LMFDB - Embedded newform 768.2.o.b.671.6

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			671.6
Character	$\chi$	$=$	768.671
Dual form			768.2.o.b.95.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.602068 + 1.62404i) q^{3} +(-0.378520 - 0.156788i) q^{5} +(2.01144 - 2.01144i) q^{7} +(-2.27503 - 1.95557i) q^{9} +O(q^{10})$	\(q+(-0.602068 + 1.62404i) q^{3} +(-0.378520 - 0.156788i) q^{5} +(2.01144 - 2.01144i) q^{7} +(-2.27503 - 1.95557i) q^{9} +(-0.709852 - 0.294030i) q^{11} +(-2.08393 - 5.03104i) q^{13} +(0.482526 - 0.520336i) q^{15} -6.33777 q^{17} +(-0.646487 + 0.267784i) q^{19} +(2.05564 + 4.47769i) q^{21} +(1.61798 - 1.61798i) q^{23} +(-3.41684 - 3.41684i) q^{25} +(4.54565 - 2.51736i) q^{27} +(-2.04571 - 4.93879i) q^{29} +5.75464i q^{31} +(0.904897 - 0.975803i) q^{33} +(-1.07674 + 0.446001i) q^{35} +(2.50232 - 6.04113i) q^{37} +(9.42529 - 0.355354i) q^{39} +(5.52228 + 5.52228i) q^{41} +(0.406593 - 0.981601i) q^{43} +(0.554534 + 1.09692i) q^{45} -10.4826i q^{47} -1.09178i q^{49} +(3.81577 - 10.2928i) q^{51} +(-0.674566 + 1.62855i) q^{53} +(0.222593 + 0.222593i) q^{55} +(-0.0456628 - 1.21115i) q^{57} +(3.35082 - 8.08960i) q^{59} +(-4.14715 + 1.71781i) q^{61} +(-8.50959 + 0.642573i) q^{63} +2.23109i q^{65} +(2.65183 + 6.40208i) q^{67} +(1.65353 + 3.60179i) q^{69} +(-1.97014 - 1.97014i) q^{71} +(9.48914 - 9.48914i) q^{73} +(7.60626 - 3.49192i) q^{75} +(-2.01925 + 0.836400i) q^{77} -8.75751 q^{79} +(1.35150 + 8.89795i) q^{81} +(6.60293 + 15.9409i) q^{83} +(2.39898 + 0.993689i) q^{85} +(9.25246 - 0.348838i) q^{87} +(6.11535 - 6.11535i) q^{89} +(-14.3113 - 5.92795i) q^{91} +(-9.34579 - 3.46469i) q^{93} +0.286694 q^{95} -5.09195 q^{97} +(1.03994 + 2.05709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

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

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
$3$	−0.602068	+	1.62404i	−0.347604	+	0.937641i
$3$	−0.602068	+	1.62404i	−0.347604	+	0.937641i
$4$		0			0
$5$	−0.378520	−	0.156788i	−0.169279	−	0.0701179i	0.296434	−	0.955053i	$-0.404202\pi$
$5$	−0.378520	−	0.156788i	−0.169279	−	0.0701179i	−0.465714	+	0.884935i	$0.654202\pi$
$6$		0			0
$7$	2.01144	−	2.01144i	0.760253	−	0.760253i	−0.216115	−	0.976368i	$-0.569339\pi$
$7$	2.01144	−	2.01144i	0.760253	−	0.760253i	0.976368	+	0.216115i	$0.0693386\pi$
$8$		0			0
$9$	−2.27503	−	1.95557i	−0.758343	−	0.651856i
$10$		0			0
$11$	−0.709852	−	0.294030i	−0.214028	−	0.0886534i	0.273093	−	0.961988i	$-0.411953\pi$
$11$	−0.709852	−	0.294030i	−0.214028	−	0.0886534i	−0.487122	+	0.873334i	$0.661953\pi$
$12$		0			0
$13$	−2.08393	−	5.03104i	−0.577977	−	1.39536i	−0.894625	−	0.446817i	$-0.852557\pi$
$13$	−2.08393	−	5.03104i	−0.577977	−	1.39536i	0.316648	−	0.948543i	$-0.397443\pi$
$14$		0			0
$15$	0.482526	−	0.520336i	0.124588	−	0.134350i
$16$		0			0
$17$	−6.33777			−1.53714			−0.768568	−	0.639768i	$-0.779030\pi$
$17$	−6.33777			−1.53714			−0.768568	+	0.639768i	$0.779030\pi$
$18$		0			0
$19$	−0.646487	+	0.267784i	−0.148314	+	0.0614338i	−0.455606	−	0.890182i	$-0.650577\pi$
$19$	−0.646487	+	0.267784i	−0.148314	+	0.0614338i	0.307291	+	0.951615i	$0.400577\pi$
$20$		0			0
$21$	2.05564	+	4.47769i	0.448577	+	0.977112i
$22$		0			0
$23$	1.61798	−	1.61798i	0.337371	−	0.337371i	−0.518006	−	0.855377i	$-0.673325\pi$
$23$	1.61798	−	1.61798i	0.337371	−	0.337371i	0.855377	+	0.518006i	$0.173325\pi$
$24$		0			0
$25$	−3.41684	−	3.41684i	−0.683368	−	0.683368i
$26$		0			0
$27$	4.54565	−	2.51736i	0.874810	−	0.484465i
$28$		0			0
$29$	−2.04571	−	4.93879i	−0.379879	−	0.917110i	−0.991988	−	0.126336i	$-0.959678\pi$
$29$	−2.04571	−	4.93879i	−0.379879	−	0.917110i	0.612108	−	0.790774i	$-0.290322\pi$
$30$		0			0
$31$			5.75464i			1.03356i	0.856117	+	0.516782i	$0.172870\pi$
$31$			5.75464i			1.03356i	−0.856117	+	0.516782i	$0.827130\pi$
$32$		0			0
$33$	0.904897	−	0.975803i	0.157522	−	0.169866i
$34$		0			0
$35$	−1.07674	+	0.446001i	−0.182002	+	0.0753879i
$36$		0			0
$37$	2.50232	−	6.04113i	0.411379	−	0.993156i	−0.573389	−	0.819283i	$-0.694372\pi$
$37$	2.50232	−	6.04113i	0.411379	−	0.993156i	0.984768	−	0.173873i	$-0.0556282\pi$
$38$		0			0
$39$	9.42529	−	0.355354i	1.50925	−	0.0569021i
$40$		0			0
$41$	5.52228	+	5.52228i	0.862435	+	0.862435i	0.991620	−	0.129185i	$-0.0412361\pi$
$41$	5.52228	+	5.52228i	0.862435	+	0.862435i	−0.129185	+	0.991620i	$0.541236\pi$
$42$		0			0
$43$	0.406593	−	0.981601i	0.0620048	−	0.149693i	−0.889840	−	0.456272i	$-0.849184\pi$
$43$	0.406593	−	0.981601i	0.0620048	−	0.149693i	0.951845	+	0.306579i	$0.0991844\pi$
$44$		0			0
$45$	0.554534	+	1.09692i	0.0826651	+	0.163519i
$46$		0			0
$47$		−	10.4826i		−	1.52904i	−0.644597	−	0.764522i	$-0.722975\pi$
$47$		−	10.4826i		−	1.52904i	0.644597	−	0.764522i	$-0.277025\pi$
$48$		0			0
$49$		−	1.09178i		−	0.155969i
$50$		0			0
$51$	3.81577	−	10.2928i	0.534315	−	1.44128i
$52$		0			0
$53$	−0.674566	+	1.62855i	−0.0926588	+	0.223698i	−0.963413	−	0.268020i	$-0.913631\pi$
$53$	−0.674566	+	1.62855i	−0.0926588	+	0.223698i	0.870755	+	0.491718i	$0.163631\pi$
$54$		0			0
$55$	0.222593	+	0.222593i	0.0300144	+	0.0300144i
$56$		0			0
$57$	−0.0456628	−	1.21115i	−0.00604819	−	0.160420i
