−	1.31969i	0.188723	−	0.0781716i
$286$		0			0
$287$	−7.11474			−0.419970
$288$		0			0
$289$	−11.2351			−0.660890
$290$		0			0
$291$	−13.4240	+	5.56041i	−0.786930	+	0.325957i
$292$		0			0
$293$	4.95811	−	11.9699i	0.289656	−	0.699292i	−0.710333	−	0.703865i	$-0.751456\pi$
$293$	4.95811	−	11.9699i	0.289656	−	0.699292i	0.999990	+	0.00457366i	$0.00145584\pi$
$294$		0			0
$295$	1.33111	+	1.33111i	0.0775005	+	0.0775005i
$296$		0			0
$297$	2.28777	−	2.28777i	0.132750	−	0.132750i
$298$		0			0
$299$	19.7684	+	8.18834i	1.14324	+	0.473544i
$300$		0			0
$301$	−3.95618	−	9.55106i	−0.228030	−	0.550514i
$302$		0			0
$303$		−	1.94040i		−	0.111473i
$304$		0			0
$305$		−	13.3129i		−	0.762293i
$306$		0			0
$307$	8.37498	+	20.2190i	0.477985	+	1.15396i	0.960552	+	0.278099i	$0.0897044\pi$
$307$	8.37498	+	20.2190i	0.477985	+	1.15396i	−0.482567	+	0.875859i	$0.660296\pi$
$308$		0			0
$309$	−2.76338	−	1.14463i	−0.157203	−	0.0651157i
$310$		0			0
$311$	−5.71820	+	5.71820i	−0.324249	+	0.324249i	−0.850395	−	0.526145i	$-0.823637\pi$
$311$	−5.71820	+	5.71820i	−0.324249	+	0.324249i	0.526145	+	0.850395i	$0.323637\pi$
$312$		0			0
$313$	11.6027	+	11.6027i	0.655823	+	0.655823i	0.954389	−	0.298566i	$-0.0965083\pi$
$313$	11.6027	+	11.6027i	0.655823	+	0.655823i	−0.298566	+	0.954389i	$0.596508\pi$
$314$		0			0
$315$	−2.18265	+	5.26938i	−0.122978	+	0.296896i
$316$		0			0
$317$	19.5616	−	8.10268i	1.09869	−	0.455092i	0.241660	−	0.970361i	$-0.422308\pi$
$317$	19.5616	−	8.10268i	1.09869	−	0.455092i	0.857028	+	0.515269i	$0.172308\pi$
$318$		0			0
$319$	20.2487			1.13371
$320$		0			0
$321$	−5.00379			−0.279284
$322$		0			0
$323$	4.35812	−	1.80519i	0.242492	−	0.100444i
$324$		0			0
$325$	−13.5175	+	32.6341i	−0.749816	+	1.81022i
$326$		0			0
$327$	0.251083	+	0.251083i	0.0138849	+	0.0138849i
$328$		0			0
$329$	−10.9806	+	10.9806i	−0.605379	+	0.605379i
$330$		0			0
$331$	0.922294	+	0.382027i	0.0506939	+	0.0209981i	0.407886	−	0.913033i	$-0.366266\pi$
$331$	0.922294	+	0.382027i	0.0506939	+	0.0209981i	−0.357192	+	0.934031i	$0.616266\pi$
$332$		0			0
$333$	0.646238	+	1.56016i	0.0354136	+	0.0854961i
$334$		0			0
$335$			25.6178i			1.39965i
$336$		0			0
$337$		−	32.5245i		−	1.77172i	−0.463949	−	0.885862i	$-0.653568\pi$
$337$		−	32.5245i		−	1.77172i	0.463949	−	0.885862i	$-0.346432\pi$
$338$		0			0
$339$	−0.913437	−	2.20523i	−0.0496111	−	0.119772i
$340$		0			0
$341$	−4.25311	−	1.76170i	−0.230319	−	0.0954012i
$342$		0			0
$343$	−12.2968	+	12.2968i	−0.663966	+	0.663966i
$344$		0			0
$345$	−16.7886	−	16.7886i	−0.903867	−	0.903867i
$346$		0			0
$347$	−11.0057	+	26.5700i	−0.590815	+	1.42635i	0.291901	+	0.956448i	$0.405712\pi$
$347$	−11.0057	+	26.5700i	−0.590815	+	1.42635i	−0.882717	+	0.469906i	$0.844288\pi$
$348$		0			0
$349$	6.12429	−	2.53676i	0.327826	−	0.135790i	−0.212700	−	0.977118i	$-0.568226\pi$
$349$	6.12429	−	2.53676i	0.327826	−	0.135790i	0.540525	+	0.841328i	$0.318226\pi$
$350$		0			0
$351$	3.50082			0.186860
$352$		0			0
$353$	−27.1372			−1.44437			−0.722185	−	0.691700i	$-0.756862\pi$
$353$	−27.1372			−1.44437			−0.722185	+	0.691700i	$0.756862\pi$
$354$		0			0
$355$	−14.7974	+	6.12928i	−0.785364	+	0.325309i
$356$		0			0
$357$	−2.98563	+	7.20794i	−0.158016	+	0.381485i
$358$		0			0
$359$	6.86522	+	6.86522i	0.362332	+	0.362332i	0.864671	−	0.502339i	$-0.167527\pi$
$359$	6.86522	+	6.86522i	0.362332	+	0.362332i	−0.502339	+	0.864671i	$0.667527\pi$
$360$		0			0
$361$	12.8778	−	12.8778i	0.677777	−	0.677777i
$362$		0			0
$363$	0.491715	+	0.203675i	0.0258084	+	0.0106902i
$364$		0			0
$365$	−2.14573	−	5.18025i	−0.112313	−	0.271147i
$366$		0			0
$367$			32.3050i			1.68631i	0.537671	+	0.843154i	$0.319304\pi$
$367$			32.3050i			1.68631i	−0.537671	+	0.843154i	$0.680696\pi$
$368$		0			0
$369$		−	4.84572i		−	0.252258i
$370$		0			0
$371$	4.03502	+	9.74139i	0.209488	+	0.505748i
$372$		0			0
$373$	−1.12962	−	0.467902i	−0.0584893	−	0.0242271i	0.353247	−	0.935530i	$-0.385078\pi$
$373$	−1.12962	−	0.467902i	−0.0584893	−	0.0242271i	−0.411736	+	0.911303i	$0.635078\pi$
$374$		0			0
$375$	13.9809	−	13.9809i	0.721973	−	0.721973i
$376$		0			0
$377$	15.4926	+	15.4926i	0.797911	+	0.797911i
$378$		0			0
$379$	−12.6694	+	30.5866i	−0.650783	+	1.57113i	0.160861	+	0.986977i	$0.448573\pi$
$379$	−12.6694	+	30.5866i	−0.650783	+	1.57113i	−0.811644	+	0.584152i	$0.801427\pi$
$380$		0			0
$381$	−12.4004	+	5.13640i	−0.635289	+	0.263145i
