LMFDB - Embedded newform 768.2.o.b.95.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	768.95
Dual form			768.2.o.b.671.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +O(q^{10})$	\(q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +(-3.96678 + 1.64309i) q^{11} +(-1.13904 + 2.74988i) q^{13} +(-5.21329 + 0.819208i) q^{15} -5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(-0.694704 - 1.13675i) q^{21} +(1.46457 + 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(3.93885 + 3.38902i) q^{27} +(0.520422 - 1.25641i) q^{29} +5.64072i q^{31} +(-7.34659 + 1.15443i) q^{33} +(2.16511 + 0.896820i) q^{35} +(-4.19628 - 10.1307i) q^{37} +(-3.03532 + 4.16709i) q^{39} +(-4.93573 + 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(-9.11055 - 0.739312i) q^{45} +8.98904i q^{47} -6.40839i q^{49} +(-9.65507 - 2.33040i) q^{51} +(1.04873 + 2.53186i) q^{53} +(9.25030 - 9.25030i) q^{55} +(-0.120201 - 0.0875545i) q^{57} +(-0.498592 - 1.20371i) q^{59} +(3.69353 + 1.52991i) q^{61} +(-0.707713 - 2.19627i) q^{63} -9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(1.87072 + 3.06109i) q^{69} +(4.08070 - 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(6.33018 - 3.86856i) q^{75} +(3.05109 + 1.26380i) q^{77} +0.637492 q^{79} +(5.25459 + 7.30679i) q^{81} +(-1.94530 + 4.69638i) q^{83} +(16.1419 - 6.68618i) q^{85} +(1.38682 - 1.90393i) q^{87} +(-0.902588 - 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(-2.29231 + 9.49729i) q^{93} +0.261590 q^{95} -13.3054 q^{97} +(-12.8386 - 1.04184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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
$3$	1.68370	+	0.406387i	0.972085	+	0.234627i
$3$	1.68370	+	0.406387i	0.972085	+	0.234627i
$4$		0			0
$5$	−2.81491	+	1.16597i	−1.25886	+	0.521438i	−0.909561	−	0.415571i	$-0.863582\pi$
$5$	−2.81491	+	1.16597i	−1.25886	+	0.521438i	−0.349303	+	0.937010i	$0.613582\pi$
$6$		0			0
$7$	−0.543879	−	0.543879i	−0.205567	−	0.205567i	0.596813	−	0.802380i	$-0.296433\pi$
$7$	−0.543879	−	0.543879i	−0.205567	−	0.205567i	−0.802380	+	0.596813i	$0.796433\pi$
$8$		0			0
$9$	2.66970	+	1.36847i	0.889900	+	0.456156i
$10$		0			0
$11$	−3.96678	+	1.64309i	−1.19603	+	0.495411i	−0.889713	−	0.456520i	$-0.849096\pi$
$11$	−3.96678	+	1.64309i	−1.19603	+	0.495411i	−0.306314	+	0.951930i	$0.599096\pi$
$12$		0			0
$13$	−1.13904	+	2.74988i	−0.315912	+	0.762680i	0.683550	+	0.729903i	$0.260435\pi$
$13$	−1.13904	+	2.74988i	−0.315912	+	0.762680i	−0.999463	+	0.0327767i	$0.989565\pi$
$14$		0			0
$15$	−5.21329	+	0.819208i	−1.34607	+	0.211519i
$16$		0			0
$17$	−5.73443			−1.39080			−0.695402	−	0.718621i	$-0.744774\pi$
$17$	−5.73443			−1.39080			−0.695402	+	0.718621i	$0.744774\pi$
$18$		0			0
$19$	−0.0793211	−	0.0328559i	−0.0181975	−	0.00753765i	0.373566	−	0.927604i	$-0.378135\pi$
$19$	−0.0793211	−	0.0328559i	−0.0181975	−	0.00753765i	−0.391764	+	0.920066i	$0.628135\pi$
$20$		0			0
$21$	−0.694704	−	1.13675i	−0.151597	−	0.248060i
$22$		0			0
$23$	1.46457	+	1.46457i	0.305385	+	0.305385i	0.843116	−	0.537731i	$-0.180719\pi$
$23$	1.46457	+	1.46457i	0.305385	+	0.305385i	−0.537731	+	0.843116i	$0.680719\pi$
$24$		0			0
$25$	3.02867	−	3.02867i	0.605733	−	0.605733i
$26$		0			0
$27$	3.93885	+	3.38902i	0.758032	+	0.652217i
$28$		0			0
$29$	0.520422	−	1.25641i	0.0966400	−	0.233310i	−0.868165	−	0.496275i	$-0.834701\pi$
$29$	0.520422	−	1.25641i	0.0966400	−	0.233310i	0.964805	+	0.262966i	$0.0847006\pi$
$30$		0			0
$31$			5.64072i			1.01310i	0.862210	+	0.506552i	$0.169080\pi$
$31$			5.64072i			1.01310i	−0.862210	+	0.506552i	$0.830920\pi$
$32$		0			0
$33$	−7.34659	+	1.15443i	−1.27888	+	0.200961i
$34$		0			0
$35$	2.16511	+	0.896820i	0.365971	+	0.151590i
$36$		0			0
$37$	−4.19628	−	10.1307i	−0.689864	−	1.66548i	−0.745055	−	0.667003i	$-0.767577\pi$
$37$	−4.19628	−	10.1307i	−0.689864	−	1.66548i	0.0551907	−	0.998476i	$-0.482423\pi$
$38$		0			0
$39$	−3.03532	+	4.16709i	−0.486040	+	0.667269i
$40$		0			0
$41$	−4.93573	+	4.93573i	−0.770831	+	0.770831i	−0.978252	−	0.207421i	$-0.933493\pi$
$41$	−4.93573	+	4.93573i	−0.770831	+	0.770831i	0.207421	+	0.978252i	$0.433493\pi$
$42$		0			0
$43$	3.50661	+	8.46571i	0.534753	+	1.29101i	0.928344	+	0.371722i	$0.121233\pi$
$43$	3.50661	+	8.46571i	0.534753	+	1.29101i	−0.393591	+	0.919286i	$0.628767\pi$
$44$		0			0
$45$	−9.11055	−	0.739312i	−1.35812	−	0.110210i
$46$		0			0
$47$			8.98904i			1.31119i	0.755115	+	0.655593i	$0.227581\pi$
$47$			8.98904i			1.31119i	−0.755115	+	0.655593i	$0.772419\pi$
$48$		0			0
$49$		−	6.40839i		−	0.915485i
$50$		0			0
$51$	−9.65507	−	2.33040i	−1.35198	−	0.326321i
$52$		0			0
$53$	1.04873	+	2.53186i	0.144054	+	0.347777i	0.979395	−	0.201955i	$-0.0647296\pi$
$53$	1.04873	+	2.53186i	0.144054	+	0.347777i	−0.835341	+	0.549733i	$0.814730\pi$
$54$		0			0
$55$	9.25030	−	9.25030i	1.24731	−	1.24731i
$56$		0			0
$57$	−0.120201	−	0.0875545i	−0.0159210	−	0.0115969i
$58$		0			0
$59$	−0.498592	−	1.20371i	−0.0649111	−	0.156709i	0.888095	−	0.459659i	$-0.152028\pi$
$59$	−0.498592	−	1.20371i	−0.0649111	−	0.156709i	−0.953006	+	0.302950i	$0.902028\pi$
$60$		0			0
$61$	3.69353	+	1.52991i	0.472908	+	0.195885i	0.606392	−	0.795166i	$-0.292616\pi$
$61$	3.69353	+	1.52991i	0.472908	+	0.195885i	−0.133484	+	0.991051i	$0.542616\pi$
$62$		0			0
$63$	−0.707713	−	2.19627i	−0.0891634	−	0.276704i
$64$		0			0
$65$		−	9.06875i		−	1.12484i
$66$		0			0
$67$	3.35550	−	8.10090i	0.409940	−	0.989682i	−0.575213	−	0.818004i	$-0.695081\pi$
$67$	3.35550	−	8.10090i	0.409940	−	0.989682i	0.985153	−	0.171679i	$-0.0549191\pi$
$68$		0			0
$69$	1.87072	+	3.06109i	0.225209	+	0.368512i
$70$		0			0
$71$	4.08070	−	4.08070i	0.484290	−	0.484290i	−0.422209	−	0.906499i	$-0.638745\pi$
$71$	4.08070	−	4.08070i	0.484290	−	0.484290i	0.906499	+	0.422209i	$0.138745\pi$
$72$		0			0
$73$	1.59075	+	1.59075i	0.186183	+	0.186183i	0.794044	−	0.607861i	$-0.207972\pi$
$73$	1.59075	+	1.59075i	0.186183	+	0.186183i	−0.607861	+	0.794044i	$0.707972\pi$
$74$		0			0
$75$	6.33018	−	3.86856i	0.730946	−	0.446703i
$76$		0			0
$77$	3.05109	+	1.26380i	0.347704	+	0.144024i
$78$		0			0
$79$	0.637492			0.0717235			0.0358618	−	0.999357i	$-0.488582\pi$
$79$	0.637492			0.0717235			0.0358618	+	0.999357i	$0.488582\pi$
$80$		0			0
$81$	5.25459	+	7.30679i	0.583844	+	0.811866i
$82$		0			0
$83$	−1.94530	+	4.69638i	−0.213525	+	0.515495i	−0.993960	−	0.109742i	$-0.964998\pi$
$83$	−1.94530	+	4.69638i	−0.213525	+	0.515495i	0.780435	+	0.625237i	$0.214998\pi$
$84$		0			0
$85$	16.1419	−	6.68618i	1.75083	−	0.725218i
$86$		0			0
$87$	1.38682	−	1.90393i	0.148683	−	0.204122i
$88$		0			0