$58$		0			0
$59$	3.35082	−	8.08960i	0.436240	−	1.05318i	−0.540997	−	0.841025i	$-0.681953\pi$
$59$	3.35082	−	8.08960i	0.436240	−	1.05318i	0.977237	−	0.212152i	$-0.0680472\pi$
$60$		0			0
$61$	−4.14715	+	1.71781i	−0.530988	+	0.219943i	−0.632036	−	0.774939i	$-0.717781\pi$
$61$	−4.14715	+	1.71781i	−0.530988	+	0.219943i	0.101048	+	0.994882i	$0.467781\pi$
$62$		0			0
$63$	−8.50959	+	0.642573i	−1.07211	+	0.0809566i
$64$		0			0
$65$			2.23109i			0.276732i
$66$		0			0
$67$	2.65183	+	6.40208i	0.323972	+	0.782138i	0.999016	+	0.0443601i	$0.0141249\pi$
$67$	2.65183	+	6.40208i	0.323972	+	0.782138i	−0.675043	+	0.737778i	$0.735875\pi$
$68$		0			0
$69$	1.65353	+	3.60179i	0.199061	+	0.433605i
$70$		0			0
$71$	−1.97014	−	1.97014i	−0.233813	−	0.233813i	0.580469	−	0.814282i	$-0.302869\pi$
$71$	−1.97014	−	1.97014i	−0.233813	−	0.233813i	−0.814282	+	0.580469i	$0.802869\pi$
$72$		0			0
$73$	9.48914	−	9.48914i	1.11062	−	1.11062i	0.117554	−	0.993067i	$-0.462495\pi$
$73$	9.48914	−	9.48914i	1.11062	−	1.11062i	0.993067	−	0.117554i	$-0.0375052\pi$
$74$		0			0
$75$	7.60626	−	3.49192i	0.878295	−	0.403212i
$76$		0			0
$77$	−2.01925	+	0.836400i	−0.230115	+	0.0953166i
$78$		0			0
$79$	−8.75751			−0.985297			−0.492649	−	0.870228i	$-0.663971\pi$
$79$	−8.75751			−0.985297			−0.492649	+	0.870228i	$0.663971\pi$
$80$		0			0
$81$	1.35150	+	8.89795i	0.150167	+	0.988661i
$82$		0			0
$83$	6.60293	+	15.9409i	0.724766	+	1.74974i	0.659294	+	0.751885i	$0.270855\pi$
$83$	6.60293	+	15.9409i	0.724766	+	1.74974i	0.0654719	+	0.997854i	$0.479145\pi$
$84$		0			0
$85$	2.39898	+	0.993689i	0.260206	+	0.107781i
$86$		0			0
$87$	9.25246	−	0.348838i	0.991968	−	0.0373993i
$88$		0			0
$89$	6.11535	−	6.11535i	0.648226	−	0.648226i	−0.304338	−	0.952564i	$-0.598435\pi$
$89$	6.11535	−	6.11535i	0.648226	−	0.648226i	0.952564	+	0.304338i	$0.0984353\pi$
$90$		0			0
$91$	−14.3113	−	5.92795i	−1.50024	−	0.621418i
$92$		0			0
$93$	−9.34579	−	3.46469i	−0.969113	−	0.359271i
$94$		0			0
$95$	0.286694			0.0294142
$96$		0			0
$97$	−5.09195			−0.517009			−0.258505	−	0.966010i	$-0.583230\pi$
$97$	−5.09195			−0.517009			−0.258505	+	0.966010i	$0.583230\pi$
$98$		0			0
$99$	1.03994	+	2.05709i	0.104518	+	0.206745i
$100$		0			0
$101$	−2.33659	−	0.967847i	−0.232499	−	0.0963044i	0.263392	−	0.964689i	$-0.415159\pi$
$101$	−2.33659	−	0.967847i	−0.232499	−	0.0963044i	−0.495892	+	0.868384i	$0.665159\pi$
$102$		0			0
$103$	−6.15411	+	6.15411i	−0.606383	+	0.606383i	−0.941999	−	0.335616i	$-0.891055\pi$
$103$	−6.15411	+	6.15411i	−0.606383	+	0.606383i	0.335616	+	0.941999i	$0.391055\pi$
$104$		0			0
$105$	−0.0760526	−	2.01720i	−0.00742198	−	0.196858i
$106$		0			0
$107$	1.19264	+	0.494009i	0.115297	+	0.0477576i	0.439586	−	0.898200i	$-0.355125\pi$
$107$	1.19264	+	0.494009i	0.115297	+	0.0477576i	−0.324289	+	0.945958i	$0.605125\pi$
$108$		0			0
$109$	0.933827	+	2.25446i	0.0894444	+	0.215938i	0.962271	−	0.272092i	$-0.0877156\pi$
$109$	0.933827	+	2.25446i	0.0894444	+	0.215938i	−0.872827	+	0.488030i	$0.837716\pi$
$110$		0			0
$111$	8.30449	+	7.70104i	0.788227	+	0.730951i
$112$		0			0
$113$	−7.02329			−0.660696			−0.330348	−	0.943859i	$-0.607166\pi$
$113$	−7.02329			−0.660696			−0.330348	+	0.943859i	$0.607166\pi$
$114$		0			0
$115$	−0.866116	+	0.358757i	−0.0807657	+	0.0334543i
$116$		0			0
$117$	−5.09756	+	15.5210i	−0.471270	+	1.43492i
$118$		0			0
$119$	−12.7481	+	12.7481i	−1.16861	+	1.16861i
$120$		0			0
$121$	−7.36074	−	7.36074i	−0.669158	−	0.669158i
$122$		0			0
$123$	−12.2932	+	5.64363i	−1.10844	+	0.508869i
$124$		0			0
$125$	1.54156	+	3.72167i	0.137882	+	0.332876i
$126$		0			0
$127$		−	5.12307i		−	0.454599i	−0.973825	−	0.227299i	$-0.927010\pi$
$127$		−	5.12307i		−	0.454599i	0.973825	−	0.227299i	$-0.0729896\pi$
$128$		0			0
$129$	1.34937	+	1.25131i	0.118805	+	0.110172i
$130$		0			0
$131$	−13.0406	+	5.40161i	−1.13937	+	0.471941i	−0.870955	−	0.491363i	$-0.836499\pi$
$131$	−13.0406	+	5.40161i	−1.13937	+	0.471941i	−0.268412	+	0.963304i	$0.586499\pi$
$132$		0			0
$133$	−0.761739	+	1.83900i	−0.0660512	+	0.159462i
$134$		0			0
$135$	−2.11531	+	0.240166i	−0.182057	+	0.0206702i
$136$		0			0
$137$	5.19191	+	5.19191i	0.443575	+	0.443575i	0.893211	−	0.449637i	$-0.148447\pi$
$137$	5.19191	+	5.19191i	0.443575	+	0.443575i	−0.449637	+	0.893211i	$0.648447\pi$
$138$		0			0
$139$	−2.91660	+	7.04129i	−0.247383	+	0.597234i	−0.997980	−	0.0635252i	$-0.979766\pi$
$139$	−2.91660	+	7.04129i	−0.247383	+	0.597234i	0.750598	+	0.660759i	$0.229766\pi$
$140$		0			0
$141$	17.0242	+	6.31124i	1.43370	+	0.531502i
$142$		0			0
$143$			4.18403i			0.349886i
$144$		0			0
$145$			2.19018i			0.181884i
$146$		0			0
$147$	1.77310	+	0.657327i	0.146243	+	0.0542154i
$148$		0			0
$149$	7.55828	−	18.2473i	0.619199	−	1.49488i	−0.233437	−	0.972372i	$-0.574997\pi$
$149$	7.55828	−	18.2473i	0.619199	−	1.49488i	0.852636	−	0.522506i	$-0.175003\pi$
$150$		0			0
$151$	−8.19627	−	8.19627i	−0.667003	−	0.667003i	0.290018	−	0.957021i	$-0.406339\pi$
$151$	−8.19627	−	8.19627i	−0.667003	−	0.667003i	−0.957021	+	0.290018i	$0.906339\pi$
$152$		0			0
$153$	14.4186	+	12.3940i	1.16568	+	1.00199i
$154$		0			0