$382$		0			0
$383$	−9.01248			−0.460516			−0.230258	−	0.973130i	$-0.573957\pi$
$383$	−9.01248			−0.460516			−0.230258	+	0.973130i	$0.573957\pi$
$384$		0			0
$385$	18.4532			0.940461
$386$		0			0
$387$	6.50505	−	2.69448i	0.330670	−	0.136968i
$388$		0			0
$389$	0.147171	−	0.355303i	0.00746188	−	0.0180146i	−0.920105	−	0.391673i	$-0.871897\pi$
$389$	0.147171	−	0.355303i	0.00746188	−	0.0180146i	0.927567	+	0.373658i	$0.121897\pi$
$390$		0			0
$391$	−22.9650	−	22.9650i	−1.16139	−	1.16139i
$392$		0			0
$393$	−5.65467	+	5.65467i	−0.285240	+	0.285240i
$394$		0			0
$395$	−45.9731	−	19.0427i	−2.31316	−	0.958141i
$396$		0			0
$397$	10.7013	+	25.8353i	0.537084	+	1.29664i	0.926750	+	0.375679i	$0.122591\pi$
$397$	10.7013	+	25.8353i	0.537084	+	1.29664i	−0.389666	+	0.920956i	$0.627409\pi$
$398$		0			0
$399$		−	1.30344i		−	0.0652535i
$400$		0			0
$401$		−	39.5351i		−	1.97429i	−0.159825	−	0.987145i	$-0.551093\pi$
$401$		−	39.5351i		−	1.97429i	0.159825	−	0.987145i	$-0.448907\pi$
$402$		0			0
$403$	−1.90623	−	4.60204i	−0.0949559	−	0.229244i
$404$		0			0
$405$	−3.58888	−	1.48656i	−0.178333	−	0.0738678i
$406$		0			0
$407$	3.86336	−	3.86336i	0.191500	−	0.191500i
$408$		0			0
$409$	−16.6530	−	16.6530i	−0.823439	−	0.823439i	0.163160	−	0.986600i	$-0.447831\pi$
$409$	−16.6530	−	16.6530i	−0.823439	−	0.823439i	−0.986600	+	0.163160i	$0.947831\pi$
$410$		0			0
$411$	5.78010	−	13.9544i	0.285111	−	0.688319i
$412$		0			0
$413$	0.657361	−	0.272288i	0.0323466	−	0.0133984i
$414$		0			0
$415$	−65.1211			−3.19667
$416$		0			0
$417$	4.33189			0.212133
$418$		0			0
$419$	30.2809	−	12.5428i	1.47932	−	0.612754i	0.510356	−	0.859963i	$-0.329514\pi$
$419$	30.2809	−	12.5428i	1.47932	−	0.612754i	0.968962	+	0.247210i	$0.0795136\pi$
$420$		0			0
$421$	14.0297	−	33.8706i	0.683764	−	1.65075i	−0.0732174	−	0.997316i	$-0.523327\pi$
$421$	14.0297	−	33.8706i	0.683764	−	1.65075i	0.756981	−	0.653436i	$-0.226673\pi$
$422$		0			0
$423$	−7.47867	−	7.47867i	−0.363626	−	0.363626i
$424$		0			0
$425$	37.9111	−	37.9111i	1.83896	−	1.83896i
$426$		0			0
$427$	−4.64885	−	1.92561i	−0.224973	−	0.0931870i
$428$		0			0
$429$	−4.33448	−	10.4644i	−0.209271	−	0.505224i
$430$		0			0
$431$		−	11.0244i		−	0.531027i	−0.964107	−	0.265513i	$-0.914459\pi$
$431$		−	11.0244i		−	0.531027i	0.964107	−	0.265513i	$-0.0855414\pi$
$432$		0			0
$433$			26.0973i			1.25416i	0.778956	+	0.627079i	$0.215750\pi$
$433$			26.0973i			1.25416i	−0.778956	+	0.627079i	$0.784250\pi$
$434$		0			0
$435$	−9.30363	−	22.4609i	−0.446075	−	1.07692i
$436$		0			0
$437$	5.01291	+	2.07642i	0.239800	+	0.0993285i
$438$		0			0
$439$	9.89316	−	9.89316i	0.472175	−	0.472175i	−0.430443	−	0.902618i	$-0.641643\pi$
$439$	9.89316	−	9.89316i	0.472175	−	0.472175i	0.902618	+	0.430443i	$0.141643\pi$
$440$		0			0
$441$	−3.42539	−	3.42539i	−0.163114	−	0.163114i
$442$		0			0
$443$	7.29919	−	17.6218i	0.346795	−	0.837237i	−0.650200	−	0.759763i	$-0.725315\pi$
$443$	7.29919	−	17.6218i	0.346795	−	0.837237i	0.996994	−	0.0774732i	$-0.0246852\pi$
$444$		0			0
$445$	−5.03210	+	2.08436i	−0.238544	+	0.0988083i
$446$		0			0
$447$	−18.9505			−0.896330
$448$		0			0
$449$	7.16414			0.338096			0.169048	−	0.985608i	$-0.445931\pi$
$449$	7.16414			0.338096			0.169048	+	0.985608i	$0.445931\pi$
$450$		0			0
$451$	−14.4844	+	5.99964i	−0.682044	+	0.282512i
$452$		0			0
$453$	0.612243	−	1.47809i	0.0287657	−	0.0694465i
$454$		0			0
$455$	14.1189	+	14.1189i	0.661902	+	0.661902i
$456$		0			0
$457$	−15.2704	+	15.2704i	−0.714317	+	0.714317i	−0.967435	−	0.253118i	$-0.918544\pi$
$457$	−15.2704	+	15.2704i	−0.714317	+	0.714317i	0.253118	+	0.967435i	$0.418544\pi$
$458$		0			0
$459$	−4.90919	−	2.03345i	−0.229142	−	0.0949135i
$460$		0			0
$461$	5.40240	+	13.0425i	0.251615	+	0.607452i	0.998335	−	0.0576867i	$-0.0183724\pi$
$461$	5.40240	+	13.0425i	0.251615	+	0.607452i	−0.746720	+	0.665139i	$0.768372\pi$
$462$		0			0
$463$			13.5410i			0.629305i	0.949207	+	0.314652i	$0.101888\pi$
$463$			13.5410i			0.629305i	−0.949207	+	0.314652i	$0.898112\pi$
$464$		0			0
$465$			5.52723i			0.256319i
$466$		0			0
$467$	6.18122	+	14.9228i	0.286033	+	0.690544i	0.999953	−	0.00968289i	$-0.00308221\pi$
$467$	6.18122	+	14.9228i	0.286033	+	0.690544i	−0.713920	+	0.700227i	$0.753082\pi$
$468$		0			0
$469$	8.94573	+	3.70544i	0.413075	+	0.171101i
$470$		0			0
$471$	1.29494	−	1.29494i	0.0596676	−	0.0596676i
$472$		0			0