$89$	−0.902588	−	0.902588i	−0.0956742	−	0.0956742i	0.657650	−	0.753324i	$-0.271551\pi$
$89$	−0.902588	−	0.902588i	−0.0956742	−	0.0956742i	−0.753324	+	0.657650i	$0.771551\pi$
$90$		0			0
$91$	2.11510	−	0.876104i	0.221723	−	0.0918406i
$92$		0			0
$93$	−2.29231	+	9.49729i	−0.237702	+	0.984823i
$94$		0			0
$95$	0.261590			0.0268386
$96$		0			0
$97$	−13.3054			−1.35095			−0.675477	−	0.737381i	$-0.736062\pi$
$97$	−13.3054			−1.35095			−0.675477	+	0.737381i	$0.736062\pi$
$98$		0			0
$99$	−12.8386	−	1.04184i	−1.29033	−	0.104709i
$100$		0			0
$101$	5.49437	−	2.27584i	0.546710	−	0.226455i	−0.0921939	−	0.995741i	$-0.529388\pi$
$101$	5.49437	−	2.27584i	0.546710	−	0.226455i	0.638904	+	0.769286i	$0.279388\pi$
$102$		0			0
$103$	7.86860	+	7.86860i	0.775316	+	0.775316i	0.979030	−	0.203714i	$-0.0653014\pi$
$103$	7.86860	+	7.86860i	0.775316	+	0.775316i	−0.203714	+	0.979030i	$0.565301\pi$
$104$		0			0
$105$	3.28095	+	2.38985i	0.320188	+	0.233226i
$106$		0			0
$107$	−0.901495	+	0.373412i	−0.0871508	+	0.0360991i	−0.425833	−	0.904802i	$-0.640019\pi$
$107$	−0.901495	+	0.373412i	−0.0871508	+	0.0360991i	0.338682	+	0.940901i	$0.390019\pi$
$108$		0			0
$109$	−0.457650	+	1.10486i	−0.0438349	+	0.105827i	−0.944280	−	0.329142i	$-0.893241\pi$
$109$	−0.457650	+	1.10486i	−0.0438349	+	0.105827i	0.900446	+	0.434969i	$0.143241\pi$
$110$		0			0
$111$	−2.94829	−	18.7624i	−0.279840	−	1.78085i
$112$		0			0
$113$	8.48446			0.798151			0.399076	−	0.916918i	$-0.369331\pi$
$113$	8.48446			0.798151			0.399076	+	0.916918i	$0.369331\pi$
$114$		0			0
$115$	−5.83029	−	2.41499i	−0.543678	−	0.225199i
$116$		0			0
$117$	−6.80402	+	5.78262i	−0.629032	+	0.534604i
$118$		0			0
$119$	3.11883	+	3.11883i	0.285903	+	0.285903i
$120$		0			0
$121$	5.25738	−	5.25738i	0.477944	−	0.477944i
$122$		0			0
$123$	−10.3161	+	6.30448i	−0.930172	+	0.568456i
$124$		0			0
$125$	0.835790	−	2.01777i	0.0747553	−	0.180475i
$126$		0			0
$127$			7.01144i			0.622165i	0.950383	+	0.311083i	$0.100692\pi$
$127$			7.01144i			0.622165i	−0.950383	+	0.311083i	$0.899308\pi$
$128$		0			0
$129$	2.46373	+	15.6788i	0.216920	+	1.38044i
$130$		0			0
$131$	4.09398	+	1.69578i	0.357693	+	0.148161i	0.554291	−	0.832323i	$-0.312989\pi$
$131$	4.09398	+	1.69578i	0.357693	+	0.148161i	−0.196598	+	0.980484i	$0.562989\pi$
$132$		0			0
$133$	0.0252714	+	0.0610107i	0.00219131	+	0.00529029i
$134$		0			0
$135$	−15.0390	−	4.94718i	−1.29435	−	0.425786i
$136$		0			0
$137$	6.04464	−	6.04464i	0.516428	−	0.516428i	−0.400061	−	0.916489i	$-0.631011\pi$
$137$	6.04464	−	6.04464i	0.516428	−	0.516428i	0.916489	+	0.400061i	$0.131011\pi$
$138$		0			0
$139$	3.82265	+	9.22869i	0.324233	+	0.782767i	0.998999	+	0.0447354i	$0.0142445\pi$
$139$	3.82265	+	9.22869i	0.324233	+	0.782767i	−0.674766	+	0.738032i	$0.735756\pi$
$140$		0			0
$141$	−3.65302	+	15.1348i	−0.307640	+	1.27458i
$142$		0			0
$143$		−	12.7797i		−	1.06869i
$144$		0			0
$145$			4.14347i			0.344097i
$146$		0			0
$147$	2.60429	−	10.7898i	0.214798	−	0.889929i
$148$		0			0
$149$	−4.03660	−	9.74522i	−0.330691	−	0.798359i	−0.998538	−	0.0540601i	$-0.982784\pi$
$149$	−4.03660	−	9.74522i	−0.330691	−	0.798359i	0.667846	−	0.744299i	$-0.267216\pi$
$150$		0			0
$151$	−7.98901	+	7.98901i	−0.650136	+	0.650136i	−0.953026	−	0.302889i	$-0.902049\pi$
$151$	−7.98901	+	7.98901i	−0.650136	+	0.650136i	0.302889	+	0.953026i	$0.402049\pi$
$152$		0			0
$153$	−15.3092	−	7.84738i	−1.23768	−	0.634423i
$154$		0			0
$155$	−6.57692	−	15.8781i	−0.528271	−	1.27536i
$156$		0			0
$157$	−2.65449	−	1.09953i	−0.211852	−	0.0877518i	0.274234	−	0.961663i	$-0.411576\pi$
$157$	−2.65449	−	1.09953i	−0.211852	−	0.0877518i	−0.486086	+	0.873911i	$0.661576\pi$
$158$		0			0
$159$	0.736834	+	4.68908i	0.0584347	+	0.371868i
$160$		0			0
$161$		−	1.59310i		−	0.125554i
$162$		0			0
$163$	−3.51824	+	8.49377i	−0.275570	+	0.665284i	−0.999703	−	0.0243763i	$-0.992240\pi$
$163$	−3.51824	+	8.49377i	−0.275570	+	0.665284i	0.724133	+	0.689660i	$0.242240\pi$
$164$		0			0
$165$	19.3339	−	11.8155i	1.50514	−	0.919838i
$166$		0			0
$167$	6.70414	−	6.70414i	0.518782	−	0.518782i	−0.398421	−	0.917203i	$-0.630442\pi$
$167$	6.70414	−	6.70414i	0.518782	−	0.518782i	0.917203	+	0.398421i	$0.130442\pi$
$168$		0			0
$169$	2.92794	+	2.92794i	0.225226	+	0.225226i
$170$		0			0
$171$	−0.166801	−	0.196264i	−0.0127556	−	0.0150087i
$172$		0			0
$173$	18.7129	+	7.75114i	1.42272	+	0.589308i	0.955541	−	0.294857i	$-0.0952720\pi$
$173$	18.7129	+	7.75114i	1.42272	+	0.589308i	0.467174	+	0.884165i	$0.345272\pi$
$174$		0			0
$175$	−3.29446			−0.249037
$176$		0			0
$177$	−0.350309	−	2.22930i	−0.0263308	−	0.167565i
$178$		0			0
$179$	7.00110	−	16.9021i	0.523286	−	1.26333i	−0.412564	−	0.910928i	$-0.635367\pi$
$179$	7.00110	−	16.9021i	0.523286	−	1.26333i	0.935851	−	0.352397i	$-0.114633\pi$
$180$		0			0
$181$	−14.4907	+	6.00226i	−1.07709	+	0.446144i	−0.849487	−	0.527610i	$-0.823088\pi$
$181$	−14.4907	+	6.00226i	−1.07709	+	0.446144i	−0.227601	+	0.973754i	$0.573088\pi$
$182$		0			0
$183$	5.59706	+	4.07691i	0.413747	+	0.301374i
$184$		0			0
$185$	23.6243	+	23.6243i	1.73689	+	1.73689i
$186$		0			0
$187$	22.7472	−	9.42220i	1.66344	−	0.689019i
$188$		0			0
$189$	−0.299040	−	3.98547i	−0.0217520	−	0.289901i
$190$		0			0
$191$	−15.7313			−1.13828			−0.569139	−	0.822241i	$-0.692723\pi$
$191$	−15.7313			−1.13828			−0.569139	+	0.822241i	$0.692723\pi$
$192$		0			0
$193$	12.2248			0.879962			0.439981	−	0.898007i	$-0.354985\pi$
$193$	12.2248			0.879962			0.439981	+	0.898007i	$0.354985\pi$
$194$		0			0
$195$	3.68542	−	15.2691i	0.263918	−	1.09344i
$196$		0			0
$197$	−21.5949	+	8.94488i	−1.53857	+	0.637297i	−0.981205	−	0.192971i	$-0.938188\pi$
$197$	−21.5949	+	8.94488i	−1.53857	+	0.637297i	−0.557365	+	0.830267i	$0.688188\pi$
$198$		0			0
$199$	−1.57778	−	1.57778i	−0.111846	−	0.111846i	0.648969	−	0.760815i	$-0.275201\pi$
$199$	−1.57778	−	1.57778i	−0.111846	−	0.111846i	−0.760815	+	0.648969i	$0.775201\pi$
$200$		0			0
$201$	8.94176	−	12.2759i	0.630703	−	0.865873i
$202$		0			0
$203$	−0.966382	+	0.400288i	−0.0678267	+	0.0280947i
$204$		0			0
$205$	8.13869	−	19.6485i	0.568431	−	1.37231i
$206$		0			0
$207$	1.90575	+	5.91420i	0.132459	+	0.411065i
$208$		0			0
$209$	0.368634			0.0254990
$210$		0			0
$211$	25.3543	+	10.5021i	1.74546	+	0.722994i	0.998296	+	0.0583569i	$0.0185861\pi$
$211$	25.3543	+	10.5021i	1.74546	+	0.722994i	0.747166	+	0.664637i	$0.231414\pi$
$212$		0			0
$213$	8.52902	−	5.21233i	0.584399	−	0.357143i
$214$		0			0
$215$	−19.7415	−	19.7415i	−1.34636	−	1.34636i
$216$		0			0
$217$	3.06787	−	3.06787i	0.208261	−	0.208261i
$218$		0			0
$219$	2.03188	+	3.32480i	0.137302	+	0.224669i