$155$	0.902261	−	2.17825i	0.0724713	−	0.174961i
$156$		0			0
$157$	1.42476	−	0.590154i	0.113708	−	0.0470994i	−0.325104	−	0.945678i	$-0.605399\pi$
$157$	1.42476	−	0.590154i	0.113708	−	0.0470994i	0.438812	+	0.898579i	$0.355399\pi$
$158$		0			0
$159$	−2.23869	−	2.07602i	−0.177540	−	0.164639i
$160$		0			0
$161$		−	6.50892i		−	0.512975i
$162$		0			0
$163$	−0.927085	−	2.23818i	−0.0726149	−	0.175308i	0.883405	−	0.468611i	$-0.155245\pi$
$163$	−0.927085	−	2.23818i	−0.0726149	−	0.175308i	−0.956019	+	0.293303i	$0.905245\pi$
$164$		0			0
$165$	−0.495516	+	0.227484i	−0.0385759	+	0.0177096i
$166$		0			0
$167$	13.4441	+	13.4441i	1.04033	+	1.04033i	0.999152	+	0.0411813i	$0.0131121\pi$
$167$	13.4441	+	13.4441i	1.04033	+	1.04033i	0.0411813	+	0.999152i	$0.486888\pi$
$168$		0			0
$169$	−11.7763	+	11.7763i	−0.905866	+	0.905866i
$170$		0			0
$171$	1.99445	+	0.655035i	0.152519	+	0.0500918i
$172$		0			0
$173$	−5.11484	+	2.11864i	−0.388874	+	0.161077i	−0.568550	−	0.822649i	$-0.692495\pi$
$173$	−5.11484	+	2.11864i	−0.388874	+	0.161077i	0.179675	+	0.983726i	$0.442495\pi$
$174$		0			0
$175$	−13.7455			−1.03906
$176$		0			0
$177$	11.1204	+	10.3124i	0.835863	+	0.775125i
$178$		0			0
$179$	−2.02160	−	4.88057i	−0.151101	−	0.364791i	0.830145	−	0.557547i	$-0.188257\pi$
$179$	−2.02160	−	4.88057i	−0.151101	−	0.364791i	−0.981247	+	0.192756i	$0.938257\pi$
$180$		0			0
$181$	−8.06344	−	3.33999i	−0.599351	−	0.248259i	0.0623171	−	0.998056i	$-0.480151\pi$
$181$	−8.06344	−	3.33999i	−0.599351	−	0.248259i	−0.661668	+	0.749797i	$0.730151\pi$
$182$		0			0
$183$	−0.292922	−	7.76939i	−0.0216535	−	0.574330i
$184$		0			0
$185$	−1.89436	+	1.89436i	−0.139276	+	0.139276i
$186$		0			0
$187$	4.49888	+	1.86350i	0.328991	+	0.136272i
$188$		0			0
$189$	4.07979	−	14.2068i	0.296761	−	1.03339i
$190$		0			0
$191$	10.8066			0.781940			0.390970	−	0.920404i	$-0.372140\pi$
$191$	10.8066			0.781940			0.390970	+	0.920404i	$0.372140\pi$
$192$		0			0
$193$	−5.82359			−0.419192			−0.209596	−	0.977788i	$-0.567215\pi$
$193$	−5.82359			−0.419192			−0.209596	+	0.977788i	$0.567215\pi$
$194$		0			0
$195$	−3.62338	−	1.34327i	−0.259476	−	0.0961933i
$196$		0			0
$197$	19.4552	+	8.05861i	1.38613	+	0.574152i	0.946112	−	0.323839i	$-0.104974\pi$
$197$	19.4552	+	8.05861i	1.38613	+	0.574152i	0.440014	+	0.897991i	$0.354974\pi$
$198$		0			0
$199$	1.63519	−	1.63519i	0.115916	−	0.115916i	−0.646770	−	0.762685i	$-0.723880\pi$
$199$	1.63519	−	1.63519i	0.115916	−	0.115916i	0.762685	+	0.646770i	$0.223880\pi$
$200$		0			0
$201$	−11.9938	+	0.452193i	−0.845979	+	0.0318952i
$202$		0			0
$203$	−14.0489	−	5.81925i	−0.986040	−	0.408431i
$204$		0			0
$205$	−1.22447	−	2.95612i	−0.0855205	−	0.206465i
$206$		0			0
$207$	−6.84500	+	0.516877i	−0.475760	+	0.0359254i
$208$		0			0
$209$	0.537647			0.0371898
$210$		0			0
$211$	−13.4379	+	5.56618i	−0.925106	+	0.383192i	−0.793820	−	0.608153i	$-0.791911\pi$
$211$	−13.4379	+	5.56618i	−0.925106	+	0.383192i	−0.131286	+	0.991344i	$0.541911\pi$
$212$		0			0
$213$	4.38575	−	2.01343i	0.300507	−	0.137958i
$214$		0			0
$215$	−0.307807	+	0.307807i	−0.0209923	+	0.0209923i
$216$		0			0
$217$	11.5751	+	11.5751i	0.785771	+	0.785771i
$218$		0			0
$219$	9.69766	+	21.1239i	0.655307	+	1.42742i
$220$		0			0
$221$	13.2075	+	31.8856i	0.888430	+	2.14486i
$222$		0			0
$223$		−	0.106627i		−	0.00714024i	−0.999994	−	0.00357012i	$-0.998864\pi$
$223$		−	0.106627i		−	0.00714024i	0.999994	−	0.00357012i	$-0.00113641\pi$
$224$		0			0
$225$	1.09154	+	14.4553i	0.0727694	+	0.963684i
$226$		0			0
$227$	21.0312	−	8.71141i	1.39589	−	0.578196i	0.447208	−	0.894430i	$-0.352418\pi$
$227$	21.0312	−	8.71141i	1.39589	−	0.578196i	0.948681	+	0.316233i	$0.102418\pi$
$228$		0			0
$229$	1.56199	−	3.77098i	0.103219	−	0.249193i	−0.863830	−	0.503784i	$-0.831941\pi$
$229$	1.56199	−	3.77098i	0.103219	−	0.249193i	0.967049	+	0.254591i	$0.0819407\pi$
$230$		0			0
$231$	−0.142624	−	3.78291i	−0.00938397	−	0.248898i
$232$		0			0
$233$	4.47635	+	4.47635i	0.293255	+	0.293255i	0.838365	−	0.545110i	$-0.183512\pi$
$233$	4.47635	+	4.47635i	0.293255	+	0.293255i	−0.545110	+	0.838365i	$0.683512\pi$
$234$		0			0
$235$	−1.64355	+	3.96788i	−0.107213	+	0.258836i
$236$		0			0
$237$	5.27262	−	14.2226i	0.342493	−	0.923855i
$238$		0			0
$239$			8.68031i			0.561483i	0.959783	+	0.280741i	$0.0905803\pi$
$239$			8.68031i			0.561483i	−0.959783	+	0.280741i	$0.909420\pi$
$240$		0			0
$241$		−	4.55656i		−	0.293514i	−0.989173	−	0.146757i	$-0.953117\pi$
$241$		−	4.55656i		−	0.293514i	0.989173	−	0.146757i	$-0.0468835\pi$
$242$		0			0
$243$	−15.2643	−	3.16227i	−0.979208	−	0.202860i
$244$		0			0
$245$	−0.171179	+	0.413262i	−0.0109362	+	0.0264023i
$246$		0			0
$247$	2.69446	+	2.69446i	0.171445	+	0.171445i
$248$		0			0
$249$	−29.8641	+	1.12594i	−1.89256	+	0.0713536i
$250$		0			0
$251$	−0.750992	+	1.81305i	−0.0474022	+	0.114439i	−0.945807	−	0.324729i	$-0.894727\pi$
$251$	−0.750992	+	1.81305i	−0.0474022	+	0.114439i	0.898405	+	0.439168i	$0.144727\pi$
$252$		0			0
$253$	−1.62426	+	0.672789i	−0.102116	+	0.0422979i
$254$		0			0
$255$	−3.05814	+	3.29777i	−0.191508	+	0.206515i
$256$		0			0
$257$		−	13.4127i		−	0.836663i	−0.908294	−	0.418332i	$-0.862615\pi$