$473$	−16.1082	−	16.1082i	−0.740656	−	0.740656i
$474$		0			0
$475$	−3.42780	+	8.27543i	−0.157278	+	0.379703i
$476$		0			0
$477$	−6.63468	+	2.74817i	−0.303781	+	0.125830i
$478$		0			0
$479$	6.44443			0.294453			0.147227	−	0.989103i	$-0.452965\pi$
$479$	6.44443			0.294453			0.147227	+	0.989103i	$0.452965\pi$
$480$		0			0
$481$	5.91185			0.269557
$482$		0			0
$483$	−8.29091	+	3.43421i	−0.377250	+	0.156262i
$484$		0			0
$485$	21.5998	−	52.1465i	0.980797	−	2.36785i
$486$		0			0
$487$	−4.42962	−	4.42962i	−0.200725	−	0.200725i	0.599585	−	0.800311i	$-0.295332\pi$
$487$	−4.42962	−	4.42962i	−0.200725	−	0.200725i	−0.800311	+	0.599585i	$0.795332\pi$
$488$		0			0
$489$	−15.4512	+	15.4512i	−0.698727	+	0.698727i
$490$		0			0
$491$	−11.7801	−	4.87947i	−0.531628	−	0.220207i	0.100688	−	0.994918i	$-0.467896\pi$
$491$	−11.7801	−	4.87947i	−0.531628	−	0.220207i	−0.632316	+	0.774711i	$0.717896\pi$
$492$		0			0
$493$	−12.7264	−	30.7242i	−0.573167	−	1.38375i
$494$		0			0
$495$			12.5681i			0.564895i
$496$		0			0
$497$			6.05380i			0.271550i
$498$		0			0
$499$	2.23679	+	5.40009i	0.100132	+	0.241741i	0.966005	−	0.258524i	$-0.0832360\pi$
$499$	2.23679	+	5.40009i	0.100132	+	0.241741i	−0.865873	+	0.500265i	$0.833236\pi$
$500$		0			0
$501$	−3.14192	−	1.30143i	−0.140371	−	0.0581434i
$502$		0			0
$503$	−2.89565	+	2.89565i	−0.129111	+	0.129111i	−0.768709	−	0.639598i	$-0.779101\pi$
$503$	−2.89565	+	2.89565i	−0.129111	+	0.129111i	0.639598	+	0.768709i	$0.279101\pi$
$504$		0			0
$505$	5.32991	+	5.32991i	0.237178	+	0.237178i
$506$		0			0
$507$	−0.284803	+	0.687575i	−0.0126485	+	0.0305363i
$508$		0			0
$509$	−5.36042	+	2.22036i	−0.237596	+	0.0984156i	−0.498305	−	0.867002i	$-0.666044\pi$
$509$	−5.36042	+	2.22036i	−0.237596	+	0.0984156i	0.260708	+	0.965418i	$0.416044\pi$
$510$		0			0
$511$	−2.11930			−0.0937525
$512$		0			0
$513$	0.887747			0.0391950
$514$		0			0
$515$	10.7345	−	4.44639i	0.473020	−	0.195931i
$516$		0			0
$517$	−13.0950	+	31.6142i	−0.575919	+	1.39039i
$518$		0			0
$519$	−6.99360	−	6.99360i	−0.306985	−	0.306985i
$520$		0			0
$521$	18.2831	−	18.2831i	0.800998	−	0.800998i	−0.182254	−	0.983252i	$-0.558339\pi$
$521$	18.2831	−	18.2831i	0.800998	−	0.800998i	0.983252	+	0.182254i	$0.0583392\pi$
$522$		0			0
$523$	−5.66441	−	2.34627i	−0.247687	−	0.102595i	0.255386	−	0.966839i	$-0.417797\pi$
$523$	−5.66441	−	2.34627i	−0.247687	−	0.102595i	−0.503073	+	0.864244i	$0.667797\pi$
$524$		0			0
$525$	−5.66927	−	13.6868i	−0.247427	−	0.597342i
$526$		0			0
$527$			7.56065i			0.329347i
$528$		0			0
$529$		−	14.3570i		−	0.624217i
$530$		0			0
$531$	0.185450	+	0.447716i	0.00804785	+	0.0194292i
$532$		0			0
$533$	−15.6727	−	6.49185i	−0.678860	−	0.281193i
$534$		0			0
$535$	13.7445	−	13.7445i	0.594224	−	0.594224i
$536$		0			0
$537$	13.0393	+	13.0393i	0.562686	+	0.562686i
$538$		0			0
$539$	−5.99780	+	14.4800i	−0.258343	+	0.623696i
$540$		0			0
$541$	−5.96613	+	2.47125i	−0.256504	+	0.106247i	−0.507230	−	0.861811i	$-0.669331\pi$
$541$	−5.96613	+	2.47125i	−0.256504	+	0.106247i	0.250726	+	0.968058i	$0.419331\pi$
$542$		0			0
$543$	18.8212			0.807696
$544$		0			0
$545$	−1.37936			−0.0590851
$546$		0			0
$547$	32.5453	−	13.4807i	1.39154	−	0.576393i	0.443996	−	0.896029i	$-0.353560\pi$
$547$	32.5453	−	13.4807i	1.39154	−	0.576393i	0.947541	+	0.319635i	$0.103560\pi$
$548$		0			0
$549$	1.31150	−	3.16624i	0.0559735	−	0.135132i
$550$		0			0
$551$	3.92865	+	3.92865i	0.167366	+	0.167366i
$552$		0			0
$553$	−13.2994	+	13.2994i	−0.565547	+	0.565547i
$554$		0			0
$555$	−6.06054	−	2.51036i	−0.257256	−	0.106559i
$556$		0			0
$557$	6.30768	+	15.2281i	0.267265	+	0.645235i	0.999353	−	0.0359756i	$-0.0114539\pi$
$557$	6.30768	+	15.2281i	0.267265	+	0.645235i	−0.732088	+	0.681210i	$0.761454\pi$
$558$		0			0
$559$		−	24.6494i		−	1.04256i
$560$		0			0
$561$			17.1918i			0.725839i
$562$		0			0
$563$	−3.06528	−	7.40024i	−0.129186	−	0.311883i	0.846031	−	0.533134i	$-0.178986\pi$
$563$	−3.06528	−	7.40024i	−0.129186	−	0.311883i	−0.975217	+	0.221251i	$0.928986\pi$
$564$		0			0
$565$	8.56638	+	3.54831i	0.360390	+	0.149279i
$566$		0			0
$567$	−1.03821	+	1.03821i	−0.0436008	+	0.0436008i
$568$		0			0
$569$	17.9001	+	17.9001i	0.750410	+	0.750410i	0.974556	−	0.224146i	$-0.0719591\pi$
$569$	17.9001	+	17.9001i	0.750410	+	0.750410i	−0.224146	+	0.974556i	$0.571959\pi$
$570$		0			0
$571$	−2.41948	+	5.84113i	−0.101252	+	0.244444i	−0.966385	−	0.257098i	$-0.917234\pi$