$220$		0			0
$221$	6.53174	−	15.7690i	0.439372	−	1.06074i
$222$		0			0
$223$		−	23.6266i		−	1.58216i	−0.611716	−	0.791078i	$-0.709520\pi$
$223$		−	23.6266i		−	1.58216i	0.611716	−	0.791078i	$-0.290480\pi$
$224$		0			0
$225$	12.2303	−	3.94100i	0.815351	−	0.262733i
$226$		0			0
$227$	16.7455	+	6.93620i	1.11144	+	0.460372i	0.861432	−	0.507873i	$-0.169568\pi$
$227$	16.7455	+	6.93620i	1.11144	+	0.460372i	0.250004	+	0.968245i	$0.419568\pi$
$228$		0			0
$229$	5.05650	+	12.2075i	0.334143	+	0.806693i	0.998254	+	0.0590592i	$0.0188101\pi$
$229$	5.05650	+	12.2075i	0.334143	+	0.806693i	−0.664111	+	0.747634i	$0.731190\pi$
$230$		0			0
$231$	4.62353	+	3.36779i	0.304206	+	0.221584i
$232$		0			0
$233$	−7.93372	+	7.93372i	−0.519756	+	0.519756i	−0.917497	−	0.397742i	$-0.869794\pi$
$233$	−7.93372	+	7.93372i	−0.519756	+	0.519756i	0.397742	+	0.917497i	$0.369794\pi$
$234$		0			0
$235$	−10.4810	−	25.3033i	−0.683703	−	1.65060i
$236$		0			0
$237$	1.07335	+	0.259068i	0.0697214	+	0.0168283i
$238$		0			0
$239$			16.7260i			1.08191i	0.841051	+	0.540956i	$0.181937\pi$
$239$			16.7260i			1.08191i	−0.841051	+	0.540956i	$0.818063\pi$
$240$		0			0
$241$		−	9.00218i		−	0.579881i	−0.957045	−	0.289941i	$-0.906364\pi$
$241$		−	9.00218i		−	0.579881i	0.957045	−	0.289941i	$-0.0936356\pi$
$242$		0			0
$243$	5.87778	+	14.4379i	0.377060	+	0.926189i
$244$		0			0
$245$	7.47200	+	18.0390i	0.477369	+	1.15247i
$246$		0			0
$247$	0.180700	−	0.180700i	0.0114976	−	0.0114976i
$248$		0			0
$249$	−5.18386	+	7.11675i	−0.328514	+	0.451006i
$250$		0			0
$251$	−0.601450	−	1.45203i	−0.0379632	−	0.0916513i	0.903761	−	0.428038i	$-0.140795\pi$
$251$	−0.601450	−	1.45203i	−0.0379632	−	0.0916513i	−0.941724	+	0.336387i	$0.890795\pi$
$252$		0			0
$253$	−8.21607	−	3.40321i	−0.516540	−	0.213958i
$254$		0			0
$255$	29.8953	−	4.69769i	1.87211	−	0.294181i
$256$		0			0
$257$		−	8.28941i		−	0.517079i	−0.966001	−	0.258539i	$-0.916759\pi$
$257$		−	8.28941i		−	0.517079i	0.966001	−	0.258539i	$-0.0832412\pi$
$258$		0			0
$259$	−3.22761	+	7.79215i	−0.200554	+	0.484181i
$260$		0			0
$261$	3.10873	−	2.64206i	0.192425	−	0.163539i
$262$		0			0
$263$	8.76126	−	8.76126i	0.540243	−	0.540243i	−0.383357	−	0.923600i	$-0.625232\pi$
$263$	8.76126	−	8.76126i	0.540243	−	0.540243i	0.923600	+	0.383357i	$0.125232\pi$
$264$		0			0
$265$	−5.90415	−	5.90415i	−0.362689	−	0.362689i
$266$		0			0
$267$	−1.15289	−	1.88649i	−0.0705557	−	0.115451i
$268$		0			0
$269$	−15.1023	−	6.25558i	−0.920804	−	0.381409i	−0.128621	−	0.991694i	$-0.541055\pi$
$269$	−15.1023	−	6.25558i	−0.920804	−	0.381409i	−0.792182	+	0.610284i	$0.791055\pi$
$270$		0			0
$271$	17.5035			1.06326			0.531631	−	0.846976i	$-0.321579\pi$
$271$	17.5035			1.06326			0.531631	+	0.846976i	$0.321579\pi$
$272$		0			0
$273$	3.91724	−	0.615548i	0.237082	−	0.0372547i
$274$		0			0
$275$	−7.03766	+	16.9904i	−0.424387	+	1.02456i
$276$		0			0
$277$	−21.3684	+	8.85109i	−1.28390	+	0.531811i	−0.917163	−	0.398512i	$-0.869527\pi$
$277$	−21.3684	+	8.85109i	−1.28390	+	0.531811i	−0.366742	+	0.930323i	$0.619527\pi$
$278$		0			0
$279$	−7.71915	+	15.0590i	−0.462133	+	0.901561i
$280$		0			0
$281$	−5.93438	−	5.93438i	−0.354015	−	0.354015i	0.507586	−	0.861601i	$-0.330538\pi$
$281$	−5.93438	−	5.93438i	−0.354015	−	0.354015i	−0.861601	+	0.507586i	$0.830538\pi$
$282$		0			0
$283$	−23.7525	+	9.83861i	−1.41194	+	0.584845i	−0.952822	−	0.303530i	$-0.901835\pi$
$283$	−23.7525	+	9.83861i	−1.41194	+	0.584845i	−0.459119	+	0.888375i	$0.651835\pi$
$284$		0			0
$285$	0.440440	+	0.106307i	0.0260894	+	0.00629707i
$286$		0			0
$287$	5.36888			0.316915
$288$		0			0
$289$	15.8837			0.934334
$290$		0			0
$291$	−22.4023	−	5.40712i	−1.31324	−	0.316971i
$292$		0			0
$293$	−4.20032	+	1.73983i	−0.245386	+	0.101642i	−0.501987	−	0.864875i	$-0.667397\pi$
$293$	−4.20032	+	1.73983i	−0.245386	+	0.101642i	0.256601	+	0.966517i	$0.417397\pi$
$294$		0			0
$295$	2.80698	+	2.80698i	0.163429	+	0.163429i
$296$		0			0
$297$	−21.1930	−	6.97159i	−1.22974	−	0.404533i
$298$		0			0
$299$	−5.69562	+	2.35920i	−0.329386	+	0.136436i
$300$		0			0
$301$	2.69715	−	6.51149i	0.155461	−	0.375316i
$302$		0			0
$303$	10.1758	−	1.59900i	0.584582	−	0.0918602i
$304$		0			0
$305$	−12.1808			−0.697469
$306$		0			0
$307$	−12.3645	−	5.12154i	−0.705678	−	0.292302i	0.000836540	−	1.00000i	$-0.499734\pi$
$307$	−12.3645	−	5.12154i	−0.705678	−	0.292302i	−0.706515	+	0.707698i	$0.749734\pi$
$308$		0			0
$309$	10.0507	+	16.4461i	0.571763	+	0.935584i
$310$		0			0
$311$	−10.7303	−	10.7303i	−0.608462	−	0.608462i	0.334082	−	0.942544i	$-0.391574\pi$
$311$	−10.7303	−	10.7303i	−0.608462	−	0.608462i	−0.942544	+	0.334082i	$0.891574\pi$
$312$		0			0
$313$	−17.8971	+	17.8971i	−1.01160	+	1.01160i	−0.0116708	+	0.999932i	$0.503715\pi$
$313$	−17.8971	+	17.8971i	−1.01160	+	1.01160i	−0.999932	+	0.0116708i	$0.996285\pi$
$314$		0			0
$315$	4.55294	+	5.35713i	0.256529	+	0.301840i
$316$		0			0
$317$	−2.59675	+	6.26910i	−0.145848	+	0.352108i	−0.979874	−	0.199617i	$-0.936030\pi$
$317$	−2.59675	+	6.26910i	−0.145848	+	0.352108i	0.834026	+	0.551725i	$0.186030\pi$
$318$		0			0
$319$			5.83900i			0.326921i
$320$		0			0
$321$	−1.66960	+	0.262358i	−0.0931879	+	0.0146434i
$322$		0			0
$323$	0.454861	+	0.188410i	0.0253091	+	0.0104834i
$324$		0			0
$325$	4.87871	+	11.7782i	0.270622	+	0.653340i
$326$		0			0
$327$	−1.21955	+	1.67428i	−0.0674411	+	0.0925878i
$328$		0			0
$329$	4.88895	−	4.88895i	0.269536	−	0.269536i
$330$		0			0
$331$	−4.00950	−	9.67979i	−0.220382	−	0.532050i	0.774560	−	0.632501i	$-0.217971\pi$
$331$	−4.00950	−	9.67979i	−0.220382	−	0.532050i	−0.994942	+	0.100451i	$0.967971\pi$
$332$		0			0
$333$	2.66075	−	32.7884i	0.145808	−	1.79680i
$334$		0			0
$335$			26.7157i			1.45963i
$336$		0			0
$337$			4.80498i			0.261744i	0.991399	+	0.130872i	$0.0417777\pi$
$337$			4.80498i			0.261744i	−0.991399	+	0.130872i	$0.958222\pi$
$338$		0			0
$339$	14.2853	+	3.44797i	0.775871	+	0.187268i
$340$		0			0
$341$	−9.26823	−	22.3755i	−0.501903	−	1.21170i
$342$		0			0
$343$	−7.29254	+	7.29254i	−0.393760	+	0.393760i
$344$		0			0
$345$	−8.83505	−	6.43547i	−0.475663	−	0.346474i
$346$		0			0
$347$	5.87587	+	14.1856i	0.315433	+	0.761523i	0.999485	+	0.0320898i	$0.0102162\pi$
$347$	5.87587	+	14.1856i	0.315433	+	0.761523i	−0.684052	+	0.729434i	$0.739784\pi$
$348$		0			0
$349$	6.41003	+	2.65512i	0.343121	+	0.142125i	0.547588	−	0.836748i	$-0.315546\pi$
$349$	6.41003	+	2.65512i	0.343121	+	0.142125i	−0.204467	+	0.978873i	$0.565546\pi$
$350$		0			0
$351$	−13.8059	+	6.97115i	−0.736905	+	0.372092i
$352$		0			0
$353$		−	10.7742i		−	0.573453i	−0.958012	−	0.286726i	$-0.907433\pi$