$257$		−	13.4127i		−	0.836663i	0.908294	−	0.418332i	$-0.137385\pi$
$258$		0			0
$259$	−7.11811	−	17.1846i	−0.442298	−	1.06780i
$260$		0			0
$261$	−5.00409	+	15.2364i	−0.309745	+	0.943110i
$262$		0			0
$263$	−18.7027	−	18.7027i	−1.15326	−	1.15326i	−0.985896	−	0.167359i	$-0.946476\pi$
$263$	−18.7027	−	18.7027i	−1.15326	−	1.15326i	−0.167359	−	0.985896i	$-0.553524\pi$
$264$		0			0
$265$	0.510674	−	0.510674i	0.0313705	−	0.0313705i
$266$		0			0
$267$	6.24973	+	13.6134i	0.382477	+	0.833130i
$268$		0			0
$269$	−6.20132	+	2.56867i	−0.378101	+	0.156615i	−0.563636	−	0.826023i	$-0.690598\pi$
$269$	−6.20132	+	2.56867i	−0.378101	+	0.156615i	0.185535	+	0.982638i	$0.440598\pi$
$270$		0			0
$271$	26.4006			1.60372			0.801860	−	0.597512i	$-0.203844\pi$
$271$	26.4006			1.60372			0.801860	+	0.597512i	$0.203844\pi$
$272$		0			0
$273$	18.2436	−	19.6732i	1.10416	−	1.19068i
$274$		0			0
$275$	1.42079	+	3.43010i	0.0856772	+	0.206843i
$276$		0			0
$277$	11.8110	+	4.89227i	0.709654	+	0.293948i	0.708161	−	0.706051i	$-0.249525\pi$
$277$	11.8110	+	4.89227i	0.709654	+	0.293948i	0.00149230	+	0.999999i	$0.499525\pi$
$278$		0			0
$279$	11.2536	−	13.0920i	0.673736	−	0.783796i
$280$		0			0
$281$	10.9033	−	10.9033i	0.650433	−	0.650433i	−0.302664	−	0.953097i	$-0.597876\pi$
$281$	10.9033	−	10.9033i	0.650433	−	0.650433i	0.953097	+	0.302664i	$0.0978760\pi$
$282$		0			0
$283$	8.86260	+	3.67101i	0.526827	+	0.218219i	0.630213	−	0.776423i	$-0.282968\pi$
$283$	8.86260	+	3.67101i	0.526827	+	0.218219i	−0.103386	+	0.994641i	$0.532968\pi$
$284$		0			0
$285$	−0.172609	+	0.465603i	−0.0102245	+	0.0275800i
$286$		0			0
$287$	22.2155			1.31134
$288$		0			0
$289$	23.1674			1.36279
$290$		0			0
$291$	3.06570	−	8.26954i	0.179715	−	0.484769i
$292$		0			0
$293$	−20.0666	−	8.31184i	−1.17230	−	0.485583i	−0.290348	−	0.956921i	$-0.593771\pi$
$293$	−20.0666	−	8.31184i	−1.17230	−	0.485583i	−0.881952	+	0.471338i	$0.843771\pi$
$294$		0			0
$295$	−2.53671	+	2.53671i	−0.147693	+	0.147693i
$296$		0			0
$297$	−3.96691	+	0.450392i	−0.230184	+	0.0261344i
$298$		0			0
$299$	−11.5118	−	4.76836i	−0.665747	−	0.275761i
$300$		0			0
$301$	−1.15660	−	2.79227i	−0.0666650	−	0.160944i
$302$		0			0
$303$	2.97861	−	3.21201i	0.171117	−	0.184525i
$304$		0			0
$305$	1.83911			0.105307
$306$		0			0
$307$	−0.548682	+	0.227272i	−0.0313149	+	0.0129711i	−0.398286	−	0.917261i	$-0.630395\pi$
$307$	−0.548682	+	0.227272i	−0.0313149	+	0.0129711i	0.366971	+	0.930232i	$0.380395\pi$
$308$		0			0
$309$	−6.28934	−	13.6997i	−0.357788	−	0.779351i
$310$		0			0
$311$	−8.31914	+	8.31914i	−0.471735	+	0.471735i	−0.902476	−	0.430741i	$-0.858252\pi$
$311$	−8.31914	+	8.31914i	−0.471735	+	0.471735i	0.430741	+	0.902476i	$0.358252\pi$
$312$		0			0
$313$	5.90243	+	5.90243i	0.333625	+	0.333625i	0.853961	−	0.520336i	$-0.174193\pi$
$313$	5.90243	+	5.90243i	0.333625	+	0.333625i	−0.520336	+	0.853961i	$0.674193\pi$
$314$		0			0
$315$	3.32180	+	1.09098i	0.187162	+	0.0614696i
$316$		0			0
$317$	0.432895	+	1.04510i	0.0243138	+	0.0586987i	0.935570	−	0.353141i	$-0.114886\pi$
$317$	0.432895	+	1.04510i	0.0243138	+	0.0586987i	−0.911256	+	0.411840i	$0.864886\pi$
$318$		0			0
$319$			4.10731i			0.229965i
$320$		0			0
$321$	−1.52034	+	1.63948i	−0.0848573	+	0.0915066i
$322$		0			0
$323$	4.09729	−	1.69715i	0.227979	−	0.0944321i
$324$		0			0
$325$	−10.0698	+	24.3107i	−0.558573	+	1.34852i
$326$		0			0
$327$	−4.22356	+	0.159237i	−0.233564	+	0.00880584i
$328$		0			0
$329$	−21.0851	−	21.0851i	−1.16246	−	1.16246i
$330$		0			0
$331$	6.16978	−	14.8952i	0.339122	−	0.818713i	−0.658679	−	0.752424i	$-0.728884\pi$
$331$	6.16978	−	14.8952i	0.339122	−	0.818713i	0.997801	−	0.0662882i	$-0.0211157\pi$
$332$		0			0
$333$	−17.5067	+	8.85029i	−0.959361	+	0.484993i
$334$		0			0
$335$		−	2.83909i		−	0.155116i
$336$		0			0
$337$		−	17.2474i		−	0.939527i	−0.882792	−	0.469763i	$-0.844339\pi$
$337$		−	17.2474i		−	0.939527i	0.882792	−	0.469763i	$-0.155661\pi$
$338$		0			0
$339$	4.22850	−	11.4061i	0.229661	−	0.619496i
$340$		0			0
$341$	1.69204	−	4.08494i	0.0916291	−	0.221212i
$342$		0			0
$343$	11.8840	+	11.8840i	0.641677	+	0.641677i
$344$		0			0
$345$	−0.0611757	−	1.62261i	−0.00329359	−	0.0873581i
$346$		0			0
$347$	3.34246	−	8.06942i	0.179433	−	0.433189i	−0.808415	−	0.588613i	$-0.799674\pi$
$347$	3.34246	−	8.06942i	0.179433	−	0.433189i	0.987848	+	0.155424i	$0.0496743\pi$
$348$		0			0
$349$	22.7745	−	9.43351i	1.21909	−	0.504964i	0.321971	−	0.946750i	$-0.395655\pi$
$349$	22.7745	−	9.43351i	1.21909	−	0.504964i	0.897121	+	0.441785i	$0.145655\pi$
$350$		0			0
$351$	−22.1377	−	17.6234i	−1.18162	−	0.940666i
$352$		0			0
$353$			7.05617i			0.375562i	0.982211	+	0.187781i	$0.0601295\pi$
$353$			7.05617i			0.375562i	−0.982211	+	0.187781i	$0.939870\pi$
$354$		0			0
$355$	0.436843	+	1.05463i	0.0231852	+	0.0559741i
$356$		0			0
$357$	−13.0282	−	28.3786i	−0.689525	−	1.50195i
$358$		0			0
$359$	−17.9832	−	17.9832i	−0.949116	−	0.949116i	0.0496509	−	0.998767i	$-0.484189\pi$
$359$	−17.9832	−	17.9832i	−0.949116	−	0.949116i	−0.998767	+	0.0496509i	$0.984189\pi$
$360$		0			0
$361$	−13.0888	+	13.0888i	−0.688884	+	0.688884i
$362$		0			0