$571$	−2.41948	+	5.84113i	−0.101252	+	0.244444i	0.865133	+	0.501542i	$0.167234\pi$
$572$		0			0
$573$	9.15996	−	3.79418i	0.382663	−	0.158504i
$574$		0			0
$575$	61.6698			2.57181
$576$		0			0
$577$	−24.5768			−1.02314			−0.511572	−	0.859240i	$-0.670937\pi$
$577$	−24.5768			−1.02314			−0.511572	+	0.859240i	$0.670937\pi$
$578$		0			0
$579$	−9.09868	+	3.76880i	−0.378128	+	0.156626i
$580$		0			0
$581$	−9.41931	+	22.7402i	−0.390779	+	0.943424i
$582$		0			0
$583$	16.4292	+	16.4292i	0.680429	+	0.680429i
$584$		0			0
$585$	−9.61609	+	9.61609i	−0.397576	+	0.397576i
$586$		0			0
$587$	29.2268	+	12.1061i	1.20632	+	0.499674i	0.893036	−	0.449985i	$-0.148571\pi$
$587$	29.2268	+	12.1061i	1.20632	+	0.499674i	0.313284	+	0.949659i	$0.398571\pi$
$588$		0			0
$589$	−0.483385	−	1.16699i	−0.0199175	−	0.0480852i
$590$		0			0
$591$		−	14.2791i		−	0.587365i
$592$		0			0
$593$			20.8403i			0.855810i	0.903824	+	0.427905i	$0.140748\pi$
$593$			20.8403i			0.855810i	−0.903824	+	0.427905i	$0.859252\pi$
$594$		0			0
$595$	−11.5979	−	27.9998i	−0.475467	−	1.14788i
$596$		0			0
$597$	−8.02847	−	3.32550i	−0.328584	−	0.136104i
$598$		0			0
$599$	−31.6901	+	31.6901i	−1.29482	+	1.29482i	−0.363053	+	0.931768i	$0.618266\pi$
$599$	−31.6901	+	31.6901i	−1.29482	+	1.29482i	−0.931768	+	0.363053i	$0.881734\pi$
$600$		0			0
$601$	−12.9864	−	12.9864i	−0.529726	−	0.529726i	0.390764	−	0.920491i	$-0.372211\pi$
$601$	−12.9864	−	12.9864i	−0.529726	−	0.529726i	−0.920491	+	0.390764i	$0.872211\pi$
$602$		0			0
$603$	−2.52371	+	6.09277i	−0.102773	+	0.248117i
$604$		0			0
$605$	−1.91010	+	0.791190i	−0.0776567	+	0.0321665i
$606$		0			0
$607$	7.55886			0.306805			0.153402	−	0.988164i	$-0.450977\pi$
$607$	7.55886			0.306805			0.153402	+	0.988164i	$0.450977\pi$
$608$		0			0
$609$	−9.18905			−0.372359
$610$		0			0
$611$	−34.2078	+	14.1693i	−1.38390	+	0.573230i
$612$		0			0
$613$	5.16053	−	12.4586i	0.208432	−	0.503199i	−0.784745	−	0.619819i	$-0.787206\pi$
$613$	5.16053	−	12.4586i	0.208432	−	0.503199i	0.993177	+	0.116620i	$0.0372061\pi$
$614$		0			0
$615$	13.3102	+	13.3102i	0.536721	+	0.536721i
$616$		0			0
$617$	−23.7425	+	23.7425i	−0.955835	+	0.955835i	−0.999065	−	0.0432297i	$-0.986235\pi$
$617$	−23.7425	+	23.7425i	−0.955835	+	0.955835i	0.0432297	+	0.999065i	$0.486235\pi$
$618$		0			0
$619$	37.9338	+	15.7127i	1.52469	+	0.631547i	0.978524	−	0.206131i	$-0.0660872\pi$
$619$	37.9338	+	15.7127i	1.52469	+	0.631547i	0.546165	+	0.837678i	$0.316087\pi$
$620$		0			0
$621$	−2.33898	−	5.64679i	−0.0938598	−	0.226598i
$622$		0			0
$623$			2.05869i			0.0824798i
$624$		0			0
$625$			26.3564i			1.05426i
$626$		0			0
$627$	−1.09915	−	2.65358i	−0.0438957	−	0.105974i
$628$		0			0
$629$	−8.29016	−	3.43390i	−0.330551	−	0.136919i
$630$		0			0
$631$	5.63001	−	5.63001i	0.224127	−	0.224127i	−0.586107	−	0.810234i	$-0.699340\pi$
$631$	5.63001	−	5.63001i	0.224127	−	0.224127i	0.810234	+	0.586107i	$0.199340\pi$
$632$		0			0
$633$	7.65129	+	7.65129i	0.304111	+	0.304111i
$634$		0			0
$635$	19.9527	−	48.1701i	0.791798	−	1.91157i
$636$		0			0
$637$	−15.6679	+	6.48986i	−0.620785	+	0.257137i
$638$		0			0
$639$	−4.12313			−0.163108
$640$		0			0
$641$	36.4242			1.43867			0.719334	−	0.694664i	$-0.244447\pi$
$641$	36.4242			1.43867			0.719334	+	0.694664i	$0.244447\pi$
$642$		0			0
$643$	−22.9769	+	9.51734i	−0.906120	+	0.375327i	−0.786570	−	0.617501i	$-0.788145\pi$
$643$	−22.9769	+	9.51734i	−0.906120	+	0.375327i	−0.119550	+	0.992828i	$0.538145\pi$
$644$		0			0
$645$	−10.4669	+	25.2693i	−0.412133	+	0.994978i
$646$		0			0
$647$	34.0895	+	34.0895i	1.34020	+	1.34020i	0.895860	+	0.444336i	$0.146560\pi$
$647$	34.0895	+	34.0895i	1.34020	+	1.34020i	0.444336	+	0.895860i	$0.353440\pi$
$648$		0			0
$649$	1.10866	−	1.10866i	0.0435188	−	0.0435188i
$650$		0			0
$651$	1.93010	+	0.799475i	0.0756468	+	0.0313339i
$652$		0			0
$653$	−11.4288	−	27.5915i	−0.447243	−	1.07974i	−0.973351	−	0.229322i	$-0.926349\pi$
$653$	−11.4288	−	27.5915i	−0.447243	−	1.07974i	0.526108	−	0.850418i	$-0.323651\pi$
$654$		0			0
$655$		−	31.0645i		−	1.21379i
$656$		0			0
$657$		−	1.44342i		−	0.0563131i
$658$		0			0
$659$	−4.60322	−	11.1132i	−0.179316	−	0.432907i	0.808507	−	0.588486i	$-0.200276\pi$
$659$	−4.60322	−	11.1132i	−0.179316	−	0.432907i	−0.987824	+	0.155579i	$0.950276\pi$
$660$		0			0
$661$	18.8580	+	7.81122i	0.733490	+	0.303821i	0.717985	−	0.696058i	$-0.245065\pi$