$353$		−	10.7742i		−	0.573453i	0.958012	−	0.286726i	$-0.0925671\pi$
$354$		0			0
$355$	−6.72880	+	16.2448i	−0.357128	+	0.862182i
$356$		0			0
$357$	3.98373	+	6.51864i	0.210841	+	0.345003i
$358$		0			0
$359$	−7.99933	+	7.99933i	−0.422189	+	0.422189i	−0.885957	−	0.463768i	$-0.846497\pi$
$359$	−7.99933	+	7.99933i	−0.422189	+	0.422189i	0.463768	+	0.885957i	$0.346497\pi$
$360$		0			0
$361$	−13.4298	−	13.4298i	−0.706832	−	0.706832i
$362$		0			0
$363$	10.9884	−	6.71533i	0.576741	−	0.352463i
$364$		0			0
$365$	−6.33256	−	2.62303i	−0.331461	−	0.137296i
$366$		0			0
$367$	−4.78544			−0.249798			−0.124899	−	0.992169i	$-0.539861\pi$
$367$	−4.78544			−0.249798			−0.124899	+	0.992169i	$0.539861\pi$
$368$		0			0
$369$	−19.9313	+	6.42253i	−1.03758	+	0.334343i
$370$		0			0
$371$	0.806641	−	1.94740i	0.0418787	−	0.101104i
$372$		0			0
$373$	24.5505	−	10.1691i	1.27118	−	0.526538i	0.357855	−	0.933777i	$-0.383508\pi$
$373$	24.5505	−	10.1691i	1.27118	−	0.526538i	0.913322	+	0.407239i	$0.133508\pi$
$374$		0			0
$375$	2.22722	−	3.05768i	0.115013	−	0.157898i
$376$		0			0
$377$	2.86220	+	2.86220i	0.147411	+	0.147411i
$378$		0			0
$379$	−26.9921	+	11.1805i	−1.38649	+	0.574304i	−0.946209	−	0.323556i	$-0.895122\pi$
$379$	−26.9921	+	11.1805i	−1.38649	+	0.574304i	−0.440282	+	0.897859i	$0.645122\pi$
$380$		0			0
$381$	−2.84936	+	11.8052i	−0.145977	+	0.604798i
$382$		0			0
$383$	−16.7272			−0.854721			−0.427360	−	0.904081i	$-0.640556\pi$
$383$	−16.7272			−0.854721			−0.427360	+	0.904081i	$0.640556\pi$
$384$		0			0
$385$	−10.0621			−0.512811
$386$		0			0
$387$	−2.22345	+	27.3996i	−0.113024	+	1.39280i
$388$		0			0
$389$	−30.3193	+	12.5587i	−1.53725	+	0.636749i	−0.980955	−	0.194236i	$-0.937777\pi$
$389$	−30.3193	+	12.5587i	−1.53725	+	0.636749i	−0.556294	+	0.830985i	$0.687777\pi$
$390$		0			0
$391$	−8.39850	−	8.39850i	−0.424730	−	0.424730i
$392$		0			0
$393$	6.20390	+	4.51893i	0.312945	+	0.227950i
$394$		0			0
$395$	−1.79448	+	0.743298i	−0.0902901	+	0.0373994i
$396$		0			0
$397$	−8.13703	+	19.6445i	−0.408386	+	0.985931i	0.577177	+	0.816619i	$0.304154\pi$
$397$	−8.13703	+	19.6445i	−0.408386	+	0.985931i	−0.985563	+	0.169312i	$0.945846\pi$
$398$		0			0
$399$	0.0177556	+	0.112994i	0.000888894	+	0.00565676i
$400$		0			0
$401$	0.509396			0.0254380			0.0127190	−	0.999919i	$-0.495951\pi$
$401$	0.509396			0.0254380			0.0127190	+	0.999919i	$0.495951\pi$
$402$		0			0
$403$	−15.5113	−	6.42500i	−0.772674	−	0.320052i
$404$		0			0
$405$	−23.3107	−	14.4412i	−1.15832	−	0.717590i
$406$		0			0
$407$	33.2914	+	33.2914i	1.65019	+	1.65019i
$408$		0			0
$409$	−6.54063	+	6.54063i	−0.323413	+	0.323413i	−0.850075	−	0.526662i	$-0.823443\pi$
$409$	−6.54063	+	6.54063i	−0.323413	+	0.323413i	0.526662	+	0.850075i	$0.323443\pi$
$410$		0			0
$411$	12.6338	−	7.72090i	0.623180	−	0.380844i
$412$		0			0
$413$	−0.383497	+	0.925844i	−0.0188707	+	0.0455578i
$414$		0			0
$415$		−	15.4880i		−	0.760278i
$416$		0			0
$417$	2.68578	+	17.0918i	0.131523	+	0.836990i
$418$		0			0
$419$	20.7965	+	8.61418i	1.01597	+	0.420830i	0.827631	−	0.561273i	$-0.189688\pi$
$419$	20.7965	+	8.61418i	1.01597	+	0.420830i	0.188343	+	0.982103i	$0.439688\pi$
$420$		0			0
$421$	8.30131	+	20.0411i	0.404581	+	0.976745i	0.986539	+	0.163526i	$0.0522868\pi$
$421$	8.30131	+	20.0411i	0.404581	+	0.976745i	−0.581958	+	0.813219i	$0.697713\pi$
$422$		0			0
$423$	−12.3012	+	23.9980i	−0.598105	+	1.16682i
$424$		0			0
$425$	−17.3677	+	17.3677i	−0.842456	+	0.842456i
$426$		0			0
$427$	−1.17675	−	2.84092i	−0.0569468	−	0.137482i
$428$		0			0
$429$	5.19350	−	21.5172i	0.250745	−	1.03886i
$430$		0			0
$431$		−	1.97237i		−	0.0950057i	−0.998871	−	0.0475028i	$-0.984874\pi$
$431$		−	1.97237i		−	0.0950057i	0.998871	−	0.0475028i	$-0.0151263\pi$
$432$		0			0
$433$			29.4876i			1.41709i	0.705668	+	0.708543i	$0.250647\pi$
$433$			29.4876i			1.41709i	−0.705668	+	0.708543i	$0.749353\pi$
$434$		0			0
$435$	−1.68385	+	6.97637i	−0.0807346	+	0.334491i
$436$		0			0
$437$	−0.0680518	−	0.164292i	−0.00325536	−	0.00785913i
$438$		0			0
$439$	−17.1823	+	17.1823i	−0.820067	+	0.820067i	−0.986117	−	0.166050i	$-0.946899\pi$
$439$	−17.1823	+	17.1823i	−0.820067	+	0.820067i	0.166050	+	0.986117i	$0.446899\pi$
$440$		0			0
$441$	8.76968	−	17.1085i	0.417604	−	0.814690i
$442$		0			0
$443$	−4.22858	−	10.2087i	−0.200906	−	0.485029i	0.791029	−	0.611779i	$-0.209546\pi$
$443$	−4.22858	−	10.2087i	−0.200906	−	0.485029i	−0.991935	+	0.126749i	$0.959546\pi$
$444$		0			0
$445$	3.59309	+	1.48831i	0.170329	+	0.0705526i
$446$		0			0
$447$	−2.83610	−	18.0485i	−0.134143	−	0.853663i
$448$		0			0
$449$			27.4116i			1.29363i	0.762645	+	0.646817i	$0.223900\pi$
$449$			27.4116i			1.29363i	−0.762645	+	0.646817i	$0.776100\pi$
$450$		0			0
$451$	11.4691	−	27.6888i	0.540057	−	1.30381i
$452$		0			0
$453$	−16.6977	+	10.2045i	−0.784528	+	0.479448i
$454$		0			0
$455$	−4.93230	+	4.93230i	−0.231230	+	0.231230i
$456$		0			0
$457$	5.05963	+	5.05963i	0.236680	+	0.236680i	0.815474	−	0.578794i	$-0.196477\pi$
$457$	5.05963	+	5.05963i	0.236680	+	0.236680i	−0.578794	+	0.815474i	$0.696477\pi$
$458$		0			0
$459$	−22.5871	−	19.4341i	−1.05427	−	0.907106i
$460$		0			0
$461$	28.5768	+	11.8369i	1.33095	+	0.551298i	0.930927	−	0.365206i	$-0.119001\pi$
$461$	28.5768	+	11.8369i	1.33095	+	0.551298i	0.400025	+	0.916504i	$0.369001\pi$
$462$		0			0
$463$	8.48410			0.394290			0.197145	−	0.980374i	$-0.436833\pi$
$463$	8.48410			0.394290			0.197145	+	0.980374i	$0.436833\pi$
$464$		0			0
$465$	−4.62093	−	29.4067i	−0.214290	−	1.36371i
$466$		0			0
$467$	−6.00576	+	14.4992i	−0.277913	+	0.670942i	−0.999778	−	0.0210925i	$-0.993286\pi$
$467$	−6.00576	+	14.4992i	−0.277913	+	0.670942i	0.721864	+	0.692035i	$0.243286\pi$
$468$		0			0
$469$	−6.23089	+	2.58092i	−0.287716	+	0.119176i
$470$		0			0
$471$	−4.02254	−	2.93003i	−0.185349	−	0.135008i
$472$		0			0
$473$	−27.8199	−	27.8199i	−1.27916	−	1.27916i
$474$		0			0
$475$	−0.339747	+	0.140728i	−0.0155886	+	0.00645703i
$476$		0			0
$477$	−0.664971	+	8.19445i	−0.0304469	+	0.375198i
$478$		0			0
$479$	28.2696			1.29167			0.645835	−	0.763477i	$-0.276509\pi$
$479$	28.2696			1.29167			0.645835	+	0.763477i	$0.276509\pi$
$480$		0			0
$481$	32.6380			1.48816
$482$		0			0
$483$	0.647416	−	2.68231i	0.0294584	−	0.122049i
$484$		0			0
$485$	37.4533	−	15.5137i	1.70067	−	0.704440i
$486$		0			0
$487$	−22.4971	−	22.4971i	−1.01944	−	1.01944i	−0.999807	−	0.0196335i	$-0.993750\pi$
$487$	−22.4971	−	22.4971i	−1.01944	−	1.01944i	−0.0196335	−	0.999807i	$-0.506250\pi$
$488$		0			0
$489$	−9.37542	+	12.8712i	−0.423971	+	0.582056i
$490$		0			0