$363$	16.3858	−	7.52249i	0.860032	−	0.394828i
$364$		0			0
$365$	−5.07962	+	2.10405i	−0.265879	+	0.110131i
$366$		0			0
$367$	9.28729			0.484792			0.242396	−	0.970177i	$-0.422067\pi$
$367$	9.28729			0.484792			0.242396	+	0.970177i	$0.422067\pi$
$368$		0			0
$369$	−1.76414	−	23.3625i	−0.0918376	−	1.21621i
$370$		0			0
$371$	1.91887	+	4.63257i	0.0996230	+	0.240511i
$372$		0			0
$373$	−31.7209	−	13.1392i	−1.64244	−	0.680323i	−0.645902	−	0.763420i	$-0.723519\pi$
$373$	−31.7209	−	13.1392i	−1.64244	−	0.680323i	−0.996541	+	0.0830975i	$0.973519\pi$
$374$		0			0
$375$	−6.97227	+	0.262869i	−0.360046	+	0.0135745i
$376$		0			0
$377$	−20.5841	+	20.5841i	−1.06014	+	1.06014i
$378$		0			0
$379$	28.0588	+	11.6223i	1.44128	+	0.596999i	0.960109	−	0.279626i	$-0.0902105\pi$
$379$	28.0588	+	11.6223i	1.44128	+	0.596999i	0.481174	+	0.876625i	$0.340211\pi$
$380$		0			0
$381$	8.32008	+	3.08444i	0.426251	+	0.158021i
$382$		0			0
$383$	5.32676			0.272185			0.136092	−	0.990696i	$-0.456546\pi$
$383$	5.32676			0.272185			0.136092	+	0.990696i	$0.456546\pi$
$384$		0			0
$385$	0.895464			0.0456371
$386$		0			0
$387$	−2.84460	+	1.43805i	−0.144599	+	0.0731002i
$388$		0			0
$389$	−20.0435	−	8.30227i	−1.01624	−	0.420942i	−0.188515	−	0.982070i	$-0.560367\pi$
$389$	−20.0435	−	8.30227i	−1.01624	−	0.420942i	−0.827729	+	0.561128i	$0.810367\pi$
$390$		0			0
$391$	−10.2544	+	10.2544i	−0.518585	+	0.518585i
$392$		0			0
$393$	−0.921090	−	24.4307i	−0.0464628	−	1.23237i
$394$		0			0
$395$	3.31490	+	1.37308i	0.166791	+	0.0690869i
$396$		0			0
$397$	2.65193	+	6.40233i	0.133097	+	0.321323i	0.976351	−	0.216191i	$-0.0693634\pi$
$397$	2.65193	+	6.40233i	0.133097	+	0.321323i	−0.843255	+	0.537514i	$0.819363\pi$
$398$		0			0
$399$	−2.52800	−	2.34430i	−0.126558	−	0.117362i
$400$		0			0
$401$	−5.61080			−0.280190			−0.140095	−	0.990138i	$-0.544741\pi$
$401$	−5.61080			−0.280190			−0.140095	+	0.990138i	$0.544741\pi$
$402$		0			0
$403$	28.9519	−	11.9923i	1.44220	−	0.597377i
$404$		0			0
$405$	0.883522	−	3.57995i	0.0439026	−	0.177889i
$406$		0			0
$407$	−3.55255	+	3.55255i	−0.176093	+	0.176093i
$408$		0			0
$409$	−0.683364	−	0.683364i	−0.0337902	−	0.0337902i	0.690010	−	0.723800i	$-0.257606\pi$
$409$	−0.683364	−	0.683364i	−0.0337902	−	0.0337902i	−0.723800	+	0.690010i	$0.757606\pi$
$410$		0			0
$411$	−11.5578	+	5.30600i	−0.570102	+	0.261725i
$412$		0			0
$413$	−9.53177	−	23.0117i	−0.469028	−	1.13233i
$414$		0			0
$415$		−	7.06921i		−	0.347014i
$416$		0			0
$417$	−9.67936	−	8.97601i	−0.474000	−	0.439557i
$418$		0			0
$419$	16.8772	−	6.99075i	0.824503	−	0.341521i	0.0697790	−	0.997562i	$-0.477771\pi$
$419$	16.8772	−	6.99075i	0.824503	−	0.341521i	0.754724	+	0.656042i	$0.227771\pi$
$420$		0			0
$421$	7.36473	−	17.7800i	0.358935	−	0.866546i	−0.636515	−	0.771264i	$-0.719625\pi$
$421$	7.36473	−	17.7800i	0.358935	−	0.866546i	0.995450	−	0.0952818i	$-0.0303752\pi$
$422$		0			0
$423$	−20.4994	+	23.8482i	−0.996717	+	1.15954i
$424$		0			0
$425$	21.6552	+	21.6552i	1.05043	+	1.05043i
$426$		0			0
$427$	−4.88648	+	11.7970i	−0.236473	+	0.570897i
$428$		0			0
$429$	−6.79505	−	2.51907i	−0.328068	−	0.121622i
$430$		0			0
$431$			18.7398i			0.902664i	0.892356	+	0.451332i	$0.149051\pi$
$431$			18.7398i			0.902664i	−0.892356	+	0.451332i	$0.850949\pi$
$432$		0			0
$433$			2.88137i			0.138470i	0.997600	+	0.0692349i	$0.0220558\pi$
$433$			2.88137i			0.138470i	−0.997600	+	0.0692349i	$0.977944\pi$
$434$		0			0
$435$	−3.55694	−	1.31864i	−0.170542	−	0.0632237i
$436$		0			0
$437$	−0.612733	+	1.47927i	−0.0293110	+	0.0707630i
$438$		0			0
$439$	6.54440	+	6.54440i	0.312347	+	0.312347i	0.845818	−	0.533471i	$-0.179113\pi$
$439$	6.54440	+	6.54440i	0.312347	+	0.312347i	−0.533471	+	0.845818i	$0.679113\pi$
$440$		0			0
$441$	−2.13505	+	2.48383i	−0.101669	+	0.118278i
$442$		0			0
$443$	−5.97491	+	14.4247i	−0.283877	+	0.685339i	−0.999919	−	0.0127177i	$-0.995952\pi$
$443$	−5.97491	+	14.4247i	−0.283877	+	0.685339i	0.716042	+	0.698057i	$0.245952\pi$
$444$		0			0
$445$	−3.27360	+	1.35597i	−0.155184	+	0.0642791i
$446$		0			0
$447$	25.0838	+	23.2611i	1.18642	+	1.10021i
$448$		0			0
$449$		−	2.52116i		−	0.118981i	−0.998229	−	0.0594905i	$-0.981052\pi$
$449$		−	2.52116i		−	0.118981i	0.998229	−	0.0594905i	$-0.0189476\pi$
$450$		0			0
$451$	−2.29628	−	5.54372i	−0.108128	−	0.261043i
$452$		0			0
$453$	18.2458	−	8.37638i	0.857263	−	0.393557i
$454$		0			0
$455$	4.48770	+	4.48770i	0.210387	+	0.210387i
$456$		0			0
$457$	26.6180	−	26.6180i	1.24514	−	1.24514i	0.287295	−	0.957842i	$-0.407244\pi$
$457$	26.6180	−	26.6180i	1.24514	−	1.24514i	0.957842	−	0.287295i	$-0.0927560\pi$
$458$		0			0
$459$	−28.8093	+	15.9544i	−1.34470	+	0.744689i
$460$		0			0
$461$	−16.9365	+	7.01532i	−0.788810	+	0.326736i	−0.740465	−	0.672095i	$-0.765395\pi$
$461$	−16.9365	+	7.01532i	−0.788810	+	0.326736i	−0.0483450	+	0.998831i	$0.515395\pi$
$462$		0			0
$463$	22.1078			1.02744			0.513719	−	0.857959i	$-0.328268\pi$
$463$	22.1078			1.02744			0.513719	+	0.857959i	$0.328268\pi$
$464$		0			0
$465$	2.99435	+	2.77677i	0.138860	+	0.128769i
$466$		0			0
$467$	−11.0935	−	26.7822i	−0.513348	−	1.23933i	−0.941924	−	0.335825i	$-0.890985\pi$