$661$	18.8580	+	7.81122i	0.733490	+	0.303821i	0.0155046	+	0.999880i	$0.495065\pi$
$662$		0			0
$663$	−13.1538	+	13.1538i	−0.510850	+	0.510850i
$664$		0			0
$665$	3.58029	+	3.58029i	0.138838	+	0.138838i
$666$		0			0
$667$	14.6385	−	35.3404i	0.566803	−	1.36838i
$668$		0			0
$669$	−13.0451	+	5.40346i	−0.504353	+	0.208910i
$670$		0			0
$671$	−11.0881			−0.428050
$672$		0			0
$673$	−46.7689			−1.80281			−0.901404	−	0.432979i	$-0.857463\pi$
$673$	−46.7689			−1.80281			−0.901404	+	0.432979i	$0.857463\pi$
$674$		0			0
$675$	9.32184	−	3.86123i	0.358798	−	0.148619i
$676$		0			0
$677$	7.05433	−	17.0307i	0.271120	−	0.654541i	−0.728412	−	0.685140i	$-0.759741\pi$
$677$	7.05433	−	17.0307i	0.271120	−	0.654541i	0.999532	+	0.0305981i	$0.00974121\pi$
$678$		0			0
$679$	−15.0853	−	15.0853i	−0.578920	−	0.578920i
$680$		0			0
$681$	12.9222	−	12.9222i	0.495179	−	0.495179i
$682$		0			0
$683$	36.1287	+	14.9650i	1.38243	+	0.572620i	0.945129	−	0.326697i	$-0.105936\pi$
$683$	36.1287	+	14.9650i	1.38243	+	0.572620i	0.437297	+	0.899317i	$0.355936\pi$
$684$		0			0
$685$	22.4532	+	54.2068i	0.857893	+	2.07114i
$686$		0			0
$687$		−	10.2437i		−	0.390823i
$688$		0			0
$689$			25.1406i			0.957779i
$690$		0			0
$691$	−11.2605	−	27.1853i	−0.428371	−	1.03418i	−0.979804	−	0.199959i	$-0.935919\pi$
$691$	−11.2605	−	27.1853i	−0.428371	−	1.03418i	0.551434	−	0.834219i	$-0.314081\pi$
$692$		0			0
$693$	4.38878	+	1.81789i	0.166716	+	0.0690560i
$694$		0			0
$695$	−11.8989	+	11.8989i	−0.451349	+	0.451349i
$696$		0			0
$697$	18.2070	+	18.2070i	0.689639	+	0.689639i
$698$		0			0
$699$	−1.65621	+	3.99844i	−0.0626435	+	0.151235i
$700$		0			0
$701$	21.0746	−	8.72940i	0.795978	−	0.329705i	0.0526339	−	0.998614i	$-0.483238\pi$
$701$	21.0746	−	8.72940i	0.795978	−	0.329705i	0.743344	+	0.668909i	$0.233238\pi$
$702$		0			0
$703$	1.49914			0.0565411
$704$		0			0
$705$	41.0849			1.54735
$706$		0			0
$707$	2.63214	−	1.09027i	0.0989917	−	0.0410037i
$708$		0			0
$709$	−0.617186	+	1.49002i	−0.0231789	+	0.0559588i	−0.935045	−	0.354528i	$-0.884641\pi$
$709$	−0.617186	+	1.49002i	−0.0231789	+	0.0559588i	0.911866	+	0.410487i	$0.134641\pi$
$710$		0			0
$711$	−9.05796	−	9.05796i	−0.339700	−	0.339700i
$712$		0			0
$713$	−6.14944	+	6.14944i	−0.230298	+	0.230298i
$714$		0			0
$715$	40.6496	+	16.8376i	1.52021	+	0.629691i
$716$		0			0
$717$	0.0804880	+	0.194315i	0.00300588	+	0.00725683i
$718$		0			0
$719$			11.8288i			0.441140i	0.975371	+	0.220570i	$0.0707917\pi$
$719$			11.8288i			0.441140i	−0.975371	+	0.220570i	$0.929208\pi$
$720$		0			0
$721$		−	4.39163i		−	0.163553i
$722$		0			0
$723$	5.00259	+	12.0773i	0.186048	+	0.449161i
$724$		0			0
$725$	58.3407	+	24.1655i	2.16672	+	0.897484i
$726$		0			0
$727$	12.9471	−	12.9471i	0.480182	−	0.480182i	−0.425008	−	0.905190i	$-0.639729\pi$
$727$	12.9471	−	12.9471i	0.480182	−	0.480182i	0.905190	+	0.425008i	$0.139729\pi$
$728$		0			0
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$		0			0
$731$	−14.3176	+	34.5657i	−0.529555	+	1.27846i
$732$		0			0
$733$	−8.82183	+	3.65412i	−0.325842	+	0.134968i	−0.539607	−	0.841917i	$-0.681427\pi$
$733$	−8.82183	+	3.65412i	−0.325842	+	0.134968i	0.213765	+	0.976885i	$0.431427\pi$
$734$		0			0
$735$	18.8178			0.694104
$736$		0			0
$737$	21.3367			0.785946
$738$		0			0
$739$	2.54866	−	1.05569i	0.0937540	−	0.0388342i	−0.335313	−	0.942107i	$-0.608842\pi$
$739$	2.54866	−	1.05569i	0.0937540	−	0.0388342i	0.429068	+	0.903272i	$0.358842\pi$
$740$		0			0
$741$	1.18932	−	2.87127i	0.0436908	−	0.105479i
$742$		0			0
$743$	−14.0090	−	14.0090i	−0.513942	−	0.513942i	0.401790	−	0.915732i	$-0.368388\pi$
$743$	−14.0090	−	14.0090i	−0.513942	−	0.513942i	−0.915732	+	0.401790i	$0.868388\pi$
$744$		0			0
$745$	52.0535	−	52.0535i	1.90709	−	1.90709i
$746$		0			0
$747$	−15.4879	−	6.41532i	−0.566674	−	0.234724i
$748$		0			0
$749$	−2.81151	−	6.78759i	−0.102730	−	0.248013i
$750$		0			0
$751$		−	1.69567i		−	0.0618757i	−0.999521	−	0.0309379i	$-0.990151\pi$
$751$		−	1.69567i		−	0.0618757i	0.999521	−	0.0309379i	$-0.00984940\pi$
$752$		0			0
$753$		−	3.17568i		−	0.115728i
$754$		0			0
$755$	2.37830	+	5.74173i	0.0865553	+	0.208963i
$756$		0			0
$757$	−21.3707	−	8.85204i	−0.776731	−	0.321733i	−0.0411358	−	0.999154i	$-0.513098\pi$
$757$	−21.3707	−	8.85204i	−0.776731	−	0.321733i	−0.735596	+	0.677421i	$0.763098\pi$
$758$		0			0
$759$	−13.9829	+	13.9829i	−0.507548	+	0.507548i
$760$		0			0