$491$	−0.871501	+	0.360988i	−0.0393303	+	0.0162911i	−0.402262	−	0.915525i	$-0.631776\pi$
$491$	−0.871501	+	0.360988i	−0.0393303	+	0.0162911i	0.362932	+	0.931816i	$0.381776\pi$
$492$		0			0
$493$	−2.98432	+	7.20480i	−0.134407	+	0.324488i
$494$		0			0
$495$	37.3542	−	12.0368i	1.67895	−	0.541013i
$496$		0			0
$497$	−4.43881			−0.199108
$498$		0			0
$499$	29.0833	+	12.0467i	1.30195	+	0.539284i	0.922524	−	0.385939i	$-0.126122\pi$
$499$	29.0833	+	12.0467i	1.30195	+	0.539284i	0.379423	+	0.925223i	$0.376122\pi$
$500$		0			0
$501$	14.0122	−	8.56329i	0.626021	−	0.382580i
$502$		0			0
$503$	15.9266	+	15.9266i	0.710132	+	0.710132i	0.966563	−	0.256431i	$-0.0825465\pi$
$503$	15.9266	+	15.9266i	0.710132	+	0.710132i	−0.256431	+	0.966563i	$0.582546\pi$
$504$		0			0
$505$	−12.8126	+	12.8126i	−0.570152	+	0.570152i
$506$		0			0
$507$	3.73990	+	6.11966i	0.166095	+	0.271784i
$508$		0			0
$509$	−0.374204	+	0.903408i	−0.0165863	+	0.0400428i	−0.931956	−	0.362572i	$-0.881899\pi$
$509$	−0.374204	+	0.903408i	−0.0165863	+	0.0400428i	0.915369	+	0.402615i	$0.131899\pi$
$510$		0			0
$511$		−	1.73035i		−	0.0765460i
$512$		0			0
$513$	−0.201085	−	0.398235i	−0.00887810	−	0.0175825i
$514$		0			0
$515$	−31.3239	−	12.9748i	−1.38030	−	0.571738i
$516$		0			0
$517$	−14.7698	−	35.6575i	−0.649576	−	1.56821i
$518$		0			0
$519$	28.3570	+	20.6553i	1.24473	+	0.906666i
$520$		0			0
$521$	31.7757	−	31.7757i	1.39212	−	1.39212i	0.571558	−	0.820562i	$-0.306339\pi$
$521$	31.7757	−	31.7757i	1.39212	−	1.39212i	0.820562	−	0.571558i	$-0.193661\pi$
$522$		0			0
$523$	2.56429	+	6.19074i	0.112128	+	0.270702i	0.969975	−	0.243203i	$-0.0781982\pi$
$523$	2.56429	+	6.19074i	0.112128	+	0.270702i	−0.857847	+	0.513905i	$0.828198\pi$
$524$		0			0
$525$	−5.54688	−	1.33882i	−0.242086	−	0.0584310i
$526$		0			0
$527$		−	32.3463i		−	1.40903i
$528$		0			0
$529$		−	18.7100i		−	0.813480i
$530$		0			0
$531$	0.316144	−	3.89584i	0.0137195	−	0.169065i
$532$		0			0
$533$	−7.95069	−	19.1947i	−0.344382	−	0.831413i
$534$		0			0
$535$	2.10224	−	2.10224i	0.0908876	−	0.0908876i
$536$		0			0
$537$	18.6566	−	25.6130i	0.805090	−	1.10528i
$538$		0			0
$539$	10.5296	+	25.4206i	0.453541	+	1.09494i
$540$		0			0
$541$	−25.9983	−	10.7689i	−1.11776	−	0.462989i	−0.254154	−	0.967164i	$-0.581797\pi$
$541$	−25.9983	−	10.7689i	−1.11776	−	0.462989i	−0.863602	+	0.504174i	$0.831797\pi$
$542$		0			0
$543$	−26.8373	+	4.21717i	−1.15170	+	0.180976i
$544$		0			0
$545$		−	3.64369i		−	0.156079i
$546$		0			0
$547$	8.74735	−	21.1180i	0.374010	−	0.902939i	−0.619053	−	0.785349i	$-0.712483\pi$
$547$	8.74735	−	21.1180i	0.374010	−	0.902939i	0.993062	−	0.117590i	$-0.0375167\pi$
$548$		0			0
$549$	7.76698	+	9.13887i	0.331487	+	0.390038i
$550$		0			0
$551$	−0.0825609	+	0.0825609i	−0.00351721	+	0.00351721i
$552$		0			0
$553$	−0.346719	−	0.346719i	−0.0147440	−	0.0147440i
$554$		0			0
$555$	30.1756	+	49.3768i	1.28088	+	2.09593i
$556$		0			0
$557$	−21.4222	−	8.87338i	−0.907689	−	0.375977i	−0.120517	−	0.992711i	$-0.538455\pi$
$557$	−21.4222	−	8.87338i	−0.907689	−	0.375977i	−0.787171	+	0.616734i	$0.788455\pi$
$558$		0			0
$559$	−27.2739			−1.15356
$560$		0			0
$561$	42.1285	−	6.62001i	1.77867	−	0.279497i
$562$		0			0
$563$	−3.72042	+	8.98190i	−0.156797	+	0.378542i	−0.982683	−	0.185296i	$-0.940676\pi$
$563$	−3.72042	+	8.98190i	−0.156797	+	0.378542i	0.825886	+	0.563838i	$0.190676\pi$
$564$		0			0
$565$	−23.8830	+	9.89265i	−1.00476	+	0.416187i
$566$		0			0
$567$	1.11615	−	6.83187i	0.0468739	−	0.286912i
$568$		0			0
$569$	8.43864	+	8.43864i	0.353766	+	0.353766i	0.861509	−	0.507743i	$-0.169520\pi$
$569$	8.43864	+	8.43864i	0.353766	+	0.353766i	−0.507743	+	0.861509i	$0.669520\pi$
$570$		0			0
$571$	17.9095	−	7.41834i	0.749488	−	0.310448i	0.0249551	−	0.999689i	$-0.492056\pi$
$571$	17.9095	−	7.41834i	0.749488	−	0.310448i	0.724532	+	0.689241i	$0.242056\pi$
$572$		0			0
$573$	−26.4868	−	6.39300i	−1.10650	−	0.267071i
$574$		0			0
$575$	8.87142			0.369964
$576$		0			0
$577$	−31.3503			−1.30513			−0.652565	−	0.757733i	$-0.726307\pi$
$577$	−31.3503			−1.30513			−0.652565	+	0.757733i	$0.726307\pi$
$578$		0			0
$579$	20.5829	+	4.96800i	0.855398	+	0.206463i
$580$		0			0
$581$	3.61227	−	1.49625i	0.149862	−	0.0620750i
$582$		0			0
$583$	−8.32014	−	8.32014i	−0.344585	−	0.344585i
$584$		0			0
$585$	12.4103	−	24.2108i	0.513102	−	1.00099i
$586$		0			0
$587$	14.6871	−	6.08361i	0.606202	−	0.251097i	−0.0584014	−	0.998293i	$-0.518600\pi$
$587$	14.6871	−	6.08361i	0.606202	−	0.251097i	0.664604	+	0.747196i	$0.268600\pi$
$588$		0			0
$589$	0.185331	−	0.447428i	0.00763642	−	0.0184360i
$590$		0			0
$591$	−39.9944	+	6.28465i	−1.64515	+	0.258516i
$592$		0			0
$593$	6.53460			0.268344			0.134172	−	0.990958i	$-0.457163\pi$
$593$	6.53460			0.268344			0.134172	+	0.990958i	$0.457163\pi$
$594$		0			0
$595$	−12.4157	−	5.14275i	−0.508994	−	0.210832i
$596$		0			0
$597$	−2.01532	−	3.29770i	−0.0824817	−	0.134966i
$598$		0			0
$599$	−20.5360	−	20.5360i	−0.839078	−	0.839078i	0.149659	−	0.988738i	$-0.452182\pi$
$599$	−20.5360	−	20.5360i	−0.839078	−	0.839078i	−0.988738	+	0.149659i	$0.952182\pi$
$600$		0			0
$601$	−1.20249	+	1.20249i	−0.0490506	+	0.0490506i	−0.731207	−	0.682156i	$-0.761042\pi$
$601$	−1.20249	+	1.20249i	−0.0490506	+	0.0490506i	0.682156	+	0.731207i	$0.261042\pi$
$602$		0			0
$603$	20.0440	−	17.0351i	0.816255	−	0.693722i
$604$		0			0
$605$	−8.66907	+	20.9290i	−0.352448	+	0.850884i
$606$		0			0
$607$			42.2470i			1.71475i	0.514692	+	0.857375i	$0.327906\pi$
$607$			42.2470i			1.71475i	−0.514692	+	0.857375i	$0.672094\pi$
$608$		0			0
$609$	−1.78977	+	0.281241i	−0.0725251	+	0.0113965i
$610$		0			0
$611$	−24.7188	−	10.2389i	−1.00002	−	0.414220i
$612$		0			0
$613$	3.20549	+	7.73873i	0.129468	+	0.312564i	0.975300	−	0.220886i	$-0.0708950\pi$
$613$	3.20549	+	7.73873i	0.129468	+	0.312564i	−0.845831	+	0.533451i	$0.820895\pi$
$614$		0			0
$615$	21.6880	−	29.7748i	0.874545	−	1.20064i
$616$		0			0
$617$	−30.2757	+	30.2757i	−1.21885	+	1.21885i	−0.250821	+	0.968034i	$0.580701\pi$
$617$	−30.2757	+	30.2757i	−1.21885	+	1.21885i	−0.968034	+	0.250821i	$0.919299\pi$
$618$		0			0
$619$	−7.03045	−	16.9730i	−0.282578	−	0.682203i	0.717317	−	0.696747i	$-0.245370\pi$
$619$	−7.03045	−	16.9730i	−0.282578	−	0.682203i	−0.999894	+	0.0145446i	$0.995370\pi$
$620$		0			0
$621$	0.805265	+	10.7322i	0.0323142	+	0.430669i
$622$		0			0
$623$			0.981797i			0.0393349i
$624$		0			0
$625$			28.0703i			1.12281i
$626$		0			0
$627$	0.620670	+	0.149808i	0.0247872	+	0.00598275i
$628$		0			0
$629$	24.0633	+	58.0939i	0.959465	+	2.31635i
$630$		0			0
$631$	0.699961	−	0.699961i	0.0278650	−	0.0278650i	−0.693037	−	0.720902i	$-0.743728\pi$