$467$	−11.0935	−	26.7822i	−0.513348	−	1.23933i	0.428577	−	0.903505i	$-0.359015\pi$
$468$		0			0
$469$	18.2114	+	7.54340i	0.840923	+	0.348322i
$470$		0			0
$471$	0.100634	+	2.66918i	0.00463696	+	0.122989i
$472$		0			0
$473$	−0.577241	+	0.577241i	−0.0265416	+	0.0265416i
$474$		0			0
$475$	3.12392	+	1.29397i	0.143335	+	0.0593714i
$476$		0			0
$477$	4.71939	−	2.38583i	0.216086	−	0.109240i
$478$		0			0
$479$	−11.5288			−0.526765			−0.263382	−	0.964692i	$-0.584838\pi$
$479$	−11.5288			−0.526765			−0.263382	+	0.964692i	$0.584838\pi$
$480$		0			0
$481$	−35.6078			−1.62358
$482$		0			0
$483$	10.5708	+	3.91881i	0.480986	+	0.178312i
$484$		0			0
$485$	1.92741	+	0.798358i	0.0875190	+	0.0362516i
$486$		0			0
$487$	24.3533	−	24.3533i	1.10355	−	1.10355i	0.109575	−	0.993979i	$-0.465051\pi$
$487$	24.3533	−	24.3533i	1.10355	−	1.10355i	0.993979	−	0.109575i	$-0.0349489\pi$
$488$		0			0
$489$	4.19307	−	0.158088i	0.189617	−	0.00714897i
$490$		0			0
$491$	−13.2408	−	5.48453i	−0.597550	−	0.247513i	0.0633450	−	0.997992i	$-0.479823\pi$
$491$	−13.2408	−	5.48453i	−0.597550	−	0.247513i	−0.660895	+	0.750478i	$0.729823\pi$
$492$		0			0
$493$	12.9653	+	31.3009i	0.583926	+	1.40972i
$494$		0			0
$495$	−0.0711093	−	0.941700i	−0.00319613	−	0.0423263i
$496$		0			0
$497$	−7.92564			−0.355513
$498$		0			0
$499$	6.79930	−	2.81636i	0.304378	−	0.126078i	−0.225266	−	0.974297i	$-0.572325\pi$
$499$	6.79930	−	2.81636i	0.304378	−	0.126078i	0.529645	+	0.848220i	$0.322325\pi$
$500$		0			0
$501$	−29.9280	+	13.7395i	−1.33708	+	0.613835i
$502$		0			0
$503$	20.7317	−	20.7317i	0.924383	−	0.924383i	−0.0729527	−	0.997335i	$-0.523242\pi$
$503$	20.7317	−	20.7317i	0.924383	−	0.924383i	0.997335	+	0.0729527i	$0.0232422\pi$
$504$		0			0
$505$	0.732700	+	0.732700i	0.0326047	+	0.0326047i
$506$		0			0
$507$	−12.0350	−	26.2153i	−0.534495	−	1.16426i
$508$		0			0
$509$	7.27710	+	17.5685i	0.322552	+	0.778708i	0.999104	+	0.0423143i	$0.0134731\pi$
$509$	7.27710	+	17.5685i	0.322552	+	0.778708i	−0.676553	+	0.736394i	$0.736527\pi$
$510$		0			0
$511$		−	38.1737i		−	1.68870i
$512$		0			0
$513$	−2.26460	+	2.84469i	−0.0999844	+	0.125596i
$514$		0			0
$515$	3.29435	−	1.36456i	0.145166	−	0.0601299i
$516$		0			0
$517$	−3.08220	+	7.44109i	−0.135555	+	0.327259i
$518$		0			0
$519$	−0.361273	−	9.58229i	−0.0158581	−	0.420616i
$520$		0			0
$521$	−12.9964	−	12.9964i	−0.569382	−	0.569382i	0.362573	−	0.931955i	$-0.381898\pi$
$521$	−12.9964	−	12.9964i	−0.569382	−	0.569382i	−0.931955	+	0.362573i	$0.881898\pi$
$522$		0			0
$523$	13.8611	−	33.4638i	0.606105	−	1.46327i	−0.261097	−	0.965313i	$-0.584084\pi$
$523$	13.8611	−	33.4638i	0.606105	−	1.46327i	0.867203	−	0.497955i	$-0.165916\pi$
$524$		0			0
$525$	8.27575	−	22.3233i	0.361183	−	0.974270i
$526$		0			0
$527$		−	36.4716i		−	1.58873i
$528$		0			0
$529$			17.7643i			0.772361i
$530$		0			0
$531$	−23.4430	+	11.8513i	−1.01734	+	0.514303i
$532$		0			0
$533$	16.2748	−	39.2909i	0.704940	−	1.70188i
$534$		0			0
$535$	−0.373985	−	0.373985i	−0.0161688	−	0.0161688i
$536$		0			0
$537$	9.14339	−	0.344725i	0.394566	−	0.0148760i
$538$		0			0
$539$	−0.321017	+	0.775003i	−0.0138272	+	0.0333817i
$540$		0			0
$541$	−0.814609	+	0.337422i	−0.0350228	+	0.0145069i	−0.400126	−	0.916460i	$-0.631034\pi$
$541$	−0.814609	+	0.337422i	−0.0350228	+	0.0145069i	0.365103	+	0.930967i	$0.381034\pi$
$542$		0			0
$543$	10.2790	−	11.0845i	0.441115	−	0.475680i
$544$		0			0
$545$		−	0.999771i		−	0.0428255i
$546$		0			0
$547$	11.6045	+	28.0158i	0.496173	+	1.19787i	0.951529	+	0.307559i	$0.0995121\pi$
$547$	11.6045	+	28.0158i	0.496173	+	1.19787i	−0.455356	+	0.890310i	$0.650488\pi$
$548$		0			0
$549$	12.7942	+	4.20198i	0.546042	+	0.179336i
$550$		0			0
$551$	2.64506	+	2.64506i	0.112683	+	0.112683i
$552$		0			0
$553$	−17.6152	+	17.6152i	−0.749075	+	0.749075i
$554$		0			0
$555$	−1.93598	−	4.21705i	−0.0821780	−	0.179004i
$556$		0			0
$557$	9.67547	−	4.00771i	0.409963	−	0.169812i	−0.168164	−	0.985759i	$-0.553784\pi$
$557$	9.67547	−	4.00771i	0.409963	−	0.169812i	0.578127	+	0.815947i	$0.303784\pi$
$558$		0			0
$559$	−5.78579			−0.244713
$560$		0			0
$561$	−5.73503	+	6.18442i	−0.242133	+	0.261106i
$562$		0			0
$563$	7.67115	+	18.5198i	0.323300	+	0.780516i	0.999058	+	0.0433923i	$0.0138165\pi$
$563$	7.67115	+	18.5198i	0.323300	+	0.780516i	−0.675758	+	0.737124i	$0.736183\pi$
$564$		0			0
$565$	2.65846	+	1.10117i	0.111842	+	0.0463266i
$566$		0			0
$567$	20.6162	+	15.1792i	0.865797	+	0.637467i
$568$		0			0
$569$	3.36174	−	3.36174i	0.140932	−	0.140932i	−0.633121	−	0.774053i	$-0.718227\pi$
$569$	3.36174	−	3.36174i	0.140932	−	0.140932i	0.774053	+	0.633121i	$0.218227\pi$
$570$		0			0
$571$	−14.6718	−	6.07726i	−0.613996	−	0.254325i	0.0539402	−	0.998544i	$-0.482822\pi$
$571$	−14.6718	−	6.07726i	−0.613996	−	0.254325i	−0.667936	+	0.744219i	$0.732822\pi$
$572$		0			0
$573$	−6.50632	+	17.5504i	−0.271806	+	0.733179i
$574$		0			0
$575$	−11.0567			−0.461097
$576$		0			0
$577$	11.1656			0.464830			0.232415	−	0.972617i	$-0.425337\pi$
$577$	11.1656			0.464830			0.232415	+	0.972617i	$0.425337\pi$
$578$		0			0
$579$	3.50620	−	9.45777i	0.145713	−	0.393051i
$580$		0			0