$761$	−16.4756	−	16.4756i	−0.597239	−	0.597239i	0.342338	−	0.939577i	$-0.388781\pi$
$761$	−16.4756	−	16.4756i	−0.597239	−	0.597239i	−0.939577	+	0.342338i	$0.888781\pi$
$762$		0			0
$763$	−0.199514	+	0.481670i	−0.00722290	+	0.0174376i
$764$		0			0
$765$	19.0701	−	7.89910i	0.689481	−	0.285593i
$766$		0			0
$767$	1.69652			0.0612576
$768$		0			0
$769$	−10.8924			−0.392791			−0.196395	−	0.980525i	$-0.562924\pi$
$769$	−10.8924			−0.392791			−0.196395	+	0.980525i	$0.562924\pi$
$770$		0			0
$771$	−2.37719	+	0.984663i	−0.0856123	+	0.0354618i
$772$		0			0
$773$	−19.5101	+	47.1015i	−0.701728	+	1.69412i	0.0179727	+	0.999838i	$0.494279\pi$
$773$	−19.5101	+	47.1015i	−0.701728	+	1.69412i	−0.719701	+	0.694284i	$0.755721\pi$
$774$		0			0
$775$	−10.1516	−	10.1516i	−0.364657	−	0.364657i
$776$		0			0
$777$	−1.75323	+	1.75323i	−0.0628968	+	0.0628968i
$778$		0			0
$779$	−3.97432	−	1.64622i	−0.142395	−	0.0589818i
$780$		0			0
$781$	5.10498	+	12.3245i	0.182670	+	0.441005i
$782$		0			0
$783$		−	6.25849i		−	0.223660i
$784$		0			0
$785$			7.11388i			0.253905i
$786$		0			0
$787$	10.4222	+	25.1613i	0.371510	+	0.896905i	0.993495	+	0.113876i	$0.0363266\pi$
$787$	10.4222	+	25.1613i	0.371510	+	0.896905i	−0.621985	+	0.783029i	$0.713673\pi$
$788$		0			0
$789$	16.7850	+	6.95257i	0.597561	+	0.247518i
$790$		0			0
$791$	2.47814	−	2.47814i	0.0881124	−	0.0881124i
$792$		0			0
$793$	−8.48368	−	8.48368i	−0.301264	−	0.301264i
$794$		0			0
$795$	10.6755	−	25.7729i	0.378620	−	0.914070i
$796$		0			0
$797$	−11.4090	+	4.72576i	−0.404128	+	0.167395i	−0.575482	−	0.817814i	$-0.695186\pi$
$797$	−11.4090	+	4.72576i	−0.404128	+	0.167395i	0.171355	+	0.985209i	$0.445186\pi$
$798$		0			0
$799$	56.1998			1.98820
$800$		0			0
$801$	−1.40214			−0.0495421
$802$		0			0
$803$	−4.31454	+	1.78714i	−0.152257	+	0.0630669i
$804$		0			0
$805$	13.3404	−	32.2066i	0.470188	−	1.13513i
$806$		0			0
$807$	5.88471	+	5.88471i	0.207152	+	0.207152i
$808$		0			0
$809$	15.5322	−	15.5322i	0.546082	−	0.546082i	−0.379223	−	0.925305i	$-0.623809\pi$
$809$	15.5322	−	15.5322i	0.546082	−	0.546082i	0.925305	+	0.379223i	$0.123809\pi$
$810$		0			0
$811$	−10.1946	−	4.22272i	−0.357979	−	0.148280i	0.196443	−	0.980515i	$-0.437061\pi$
$811$	−10.1946	−	4.22272i	−0.357979	−	0.148280i	−0.554423	+	0.832235i	$0.687061\pi$
$812$		0			0
$813$	11.3882	+	27.4936i	0.399403	+	0.964244i
$814$		0			0
$815$		−	84.8828i		−	2.97332i
$816$		0			0
$817$		−	6.25063i		−	0.218682i
$818$		0			0
$819$	1.96703	+	4.74883i	0.0687336	+	0.165938i
$820$		0			0
$821$	26.9571	+	11.1660i	0.940808	+	0.389695i	0.799768	−	0.600309i	$-0.204956\pi$
$821$	26.9571	+	11.1660i	0.940808	+	0.389695i	0.141039	+	0.990004i	$0.454956\pi$
$822$		0			0
$823$	−14.3701	+	14.3701i	−0.500911	+	0.500911i	−0.911721	−	0.410810i	$-0.865246\pi$
$823$	−14.3701	+	14.3701i	−0.500911	+	0.500911i	0.410810	+	0.911721i	$0.365246\pi$
$824$		0			0
$825$	−23.0833	−	23.0833i	−0.803658	−	0.803658i
$826$		0			0
$827$	−1.27090	+	3.06822i	−0.0441935	+	0.106693i	−0.944435	−	0.328699i	$-0.893390\pi$
$827$	−1.27090	+	3.06822i	−0.0441935	+	0.106693i	0.900241	+	0.435391i	$0.143390\pi$
$828$		0			0
$829$	−44.8916	+	18.5947i	−1.55915	+	0.645821i	−0.984941	−	0.172889i	$-0.944690\pi$
$829$	−44.8916	+	18.5947i	−1.55915	+	0.645821i	−0.574207	+	0.818710i	$0.694690\pi$
$830$		0			0
$831$	14.5247			0.503856
$832$		0			0
$833$	25.7407			0.891861
$834$		0			0
$835$	12.2050	−	5.05548i	0.422372	−	0.174952i
$836$		0			0
$837$	−0.544508	+	1.31456i	−0.0188209	+	0.0454378i
$838$		0			0
$839$	−1.80010	−	1.80010i	−0.0621465	−	0.0621465i	0.675350	−	0.737497i	$-0.263992\pi$
$839$	−1.80010	−	1.80010i	−0.0621465	−	0.0621465i	−0.737497	+	0.675350i	$0.763992\pi$
$840$		0			0
$841$	7.19038	−	7.19038i	0.247944	−	0.247944i
$842$		0			0
$843$	−0.560491	−	0.232163i	−0.0193043	−	0.00799612i
$844$		0			0
$845$	−1.10634	−	2.67093i	−0.0380591	−	0.0918829i
$846$		0			0
$847$			0.781447i			0.0268508i
$848$		0			0
$849$			26.8592i			0.921804i
$850$		0			0
$851$	−3.94983	−	9.53574i	−0.135398	−	0.326881i
$852$		0			0
$853$	13.8932	+	5.75474i	0.475693	+	0.197039i	0.607631	−	0.794219i	$-0.292120\pi$
$853$	13.8932	+	5.75474i	0.475693	+	0.197039i	−0.131938	+	0.991258i	$0.542120\pi$
$854$		0			0
$855$	−2.43847	+	2.43847i	−0.0833938	+	0.0833938i
$856$		0			0
$857$	−31.5080	−	31.5080i	−1.07629	−	1.07629i	−0.996838	−	0.0794556i	$-0.974682\pi$