$631$	0.699961	−	0.699961i	0.0278650	−	0.0278650i	0.720902	+	0.693037i	$0.243728\pi$
$632$		0			0
$633$	38.4212	+	27.9860i	1.52710	+	1.11235i
$634$		0			0
$635$	−8.17515	−	19.7366i	−0.324421	−	0.783221i
$636$		0			0
$637$	17.6223	+	7.29941i	0.698222	+	0.289213i
$638$		0			0
$639$	16.4785	−	5.30993i	0.651881	−	0.210058i
$640$		0			0
$641$		−	36.4715i		−	1.44054i	−0.693695	−	0.720269i	$-0.744019\pi$
$641$		−	36.4715i		−	1.44054i	0.693695	−	0.720269i	$-0.255981\pi$
$642$		0			0
$643$	−13.4470	+	32.4640i	−0.530298	+	1.28025i	0.401027	+	0.916066i	$0.368653\pi$
$643$	−13.4470	+	32.4640i	−0.530298	+	1.28025i	−0.931326	+	0.364187i	$0.881347\pi$
$644$		0			0
$645$	−25.2162	−	41.2616i	−0.992886	−	1.62467i
$646$		0			0
$647$	−7.01510	+	7.01510i	−0.275792	+	0.275792i	−0.831427	−	0.555635i	$-0.812475\pi$
$647$	−7.01510	+	7.01510i	−0.275792	+	0.275792i	0.555635	+	0.831427i	$0.312475\pi$
$648$		0			0
$649$	3.95560	+	3.95560i	0.155271	+	0.155271i
$650$		0			0
$651$	6.41212	−	3.91863i	0.251311	−	0.153583i
$652$		0			0
$653$	7.33264	+	3.03728i	0.286948	+	0.118858i	0.521515	−	0.853242i	$-0.325367\pi$
$653$	7.33264	+	3.03728i	0.286948	+	0.118858i	−0.234567	+	0.972100i	$0.575367\pi$
$654$		0			0
$655$	−13.5014			−0.527544
$656$		0			0
$657$	2.06993	+	6.42370i	0.0807556	+	0.250612i
$658$		0			0
$659$	9.46381	−	22.8477i	0.368658	−	0.890018i	−0.625313	−	0.780374i	$-0.715029\pi$
$659$	9.46381	−	22.8477i	0.368658	−	0.890018i	0.993971	−	0.109644i	$-0.0349712\pi$
$660$		0			0
$661$	4.59417	−	1.90297i	0.178693	−	0.0740169i	−0.291543	−	0.956558i	$-0.594169\pi$
$661$	4.59417	−	1.90297i	0.178693	−	0.0740169i	0.470236	+	0.882541i	$0.344169\pi$
$662$		0			0
$663$	17.4058	−	23.8959i	0.675986	−	0.928039i
$664$		0			0
$665$	−0.142273	−	0.142273i	−0.00551713	−	0.00551713i
$666$		0			0
$667$	2.60230	−	1.07791i	0.100762	−	0.0417368i
$668$		0			0
$669$	9.60154	−	39.7802i	0.371217	−	1.53799i
$670$		0			0
$671$	−17.1652			−0.662654
$672$		0			0
$673$	−14.0193			−0.540404			−0.270202	−	0.962804i	$-0.587090\pi$
$673$	−14.0193			−0.540404			−0.270202	+	0.962804i	$0.587090\pi$
$674$		0			0
$675$	22.1937	−	1.66525i	0.854235	−	0.0640954i
$676$		0			0
$677$	25.4610	−	10.5463i	0.978545	−	0.405327i	0.164659	−	0.986351i	$-0.447348\pi$
$677$	25.4610	−	10.5463i	0.978545	−	0.405327i	0.813886	+	0.581024i	$0.197348\pi$
$678$		0			0
$679$	7.23650	+	7.23650i	0.277712	+	0.277712i
$680$		0			0
$681$	25.3756	+	18.4836i	0.972395	+	0.708294i
$682$		0			0
$683$	−7.18630	+	2.97666i	−0.274976	+	0.113899i	−0.515910	−	0.856643i	$-0.672546\pi$
$683$	−7.18630	+	2.97666i	−0.274976	+	0.113899i	0.240934	+	0.970541i	$0.422546\pi$
$684$		0			0
$685$	−9.96720	+	24.0630i	−0.380827	+	0.919398i
$686$		0			0
$687$	3.55268	+	22.6086i	0.135543	+	0.862573i
$688$		0			0
$689$	−8.15685			−0.310751
$690$		0			0
$691$	−21.5412	−	8.92265i	−0.819466	−	0.339434i	−0.0667419	−	0.997770i	$-0.521260\pi$
$691$	−21.5412	−	8.92265i	−0.819466	−	0.339434i	−0.752724	+	0.658336i	$0.771260\pi$
$692$		0			0
$693$	6.41602	+	7.54929i	0.243724	+	0.286774i
$694$		0			0
$695$	−21.5208	−	21.5208i	−0.816330	−	0.816330i
$696$		0			0
$697$	28.3036	−	28.3036i	1.07207	−	1.07207i
$698$		0			0
$699$	−16.5822	+	10.1339i	−0.627196	+	0.383298i
$700$		0			0
$701$	12.8390	−	30.9961i	0.484922	−	1.17071i	−0.472322	−	0.881426i	$-0.656584\pi$
$701$	12.8390	−	30.9961i	0.484922	−	1.17071i	0.957244	−	0.289280i	$-0.0934160\pi$
$702$		0			0
$703$			0.941452i			0.0355075i
$704$		0			0
$705$	−7.36389	−	46.8625i	−0.277340	−	1.76494i
$706$		0			0
$707$	−4.22606	−	1.75049i	−0.158937	−	0.0658339i
$708$		0			0
$709$	0.0401422	+	0.0969118i	0.00150757	+	0.00363960i	0.924632	−	0.380863i	$-0.124373\pi$
$709$	0.0401422	+	0.0969118i	0.00150757	+	0.00363960i	−0.923124	+	0.384502i	$0.874373\pi$
$710$		0			0
$711$	1.70191	+	0.872388i	0.0638267	+	0.0327171i
$712$		0			0
$713$	−8.26126	+	8.26126i	−0.309387	+	0.309387i
$714$		0			0
$715$	14.9008	+	35.9737i	0.557258	+	1.34534i
$716$		0			0
$717$	−6.79720	+	28.1615i	−0.253846	+	1.05171i
$718$		0			0
$719$			7.25362i			0.270515i	0.990811	+	0.135257i	$0.0431861\pi$
$719$			7.25362i			0.270515i	−0.990811	+	0.135257i	$0.956814\pi$
$720$		0			0
$721$		−	8.55913i		−	0.318759i
$722$		0			0
$723$	3.65837	−	15.1570i	0.136056	−	0.563694i
$724$		0			0
$725$	−2.22906	−	5.38143i	−0.0827853	−	0.199861i
$726$		0			0
$727$	33.8662	−	33.8662i	1.25603	−	1.25603i	0.303055	−	0.952973i	$-0.401993\pi$
$727$	33.8662	−	33.8662i	1.25603	−	1.25603i	0.952973	−	0.303055i	$-0.0980066\pi$
$728$		0			0
$729$	4.02907	+	26.6977i	0.149225	+	0.988803i
$730$		0			0
$731$	−20.1084	−	48.5460i	−0.743736	−	1.79554i
$732$		0			0
$733$	46.5930	+	19.2995i	1.72095	+	0.712842i	0.999799	+	0.0200663i	$0.00638774\pi$
$733$	46.5930	+	19.2995i	1.72095	+	0.712842i	0.721153	+	0.692775i	$0.243612\pi$
$734$		0			0
$735$	5.24981	+	33.4088i	0.193642	+	1.23230i
$736$		0			0
$737$			37.6478i			1.38678i
$738$		0			0
$739$	11.4353	−	27.6072i	0.420653	−	1.01555i	−0.561502	−	0.827475i	$-0.689776\pi$
$739$	11.4353	−	27.6072i	0.420653	−	1.01555i	0.982155	−	0.188072i	$-0.0602237\pi$
$740$		0			0
$741$	0.377678	−	0.230810i	0.0138743	−	0.00847902i
$742$		0			0
$743$	31.4330	−	31.4330i	1.15317	−	1.15317i	0.167252	−	0.985914i	$-0.446511\pi$
$743$	31.4330	−	31.4330i	1.15317	−	1.15317i	0.985914	−	0.167252i	$-0.0534894\pi$
$744$		0			0
$745$	22.7253	+	22.7253i	0.832590	+	0.832590i
$746$		0			0
$747$	−11.6202	+	9.87584i	−0.425162	+	0.361338i
$748$		0			0
$749$	0.693395	+	0.287214i	0.0253361	+	0.0104946i
$750$		0			0
$751$	−9.38556			−0.342484			−0.171242	−	0.985229i	$-0.554778\pi$
$751$	−9.38556			−0.342484			−0.171242	+	0.985229i	$0.554778\pi$
$752$		0			0
$753$	−0.422577	−	2.68920i	−0.0153996	−	0.0980001i
$754$		0			0
$755$	13.1733	−	31.8033i	0.479427	−	1.15744i
$756$		0			0
$757$	21.2091	−	8.78508i	0.770857	−	0.319299i	0.0376373	−	0.999291i	$-0.488017\pi$
$757$	21.2091	−	8.78508i	0.770857	−	0.319299i	0.733219	+	0.679992i	$0.238017\pi$
$758$		0			0
$759$	−12.4504	−	9.06889i	−0.451921	−	0.329180i
$760$		0			0
$761$	17.8648	+	17.8648i	0.647599	+	0.647599i	0.952412	−	0.304813i	$-0.0985941\pi$
$761$	17.8648	+	17.8648i	0.647599	+	0.647599i	−0.304813	+	0.952412i	$0.598594\pi$
$762$		0			0
$763$	0.849818	−	0.352006i	0.0307655	−	0.0127435i
$764$		0			0
$765$	52.2438	+	4.23953i	1.88888	+	0.153281i
$766$		0			0
$767$	3.87797			0.140025
$768$		0			0
$769$	−1.71307			−0.0617750			−0.0308875	−	0.999523i	$-0.509833\pi$
$769$	−1.71307			−0.0617750			−0.0308875	+	0.999523i	$0.509833\pi$
$770$		0			0
$771$	3.36870	−	13.9569i	0.121321	−	0.502645i