$581$	45.3455	+	18.7827i	1.88125	+	0.779239i
$582$		0			0
$583$	0.957684	−	0.957684i	0.0396632	−	0.0396632i
$584$		0			0
$585$	4.36305	−	5.07579i	0.180390	−	0.209858i
$586$		0			0
$587$	31.3098	+	12.9689i	1.29229	+	0.535286i	0.919668	−	0.392696i	$-0.128458\pi$
$587$	31.3098	+	12.9689i	1.29229	+	0.535286i	0.372625	+	0.927982i	$0.378458\pi$
$588$		0			0
$589$	−1.54100	−	3.72030i	−0.0634958	−	0.153292i
$590$		0			0
$591$	−24.8009	+	26.7442i	−1.02017	+	1.10011i
$592$		0			0
$593$	21.0070			0.862656			0.431328	−	0.902195i	$-0.358045\pi$
$593$	21.0070			0.862656			0.431328	+	0.902195i	$0.358045\pi$
$594$		0			0
$595$	6.82414	−	2.82665i	0.279763	−	0.115881i
$596$		0			0
$597$	1.67113	+	3.64012i	0.0683947	+	0.148980i
$598$		0			0
$599$	4.73031	−	4.73031i	0.193275	−	0.193275i	−0.603835	−	0.797110i	$-0.706361\pi$
$599$	4.73031	−	4.73031i	0.193275	−	0.193275i	0.797110	+	0.603835i	$0.206361\pi$
$600$		0			0
$601$	22.8135	+	22.8135i	0.930581	+	0.930581i	0.997742	−	0.0671615i	$-0.0213943\pi$
$601$	22.8135	+	22.8135i	0.930581	+	0.930581i	−0.0671615	+	0.997742i	$0.521394\pi$
$602$		0			0
$603$	6.48672	−	19.7507i	0.264160	−	0.804312i
$604$		0			0
$605$	1.63211	+	3.94027i	0.0663548	+	0.160195i
$606$		0			0
$607$			20.5708i			0.834943i	0.908690	+	0.417472i	$0.137084\pi$
$607$			20.5708i			0.834943i	−0.908690	+	0.417472i	$0.862916\pi$
$608$		0			0
$609$	17.9091	−	19.3124i	0.725714	−	0.782579i
$610$		0			0
$611$	−52.7384	+	21.8450i	−2.13357	+	0.883753i
$612$		0			0
$613$	1.90289	−	4.59399i	0.0768571	−	0.185550i	−0.880781	−	0.473524i	$-0.842982\pi$
$613$	1.90289	−	4.59399i	0.0768571	−	0.185550i	0.957638	+	0.287974i	$0.0929818\pi$
$614$		0			0
$615$	5.53808	−	0.208798i	0.223317	−	0.00841953i
$616$		0			0
$617$	2.85391	+	2.85391i	0.114894	+	0.114894i	0.762216	−	0.647322i	$-0.224111\pi$
$617$	2.85391	+	2.85391i	0.114894	+	0.114894i	−0.647322	+	0.762216i	$0.724111\pi$
$618$		0			0
$619$	−12.0551	+	29.1035i	−0.484534	+	1.16977i	0.472901	+	0.881116i	$0.343207\pi$
$619$	−12.0551	+	29.1035i	−0.484534	+	1.16977i	−0.957434	+	0.288652i	$0.906793\pi$
$620$		0			0
$621$	3.28173	−	11.4278i	0.131691	−	0.458580i
$622$		0			0
$623$		−	24.6013i		−	0.985631i
$624$		0			0
$625$			22.5103i			0.900411i
$626$		0			0
$627$	−0.323700	+	0.873161i	−0.0129273	+	0.0348707i
$628$		0			0
$629$	−15.8591	+	38.2873i	−0.632345	+	1.52662i
$630$		0			0
$631$	−27.3014	−	27.3014i	−1.08685	−	1.08685i	−0.995851	−	0.0910003i	$-0.970994\pi$
$631$	−27.3014	−	27.3014i	−1.08685	−	1.08685i	−0.0910003	−	0.995851i	$-0.529006\pi$
$632$		0			0
$633$	−0.949152	−	25.1750i	−0.0377254	−	1.00062i
$634$		0			0
$635$	−0.803237	+	1.93919i	−0.0318755	+	0.0769543i
$636$		0			0
$637$	−5.49280	+	2.27519i	−0.217633	+	0.0901464i
$638$		0			0
$639$	0.629379	+	8.33487i	0.0248979	+	0.329722i
$640$		0			0
$641$			34.3968i			1.35859i	0.733865	+	0.679295i	$0.237714\pi$
$641$			34.3968i			1.35859i	−0.733865	+	0.679295i	$0.762286\pi$
$642$		0			0
$643$	10.4779	+	25.2960i	0.413210	+	0.997576i	0.984270	+	0.176669i	$0.0565321\pi$
$643$	10.4779	+	25.2960i	0.413210	+	0.997576i	−0.571061	+	0.820908i	$0.693468\pi$
$644$		0			0
$645$	−0.314571	−	0.685213i	−0.0123862	−	0.0269802i
$646$		0			0
$647$	26.7097	+	26.7097i	1.05007	+	1.05007i	0.998679	+	0.0513899i	$0.0163651\pi$
$647$	26.7097	+	26.7097i	1.05007	+	1.05007i	0.0513899	+	0.998679i	$0.483635\pi$
$648$		0			0
$649$	−4.75718	+	4.75718i	−0.186735	+	0.186735i
$650$		0			0
$651$	−25.7675	+	11.8295i	−1.00991	+	0.463634i
$652$		0			0
$653$	40.0093	−	16.5724i	1.56569	−	0.648528i	0.579620	−	0.814887i	$-0.303201\pi$
$653$	40.0093	−	16.5724i	1.56569	−	0.648528i	0.986065	+	0.166358i	$0.0532008\pi$
$654$		0			0
$655$	5.78306			0.225963
$656$		0			0
$657$	−40.1447	+	3.03139i	−1.56620	+	0.118266i
$658$		0			0
$659$	6.33558	+	15.2955i	0.246799	+	0.595826i	0.997929	−	0.0643286i	$-0.0204906\pi$
$659$	6.33558	+	15.2955i	0.246799	+	0.595826i	−0.751129	+	0.660155i	$0.770491\pi$
$660$		0			0
$661$	13.2351	+	5.48218i	0.514787	+	0.213232i	0.624926	−	0.780684i	$-0.285129\pi$
$661$	13.2351	+	5.48218i	0.514787	+	0.213232i	−0.110138	+	0.993916i	$0.535129\pi$
$662$		0			0
$663$	−59.7354	+	2.25215i	−2.31993	+	0.0874663i
$664$		0			0
$665$	0.576668	−	0.576668i	0.0223622	−	0.0223622i
$666$		0			0
$667$	−11.3007	−	4.68092i	−0.437567	−	0.181246i
$668$		0			0
$669$	0.173166	+	0.0641964i	0.00669499	+	0.00248198i
$670$		0			0
$671$	3.44895			0.133145
$672$		0			0
$673$	20.2651			0.781160			0.390580	−	0.920569i	$-0.372274\pi$
$673$	20.2651			0.781160			0.390580	+	0.920569i	$0.372274\pi$
$674$		0			0
$675$	−24.1331	−	6.93035i	−0.928885	−	0.266749i
$676$		0			0
$677$	−36.6561	−	15.1834i	−1.40881	−	0.583547i	−0.456785	−	0.889577i	$-0.650999\pi$
$677$	−36.6561	−	15.1834i	−1.40881	−	0.583547i	−0.952022	+	0.306030i	$0.900999\pi$
$678$		0			0
$679$	−10.2422	+	10.2422i	−0.393058	+	0.393058i
$680$		0			0
$681$	1.48548	+	39.4004i	0.0569237	+	1.50983i
$682$		0			0
$683$	24.0996	+	9.98236i	0.922144	+	0.381965i	0.792693	−	0.609621i	$-0.208678\pi$
$683$	24.0996	+	9.98236i	0.922144	+	0.381965i	0.129451	+	0.991586i	$0.458678\pi$
$684$		0			0