$857$	−31.5080	−	31.5080i	−1.07629	−	1.07629i	−0.0794556	−	0.996838i	$-0.525318\pi$
$858$		0			0
$859$	−7.59894	+	18.3455i	−0.259272	+	0.625939i	−0.998891	−	0.0470875i	$-0.985006\pi$
$859$	−7.59894	+	18.3455i	−0.259272	+	0.625939i	0.739618	+	0.673027i	$0.235006\pi$
$860$		0			0
$861$	6.57316	−	2.72269i	0.224013	−	0.0927891i
$862$		0			0
$863$	−1.95965			−0.0667073			−0.0333537	−	0.999444i	$-0.510619\pi$
$863$	−1.95965			−0.0667073			−0.0333537	+	0.999444i	$0.510619\pi$
$864$		0			0
$865$	38.4201			1.30632
$866$		0			0
$867$	10.3799	−	4.29950i	0.352520	−	0.146019i
$868$		0			0
$869$	−15.8603	+	38.2902i	−0.538025	+	1.29891i
$870$		0			0
$871$	16.3251	+	16.3251i	0.553154	+	0.553154i
$872$		0			0
$873$	10.2743	−	10.2743i	0.347732	−	0.347732i
$874$		0			0
$875$	26.8205	+	11.1094i	0.906700	+	0.375567i
$876$		0			0
$877$	8.40988	+	20.3033i	0.283982	+	0.685592i	0.999921	−	0.0125703i	$-0.00400135\pi$
$877$	8.40988	+	20.3033i	0.283982	+	0.685592i	−0.715939	+	0.698162i	$0.754001\pi$
$878$		0			0
$879$			12.9562i			0.437001i
$880$		0			0
$881$			8.86541i			0.298683i	0.988786	+	0.149342i	$0.0477154\pi$
$881$			8.86541i			0.298683i	−0.988786	+	0.149342i	$0.952285\pi$
$882$		0			0
$883$	−9.81319	−	23.6911i	−0.330240	−	0.797270i	−0.998573	−	0.0534078i	$-0.982992\pi$
$883$	−9.81319	−	23.6911i	−0.330240	−	0.797270i	0.668333	−	0.743863i	$-0.267008\pi$
$884$		0			0
$885$	−1.73918	−	0.720394i	−0.0584621	−	0.0242158i
$886$		0			0
$887$	40.7094	−	40.7094i	1.36689	−	1.36689i	0.502050	−	0.864839i	$-0.332579\pi$
$887$	40.7094	−	40.7094i	1.36689	−	1.36689i	0.864839	−	0.502050i	$-0.167421\pi$
$888$		0			0
$889$	−13.9349	−	13.9349i	−0.467362	−	0.467362i
$890$		0			0
$891$	−1.23813	+	2.98911i	−0.0414790	+	0.100139i
$892$		0			0
$893$	−8.67449	+	3.59309i	−0.290281	+	0.120238i
$894$		0			0
$895$	−71.6327			−2.39442
$896$		0			0
$897$	−21.3972			−0.714431
$898$		0			0
$899$	−8.22715	+	3.40780i	−0.274391	+	0.113656i
$900$		0			0
$901$	14.6029	−	35.2545i	0.486493	−	1.17450i
$902$		0			0
$903$	7.31006	+	7.31006i	0.243264	+	0.243264i
$904$		0			0
$905$	−51.6983	+	51.6983i	−1.71851	+	1.71851i
$906$		0			0
$907$	20.7020	+	8.57503i	0.687397	+	0.284729i	0.698915	−	0.715204i	$-0.253666\pi$
$907$	20.7020	+	8.57503i	0.687397	+	0.284729i	−0.0115180	+	0.999934i	$0.503666\pi$
$908$		0			0
$909$	0.742560	+	1.79270i	0.0246292	+	0.0594601i
$910$		0			0
$911$			49.0914i			1.62647i	0.581935	+	0.813235i	$0.302296\pi$
$911$			49.0914i			1.62647i	−0.581935	+	0.813235i	$0.697704\pi$
$912$		0			0
$913$			54.2382i			1.79502i
$914$		0			0
$915$	5.09462	+	12.2995i	0.168423	+	0.406609i
$916$		0			0
$917$	−10.8477	−	4.49327i	−0.358223	−	0.148381i
$918$		0			0
$919$	−26.2568	+	26.2568i	−0.866131	+	0.866131i	−0.992042	−	0.125910i	$-0.959815\pi$
$919$	−26.2568	+	26.2568i	−0.866131	+	0.866131i	0.125910	+	0.992042i	$0.459815\pi$
$920$		0			0
$921$	−15.4749	−	15.4749i	−0.509917	−	0.509917i
$922$		0			0
$923$	−5.52379	+	13.3356i	−0.181818	+	0.438947i
$924$		0			0
$925$	15.7418	−	6.52047i	0.517588	−	0.214392i
$926$		0			0
$927$	2.99106			0.0982393
$928$		0			0
$929$	9.33360			0.306225			0.153113	−	0.988209i	$-0.451070\pi$
$929$	9.33360			0.306225			0.153113	+	0.988209i	$0.451070\pi$
$930$		0			0
$931$	−3.97310	+	1.64571i	−0.130213	+	0.0539360i
$932$		0			0
$933$	3.09467	−	7.47119i	0.101315	−	0.244596i
$934$		0			0
$935$	−47.2226	−	47.2226i	−1.54434	−	1.54434i
$936$		0			0
$937$	−26.9828	+	26.9828i	−0.881491	+	0.881491i	−0.993686	−	0.112195i	$-0.964212\pi$
$937$	−26.9828	+	26.9828i	−0.881491	+	0.881491i	0.112195	+	0.993686i	$0.464212\pi$
$938$		0			0
$939$	−15.1596	−	6.27933i	−0.494716	−	0.204918i
$940$		0			0
$941$	−20.9573	−	50.5954i	−0.683188	−	1.64936i	−0.758073	−	0.652169i	$-0.773859\pi$
$941$	−20.9573	−	50.5954i	−0.683188	−	1.64936i	0.0748852	−	0.997192i	$-0.476141\pi$
$942$		0			0
$943$			29.6172i			0.964469i
$944$		0			0
$945$		−	5.70353i		−	0.185536i
$946$		0			0
$947$	7.14980	+	17.2611i	0.232337	+	0.560912i	0.996451	−	0.0841692i	$-0.0268236\pi$
$947$	7.14980	+	17.2611i	0.232337	+	0.560912i	−0.764114	+	0.645081i	$0.776824\pi$
$948$		0			0
$949$	−4.66851	−	1.93376i	−0.151546	−	0.0627725i
$950$		0			0
$951$	−14.9718	+	14.9718i	−0.485494	+	0.485494i
$952$		0			0
$953$	−18.0649	−	18.0649i	−0.585181	−	0.585181i	0.351142	−	0.936322i	$-0.385794\pi$
$953$	−18.0649	−	18.0649i	−0.585181	−	0.585181i	−0.936322	+	0.351142i	$0.885794\pi$