$772$		0			0
$773$	25.0667	−	10.3830i	0.901587	−	0.373450i	0.116757	−	0.993161i	$-0.462750\pi$
$773$	25.0667	−	10.3830i	0.901587	−	0.373450i	0.784830	+	0.619711i	$0.212750\pi$
$774$		0			0
$775$	17.0839	+	17.0839i	0.613671	+	0.613671i
$776$		0			0
$777$	−8.60096	+	11.8080i	−0.308558	+	0.423609i
$778$		0			0
$779$	0.553675	−	0.229340i	0.0198375	−	0.00821694i
$780$		0			0
$781$	−9.48225	+	22.8922i	−0.339302	+	0.819146i
$782$		0			0
$783$	6.30787	−	3.18509i	0.225425	−	0.113826i
$784$		0			0
$785$	8.75417			0.312450
$786$		0			0
$787$	−47.6483	−	19.7366i	−1.69848	−	0.703533i	−0.698552	−	0.715560i	$-0.746172\pi$
$787$	−47.6483	−	19.7366i	−1.69848	−	0.703533i	−0.999928	+	0.0120263i	$0.996172\pi$
$788$		0			0
$789$	18.3118	−	11.1909i	0.651918	−	0.398406i
$790$		0			0
$791$	−4.61452	−	4.61452i	−0.164073	−	0.164073i
$792$		0			0
$793$	−8.41414	+	8.41414i	−0.298795	+	0.298795i
$794$		0			0
$795$	−7.54145	−	12.3402i	−0.267468	−	0.437661i
$796$		0			0
$797$	−9.69549	+	23.4070i	−0.343432	+	0.829118i	0.653932	+	0.756553i	$0.273118\pi$
$797$	−9.69549	+	23.4070i	−0.343432	+	0.829118i	−0.997364	+	0.0725644i	$0.976882\pi$
$798$		0			0
$799$		−	51.5470i		−	1.82360i
$800$		0			0
$801$	−1.17448	−	3.64480i	−0.0414981	−	0.128783i
$802$		0			0
$803$	−8.92387	−	3.69639i	−0.314917	−	0.130443i
$804$		0			0
$805$	1.85751	+	4.48443i	0.0654687	+	0.158055i
$806$		0			0
$807$	−22.8856	−	16.6699i	−0.805611	−	0.586808i
$808$		0			0
$809$	31.1610	−	31.1610i	1.09556	−	1.09556i	0.100640	−	0.994923i	$-0.467911\pi$
$809$	31.1610	−	31.1610i	1.09556	−	1.09556i	0.994923	−	0.100640i	$-0.0320891\pi$
$810$		0			0
$811$	−3.17453	−	7.66400i	−0.111473	−	0.269120i	0.858291	−	0.513163i	$-0.171526\pi$
$811$	−3.17453	−	7.66400i	−0.111473	−	0.269120i	−0.969764	+	0.244043i	$0.921526\pi$
$812$		0			0
$813$	29.4706	+	7.11318i	1.03358	+	0.249470i
$814$		0			0
$815$		−	28.0113i		−	0.981194i
$816$		0			0
$817$		−	0.786722i		−	0.0275239i
$818$		0			0
$819$	6.84561	+	0.555514i	0.239205	+	0.0194112i
$820$		0			0
$821$	1.18631	+	2.86400i	0.0414025	+	0.0999544i	0.943228	−	0.332146i	$-0.107773\pi$
$821$	1.18631	+	2.86400i	0.0414025	+	0.0999544i	−0.901826	+	0.432100i	$0.857773\pi$
$822$		0			0
$823$	1.98030	−	1.98030i	0.0690288	−	0.0690288i	−0.671750	−	0.740778i	$-0.734457\pi$
$823$	1.98030	−	1.98030i	0.0690288	−	0.0690288i	0.740778	+	0.671750i	$0.234457\pi$
$824$		0			0
$825$	−18.7540	+	25.7468i	−0.652931	+	0.896388i
$826$		0			0
$827$	19.1750	+	46.2924i	0.666779	+	1.60975i	0.786967	+	0.616995i	$0.211650\pi$
$827$	19.1750	+	46.2924i	0.666779	+	1.60975i	−0.120189	+	0.992751i	$0.538350\pi$
$828$		0			0
$829$	−20.6566	−	8.55623i	−0.717432	−	0.297170i	−0.00605590	−	0.999982i	$-0.501928\pi$
$829$	−20.6566	−	8.55623i	−0.717432	−	0.297170i	−0.711376	+	0.702812i	$0.751928\pi$
$830$		0			0
$831$	−39.5750	+	6.21875i	−1.37284	+	0.215726i
$832$		0			0
$833$			36.7485i			1.27326i
$834$		0			0
$835$	−11.0547	+	26.6884i	−0.382563	+	0.923589i
$836$		0			0
$837$	−19.1165	+	22.2180i	−0.660764	+	0.767965i
$838$		0			0
$839$	−10.0632	+	10.0632i	−0.347420	+	0.347420i	−0.859148	−	0.511728i	$-0.829006\pi$
$839$	−10.0632	+	10.0632i	−0.347420	+	0.347420i	0.511728	+	0.859148i	$0.329006\pi$
$840$		0			0
$841$	19.1984	+	19.1984i	0.662013	+	0.662013i
$842$		0			0
$843$	−7.58007	−	12.4034i	−0.261071	−	0.427195i
$844$		0			0
$845$	−11.6558	−	4.82798i	−0.400971	−	0.166088i
$846$		0			0
$847$	−5.71875			−0.196499
$848$		0			0
$849$	−43.9904	+	6.91258i	−1.50975	+	0.237239i
$850$		0			0
$851$	8.69142	−	20.9830i	0.297938	−	0.719286i
$852$		0			0
$853$	11.2850	−	4.67440i	0.386391	−	0.160048i	−0.181027	−	0.983478i	$-0.557942\pi$
$853$	11.2850	−	4.67440i	0.386391	−	0.160048i	0.567418	+	0.823430i	$0.307942\pi$
$854$		0			0
$855$	0.698368	+	0.357978i	0.0238837	+	0.0122426i
$856$		0			0
$857$	−22.7269	−	22.7269i	−0.776335	−	0.776335i	0.202871	−	0.979206i	$-0.434973\pi$
$857$	−22.7269	−	22.7269i	−0.776335	−	0.776335i	−0.979206	+	0.202871i	$0.934973\pi$
$858$		0			0
$859$	−11.7509	+	4.86736i	−0.400934	+	0.166072i	−0.574033	−	0.818832i	$-0.694622\pi$
$859$	−11.7509	+	4.86736i	−0.400934	+	0.166072i	0.173099	+	0.984904i	$0.444622\pi$
$860$		0			0
$861$	9.03958	+	2.18184i	0.308068	+	0.0743569i
$862$		0			0
$863$	45.0560			1.53372			0.766862	−	0.641812i	$-0.221817\pi$
$863$	45.0560			1.53372			0.766862	+	0.641812i	$0.221817\pi$
$864$		0			0
$865$	−61.7127			−2.09829
$866$		0			0
$867$	26.7434	+	6.45492i	0.908252	+	0.219220i
$868$		0			0
$869$	−2.52879	+	1.04746i	−0.0857833	+	0.0355326i
$870$		0			0
$871$	18.4545	+	18.4545i	0.625306	+	0.625306i
$872$		0			0
$873$	−35.5213	−	18.2080i	−1.20221	−	0.616246i
$874$		0			0
$875$	−1.55199	+	0.642857i	−0.0524669	+	0.0217325i
$876$		0			0
$877$	6.55184	−	15.8175i	0.221240	−	0.534121i	−0.773819	−	0.633407i	$-0.781656\pi$
$877$	6.55184	−	15.8175i	0.221240	−	0.534121i	0.995059	+	0.0992863i	$0.0316560\pi$
$878$		0			0
$879$	−7.77914	+	1.22240i	−0.262384	+	0.0412305i
$880$		0			0
$881$	20.4889			0.690289			0.345144	−	0.938550i	$-0.387830\pi$
$881$	20.4889			0.690289			0.345144	+	0.938550i	$0.387830\pi$
$882$		0			0
$883$	3.85593	+	1.59718i	0.129762	+	0.0537493i	0.446620	−	0.894724i	$-0.352628\pi$
$883$	3.85593	+	1.59718i	0.129762	+	0.0537493i	−0.316857	+	0.948473i	$0.602628\pi$
$884$		0			0
$885$	3.58539	+	5.86683i	0.120522	+	0.197211i
$886$		0			0
$887$	29.9883	+	29.9883i	1.00691	+	1.00691i	0.999976	+	0.00693107i	$0.00220625\pi$
$887$	29.9883	+	29.9883i	1.00691	+	1.00691i	0.00693107	+	0.999976i	$0.497794\pi$
$888$		0			0
$889$	3.81338	−	3.81338i	0.127897	−	0.127897i
$890$		0			0
$891$	−32.8495	−	20.3506i	−1.10050	−	0.681772i
$892$		0			0
$893$	0.295343	−	0.713020i	0.00988326	−	0.0238603i
$894$		0			0
$895$			55.7410i			1.86322i
$896$		0			0
$897$	−10.5485	+	1.65757i	−0.352203	+	0.0553446i
$898$		0			0
$899$	7.08706	+	2.93556i	0.236367	+	0.0979063i
$900$		0			0
$901$	−6.01386	−	14.5187i	−0.200351	−	0.483690i
$902$		0			0
$903$	7.18737	−	9.86732i	0.239181	−	0.328364i
$904$		0			0
$905$	33.7916	−	33.7916i	1.12327	−	1.12327i
$906$		0			0
$907$	16.6011	+	40.0785i	0.551229	+	1.33078i	0.916557	+	0.399905i	$0.130957\pi$
$907$	16.6011	+	40.0785i	0.551229	+	1.33078i	−0.365328	+	0.930879i	$0.619043\pi$
$908$		0			0
$909$	17.7827	+	1.44305i	0.589816	+	0.0478630i
$910$		0			0
$911$		−	42.9300i		−	1.42233i	−0.703023	−	0.711167i	$-0.748167\pi$
$911$		−	42.9300i		−	1.42233i	0.703023	−	0.711167i	$-0.251833\pi$
$912$		0			0
$913$		−	21.8258i		−	0.722328i
$914$		0			0
$915$	−20.5088	−	4.95010i	−0.677999	−	0.163645i
$916$		0			0