$954$		0			0
$955$	−14.7388	+	35.5825i	−0.476935	+	1.15142i
$956$		0			0
$957$	−18.7073	+	7.74884i	−0.604723	+	0.250484i
$958$		0			0
$959$	22.1767			0.716122
$960$		0			0
$961$	−28.9754			−0.934692
$962$		0			0
$963$	4.62290	−	1.91487i	0.148971	−	0.0617058i
$964$		0			0
$965$	14.6402	−	35.3445i	0.471283	−	1.13778i
$966$		0			0
$967$	35.9715	+	35.9715i	1.15677	+	1.15677i	0.985167	+	0.171599i	$0.0548934\pi$
$967$	35.9715	+	35.9715i	1.15677	+	1.15677i	0.171599	+	0.985167i	$0.445107\pi$
$968$		0			0
$969$	−3.33556	+	3.33556i	−0.107154	+	0.107154i
$970$		0			0
$971$	−21.1238	−	8.74978i	−0.677896	−	0.280794i	0.0170508	−	0.999855i	$-0.494572\pi$
$971$	−21.1238	−	8.74978i	−0.677896	−	0.280794i	−0.694947	+	0.719061i	$0.744572\pi$
$972$		0			0
$973$	2.43398	+	5.87616i	0.0780300	+	0.188381i
$974$		0			0
$975$		−	35.3229i		−	1.13124i
$976$		0			0
$977$			14.2027i			0.454386i	0.973850	+	0.227193i	$0.0729548\pi$
$977$			14.2027i			0.454386i	−0.973850	+	0.227193i	$0.927045\pi$
$978$		0			0
$979$	1.73603	+	4.19115i	0.0554838	+	0.133950i
$980$		0			0
$981$	−0.328056	−	0.135885i	−0.0104740	−	0.00433849i
$982$		0			0
$983$	25.7336	−	25.7336i	0.820775	−	0.820775i	−0.165444	−	0.986219i	$-0.552906\pi$
$983$	25.7336	−	25.7336i	0.820775	−	0.820775i	0.986219	+	0.165444i	$0.0529059\pi$
$984$		0			0
$985$	39.2220	+	39.2220i	1.24972	+	1.24972i
$986$		0			0
$987$	5.94265	−	14.3468i	0.189157	−	0.456665i
$988$		0			0
$989$	−39.7591	+	16.4688i	−1.26427	+	0.523676i
$990$		0			0
$991$	13.6553			0.433776			0.216888	−	0.976197i	$-0.430409\pi$
$991$	13.6553			0.433776			0.216888	+	0.976197i	$0.430409\pi$
$992$		0			0
$993$	−0.998284			−0.0316796
$994$		0			0
$995$	31.1872	−	12.9181i	0.988700	−	0.409533i
$996$		0			0
$997$	8.35787	−	20.1777i	0.264696	−	0.639033i	−0.734521	−	0.678586i	$-0.762593\pi$
$997$	8.35787	−	20.1777i	0.264696	−	0.639033i	0.999218	+	0.0395523i	$0.0125932\pi$
$998$		0			0
$999$	−1.19409	−	1.19409i	−0.0377794	−	0.0377794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.97.4		32
4.3	odd	2		768.2.n.a.97.8		32
8.3	odd	2		96.2.n.a.85.3	yes	32
8.5	even	2		384.2.n.a.49.5		32
24.5	odd	2		1152.2.v.c.433.8		32
24.11	even	2		288.2.v.d.181.6		32
32.3	odd	8		768.2.n.a.673.8		32
32.13	even	8		384.2.n.a.337.5		32
32.19	odd	8		96.2.n.a.61.3	✓	32
32.29	even	8	inner	768.2.n.b.673.4		32
96.77	odd	8		1152.2.v.c.721.8		32
96.83	even	8		288.2.v.d.253.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.3	✓	32	32.19	odd	8
96.2.n.a.85.3	yes	32	8.3	odd	2
288.2.v.d.181.6		32	24.11	even	2
288.2.v.d.253.6		32	96.83	even	8
384.2.n.a.49.5		32	8.5	even	2
384.2.n.a.337.5		32	32.13	even	8
768.2.n.a.97.8		32	4.3	odd	2
768.2.n.a.673.8		32	32.3	odd	8
768.2.n.b.97.4		32	1.1	even	1	trivial
768.2.n.b.673.4		32	32.29	even	8	inner
1152.2.v.c.433.8		32	24.5	odd	2
1152.2.v.c.721.8		32	96.77	odd	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{3} +(1.48656 - 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.923880 + 0.382683i) q^{3} +(1.48656 - 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-2.98911 - 1.23813i) q^{11} +(-1.33971 - 3.23434i) q^{13} +3.88457i q^{15} +5.31367i q^{17} +(-0.339726 - 0.820171i) q^{19} +(1.35649 + 0.561876i) q^{21} +(-4.32186 + 4.32186i) q^{23} +(-7.13463 - 7.13463i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(-5.78209 + 2.39502i) q^{29} +1.42287 q^{31} +3.23539 q^{33} +(-5.26938 + 2.18265i) q^{35} +(-0.646238 + 1.56016i) q^{37} +(2.47546 + 2.47546i) q^{39} +(3.42644 - 3.42644i) q^{41} +(6.50505 + 2.69448i) q^{43} +(-1.48656 - 3.58888i) q^{45} -10.5764i q^{47} -4.84423i q^{49} +(-2.03345 - 4.90919i) q^{51} +(-6.63468 - 2.74817i) q^{53} +(-8.88700 + 8.88700i) q^{55} +(0.627732 + 0.627732i) q^{57} +(-0.185450 + 0.447716i) q^{59} +(3.16624 - 1.31150i) q^{61} -1.46825 q^{63} -13.5992 q^{65} +(-6.09277 + 2.52371i) q^{67} +(2.33898 - 5.64679i) q^{69} +(-2.91549 - 2.91549i) q^{71} +(1.02065 - 1.02065i) q^{73} +(9.32184 + 3.86123i) q^{75} +(1.81789 + 4.38878i) q^{77} -12.8099i q^{79} -1.00000i q^{81} +(-6.41532 - 15.4879i) q^{83} +(19.0701 + 7.89910i) q^{85} +(4.42542 - 4.42542i) q^{87} +(-0.991462 - 0.991462i) q^{89} +(-1.96703 + 4.74883i) q^{91} +(-1.31456 + 0.544508i) q^{93} -3.44851 q^{95} +14.5301 q^{97} +(-2.98911 + 1.23813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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