$917$	−1.30433	−	3.14893i	−0.0430728	−	0.103987i
$918$		0			0
$919$	27.6253	−	27.6253i	0.911275	−	0.911275i	−0.0850978	−	0.996373i	$-0.527120\pi$
$919$	27.6253	−	27.6253i	0.911275	−	0.911275i	0.996373	+	0.0850978i	$0.0271203\pi$
$920$		0			0
$921$	−18.7368	−	13.6479i	−0.617398	−	0.449714i
$922$		0			0
$923$	6.57337	+	15.8695i	0.216365	+	0.522351i
$924$		0			0
$925$	−43.3917	−	17.9734i	−1.42671	−	0.590963i
$926$		0			0
$927$	10.2389	+	31.7747i	0.336289	+	1.04362i
$928$		0			0
$929$		−	26.5634i		−	0.871518i	−0.900063	−	0.435759i	$-0.856480\pi$
$929$		−	26.5634i		−	0.871518i	0.900063	−	0.435759i	$-0.143520\pi$
$930$		0			0
$931$	−0.210553	+	0.508321i	−0.00690060	+	0.0166595i
$932$		0			0
$933$	−13.7060	−	22.4274i	−0.448715	−	0.734239i
$934$		0			0
$935$	−53.0452	+	53.0452i	−1.73476	+	1.73476i
$936$		0			0
$937$	−1.34624	−	1.34624i	−0.0439798	−	0.0439798i	0.684775	−	0.728755i	$-0.259901\pi$
$937$	−1.34624	−	1.34624i	−0.0439798	−	0.0439798i	−0.728755	+	0.684775i	$0.759901\pi$
$938$		0			0
$939$	−37.4065	+	22.8602i	−1.22071	+	0.746014i
$940$		0			0
$941$	−6.86683	−	2.84433i	−0.223852	−	0.0927226i	0.267939	−	0.963436i	$-0.413658\pi$
$941$	−6.86683	−	2.84433i	−0.223852	−	0.0927226i	−0.491791	+	0.870713i	$0.663658\pi$
$942$		0			0
$943$	−14.4575			−0.470801
$944$		0			0
$945$	5.48872	+	10.8701i	0.178548	+	0.353603i
$946$		0			0
$947$	−13.0476	+	31.4996i	−0.423989	+	1.02360i	0.557170	+	0.830398i	$0.311887\pi$
$947$	−13.0476	+	31.4996i	−0.423989	+	1.02360i	−0.981159	+	0.193201i	$0.938113\pi$
$948$		0			0
$949$	−6.18628	+	2.56244i	−0.200815	+	0.0831804i
$950$		0			0
$951$	−6.91983	+	9.50001i	−0.224391	+	0.308059i
$952$		0			0
$953$	−1.94423	−	1.94423i	−0.0629798	−	0.0629798i	0.674915	−	0.737895i	$-0.264180\pi$
$953$	−1.94423	−	1.94423i	−0.0629798	−	0.0629798i	−0.737895	+	0.674915i	$0.764180\pi$
$954$		0			0
$955$	44.2822	−	18.3423i	1.43294	−	0.593542i
$956$		0			0
$957$	−2.37289	+	9.83113i	−0.0767047	+	0.317795i
$958$		0			0
$959$	−6.57510			−0.212321
$960$		0			0
$961$	−0.817748			−0.0263790
$962$		0			0
$963$	−2.91772	−	0.236770i	−0.0940223	−	0.00762982i
$964$		0			0
$965$	−34.4117	+	14.2538i	−1.10775	+	0.458846i
$966$		0			0
$967$	30.8641	+	30.8641i	0.992522	+	0.992522i	0.999972	−	0.00745003i	$-0.00237144\pi$
$967$	30.8641	+	30.8641i	0.992522	+	0.992522i	−0.00745003	+	0.999972i	$0.502371\pi$
$968$		0			0
$969$	0.689283	+	0.502075i	0.0221430	+	0.0161290i
$970$		0			0
$971$	−10.5485	+	4.36935i	−0.338519	+	0.140219i	−0.545466	−	0.838133i	$-0.683647\pi$
$971$	−10.5485	+	4.36935i	−0.338519	+	0.140219i	0.206947	+	0.978352i	$0.433647\pi$
$972$		0			0
$973$	2.94023	−	7.09834i	0.0942594	−	0.227562i
$974$		0			0
$975$	3.42777	+	21.8137i	0.109776	+	0.698597i
$976$		0			0
$977$	19.0100			0.608184			0.304092	−	0.952643i	$-0.401647\pi$
$977$	19.0100			0.608184			0.304092	+	0.952643i	$0.401647\pi$
$978$		0			0
$979$	5.06340	+	2.09733i	0.161827	+	0.0670309i
$980$		0			0
$981$	−2.73376	+	2.32338i	−0.0872822	+	0.0741797i
$982$		0			0
$983$	20.9677	+	20.9677i	0.668767	+	0.668767i	0.957431	−	0.288664i	$-0.0932110\pi$
$983$	20.9677	+	20.9677i	0.668767	+	0.668767i	−0.288664	+	0.957431i	$0.593211\pi$
$984$		0			0
$985$	50.3580	−	50.3580i	1.60454	−	1.60454i
$986$		0			0
$987$	10.2183	−	6.24472i	0.325253	−	0.198772i
$988$		0			0
$989$	−7.26297	+	17.5344i	−0.230949	+	0.557560i
$990$		0			0
$991$		−	45.2241i		−	1.43659i	−0.695737	−	0.718296i	$-0.744922\pi$
$991$		−	45.2241i		−	1.43659i	0.695737	−	0.718296i	$-0.255078\pi$
$992$		0			0
$993$	−2.81706	−	17.9273i	−0.0893968	−	0.568905i
$994$		0			0
$995$	6.28096	+	2.60166i	0.199120	+	0.0824781i
$996$		0			0
$997$	−20.9163	−	50.4964i	−0.662425	−	1.59924i	−0.793991	−	0.607929i	$-0.792000\pi$
$997$	−20.9163	−	50.4964i	−0.662425	−	1.59924i	0.131566	−	0.991307i	$-0.458000\pi$
$998$		0			0
$999$	17.8047	−	54.1246i	0.563315	−	1.71243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.95.13		56
3.2	odd	2	inner	768.2.o.b.95.2		56
4.3	odd	2		768.2.o.a.95.2		56
8.3	odd	2		384.2.o.a.47.13		56
8.5	even	2		96.2.o.a.35.3	yes	56
12.11	even	2		768.2.o.a.95.13		56
24.5	odd	2		96.2.o.a.35.12	yes	56
24.11	even	2		384.2.o.a.47.2		56
32.5	even	8		384.2.o.a.335.2		56
32.11	odd	8	inner	768.2.o.b.671.2		56
32.21	even	8		768.2.o.a.671.13		56
32.27	odd	8		96.2.o.a.11.12	yes	56
96.5	odd	8		384.2.o.a.335.13		56
96.11	even	8	inner	768.2.o.b.671.13		56
96.53	odd	8		768.2.o.a.671.2		56
96.59	even	8		96.2.o.a.11.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.3	✓	56	96.59	even	8
96.2.o.a.11.12	yes	56	32.27	odd	8
96.2.o.a.35.3	yes	56	8.5	even	2
96.2.o.a.35.12	yes	56	24.5	odd	2
384.2.o.a.47.2		56	24.11	even	2
384.2.o.a.47.13		56	8.3	odd	2
384.2.o.a.335.2		56	32.5	even	8
384.2.o.a.335.13		56	96.5	odd	8
768.2.o.a.95.2		56	4.3	odd	2
768.2.o.a.95.13		56	12.11	even	2
768.2.o.a.671.2		56	96.53	odd	8
768.2.o.a.671.13		56	32.21	even	8
768.2.o.b.95.2		56	3.2	odd	2	inner
768.2.o.b.95.13		56	1.1	even	1	trivial
768.2.o.b.671.2		56	32.11	odd	8	inner
768.2.o.b.671.13		56	96.11	even	8	inner

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.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +O(q^{10})\)	\(q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +(-3.96678 + 1.64309i) q^{11} +(-1.13904 + 2.74988i) q^{13} +(-5.21329 + 0.819208i) q^{15} -5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(-0.694704 - 1.13675i) q^{21} +(1.46457 + 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(3.93885 + 3.38902i) q^{27} +(0.520422 - 1.25641i) q^{29} +5.64072i q^{31} +(-7.34659 + 1.15443i) q^{33} +(2.16511 + 0.896820i) q^{35} +(-4.19628 - 10.1307i) q^{37} +(-3.03532 + 4.16709i) q^{39} +(-4.93573 + 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(-9.11055 - 0.739312i) q^{45} +8.98904i q^{47} -6.40839i q^{49} +(-9.65507 - 2.33040i) q^{51} +(1.04873 + 2.53186i) q^{53} +(9.25030 - 9.25030i) q^{55} +(-0.120201 - 0.0875545i) q^{57} +(-0.498592 - 1.20371i) q^{59} +(3.69353 + 1.52991i) q^{61} +(-0.707713 - 2.19627i) q^{63} -9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(1.87072 + 3.06109i) q^{69} +(4.08070 - 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(6.33018 - 3.86856i) q^{75} +(3.05109 + 1.26380i) q^{77} +0.637492 q^{79} +(5.25459 + 7.30679i) q^{81} +(-1.94530 + 4.69638i) q^{83} +(16.1419 - 6.68618i) q^{85} +(1.38682 - 1.90393i) q^{87} +(-0.902588 - 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(-2.29231 + 9.49729i) q^{93} +0.261590 q^{95} -13.3054 q^{97} +(-12.8386 - 1.04184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

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