$685$	−1.15121	−	2.77927i	−0.0439856	−	0.106191i
$686$		0			0
$687$	5.18381	+	4.80713i	0.197775	+	0.183403i
$688$		0			0
$689$	9.59903			0.365694
$690$		0			0
$691$	−13.6860	+	5.66894i	−0.520641	+	0.215657i	−0.627499	−	0.778618i	$-0.715921\pi$
$691$	−13.6860	+	5.66894i	−0.520641	+	0.215657i	0.106857	+	0.994274i	$0.465921\pi$
$692$		0			0
$693$	6.22948	+	2.04595i	0.236638	+	0.0777190i
$694$		0			0
$695$	2.20798	−	2.20798i	0.0837536	−	0.0837536i
$696$		0			0
$697$	−34.9990	−	34.9990i	−1.32568	−	1.32568i
$698$		0			0
$699$	−9.96484	+	4.57471i	−0.376905	+	0.173031i
$700$		0			0
$701$	−15.2498	−	36.8163i	−0.575977	−	1.39053i	−0.896396	−	0.443255i	$-0.853824\pi$
$701$	−15.2498	−	36.8163i	−0.575977	−	1.39053i	0.320419	−	0.947276i	$-0.396176\pi$
$702$		0			0
$703$			4.57559i			0.172572i
$704$		0			0
$705$	−5.45447	−	5.05813i	−0.205427	−	0.190500i
$706$		0			0
$707$	−6.64668	+	2.75314i	−0.249974	+	0.103543i
$708$		0			0
$709$	−11.6037	+	28.0139i	−0.435788	+	1.05209i	0.541601	+	0.840636i	$0.317818\pi$
$709$	−11.6037	+	28.0139i	−0.435788	+	1.05209i	−0.977389	+	0.211449i	$0.932182\pi$
$710$		0			0
$711$	19.9236	+	17.1259i	0.747193	+	0.642272i
$712$		0			0
$713$	9.31087	+	9.31087i	0.348695	+	0.348695i
$714$		0			0
$715$	0.656007	−	1.58374i	0.0245333	−	0.0592286i
$716$		0			0
$717$	−14.0972	−	5.22614i	−0.526469	−	0.195174i
$718$		0			0
$719$			44.6170i			1.66393i	0.554826	+	0.831967i	$0.312785\pi$
$719$			44.6170i			1.66393i	−0.554826	+	0.831967i	$0.687215\pi$
$720$		0			0
$721$			24.7573i			0.922008i
$722$		0			0
$723$	7.40004	+	2.74336i	0.275211	+	0.102027i
$724$		0			0
$725$	−9.88517	+	23.8649i	−0.367126	+	0.886321i
$726$		0			0
$727$	15.5081	+	15.5081i	0.575162	+	0.575162i	0.933566	−	0.358405i	$-0.116679\pi$
$727$	15.5081	+	15.5081i	0.575162	+	0.575162i	−0.358405	+	0.933566i	$0.616679\pi$
$728$		0			0
$729$	14.3258	−	22.8860i	0.530587	−	0.847631i
$730$		0			0
$731$	−2.57689	+	6.22117i	−0.0953098	+	0.230098i
$732$		0			0
$733$	−43.3401	+	17.9520i	−1.60080	+	0.663074i	−0.991529	−	0.129887i	$-0.958538\pi$
$733$	−43.3401	+	17.9520i	−1.60080	+	0.663074i	−0.609273	+	0.792961i	$0.708538\pi$
$734$		0			0
$735$	−0.568093	−	0.526813i	−0.0209544	−	0.0194318i
$736$		0			0
$737$		−	5.32424i		−	0.196121i
$738$		0			0
$739$	−18.0170	−	43.4968i	−0.662765	−	1.60006i	−0.793452	−	0.608633i	$-0.791718\pi$
$739$	−18.0170	−	43.4968i	−0.662765	−	1.60006i	0.130686	−	0.991424i	$-0.458282\pi$
$740$		0			0
$741$	−5.99817	+	2.75367i	−0.220348	+	0.101159i
$742$		0			0
$743$	−3.20365	−	3.20365i	−0.117530	−	0.117530i	0.645895	−	0.763426i	$-0.276484\pi$
$743$	−3.20365	−	3.20365i	−0.117530	−	0.117530i	−0.763426	+	0.645895i	$0.776484\pi$
$744$		0			0
$745$	−5.72193	+	5.72193i	−0.209635	+	0.209635i
$746$		0			0
$747$	16.1516	−	49.1784i	0.590958	−	1.79935i
$748$		0			0
$749$	3.39260	−	1.40526i	0.123963	−	0.0513471i
$750$		0			0
$751$	−53.3838			−1.94800			−0.974001	−	0.226542i	$-0.927258\pi$
$751$	−53.3838			−1.94800			−0.974001	+	0.226542i	$0.927258\pi$
$752$		0			0
$753$	−2.49233	−	2.31123i	−0.0908255	−	0.0842257i
$754$		0			0
$755$	1.81738	+	4.38754i	0.0661411	+	0.159679i
$756$		0			0
$757$	40.7929	+	16.8970i	1.48264	+	0.614130i	0.969701	−	0.244294i	$-0.0785560\pi$
$757$	40.7929	+	16.8970i	1.48264	+	0.614130i	0.512941	+	0.858424i	$0.328556\pi$
$758$		0			0
$759$	−0.114725	−	3.04293i	−0.00416425	−	0.110451i
$760$		0			0
$761$	−2.82203	+	2.82203i	−0.102299	+	0.102299i	−0.756404	−	0.654105i	$-0.773045\pi$
$761$	−2.82203	+	2.82203i	−0.102299	+	0.102299i	0.654105	+	0.756404i	$0.273045\pi$
$762$		0			0
$763$	6.41304	+	2.65637i	0.232168	+	0.0961670i
$764$		0			0
$765$	−3.51451	−	6.95203i	−0.127067	−	0.251351i
$766$		0			0
$767$	−47.6820			−1.72170
$768$		0			0
$769$	11.4430			0.412645			0.206322	−	0.978484i	$-0.433850\pi$
$769$	11.4430			0.412645			0.206322	+	0.978484i	$0.433850\pi$
$770$		0			0
$771$	21.7828	+	8.07538i	0.784490	+	0.290828i
$772$		0			0
$773$	17.4059	+	7.20975i	0.626046	+	0.259317i	0.673072	−	0.739577i	$-0.264974\pi$
$773$	17.4059	+	7.20975i	0.626046	+	0.259317i	−0.0470263	+	0.998894i	$0.514974\pi$
$774$		0			0
$775$	19.6627	−	19.6627i	0.706305	−	0.706305i
$776$		0			0
$777$	32.1942	−	1.21379i	1.15496	−	0.0435444i
$778$		0			0
$779$	−5.04886	−	2.09131i	−0.180894	−	0.0749289i
$780$		0			0
$781$	0.819227	+	1.97779i	0.0293142	+	0.0707708i
$782$		0			0
$783$	−21.7318	−	17.3002i	−0.776631	−	0.618259i
$784$		0			0
$785$	−0.631829			−0.0225509
$786$		0			0
$787$	−26.6913	+	11.0559i	−0.951441	+	0.394100i	−0.803772	−	0.594937i	$-0.797177\pi$
$787$	−26.6913	+	11.0559i	−0.951441	+	0.394100i	−0.147669	+	0.989037i	$0.547177\pi$
$788$		0			0
$789$	41.6342	−	19.1136i	1.48222	−	0.680463i
$790$		0			0
$791$	−14.1269	+	14.1269i	−0.502296	+	0.502296i
$792$		0			0
$793$	17.2847	+	17.2847i	0.613798	+	0.613798i
$794$		0			0
$795$	0.521896	+	1.13682i	0.0185097	+	0.0403187i
$796$		0			0
$797$	−18.1728	−	43.8730i	−0.643714	−	1.55406i	−0.821633	−	0.570017i	$-0.806936\pi$
$797$	−18.1728	−	43.8730i	−0.643714	−	1.55406i	0.177919	−	0.984045i	$-0.443064\pi$
$798$		0			0
$799$			66.4364i			2.35035i
$800$		0			0
$801$	−25.8716	+	1.95361i	−0.914128	+	0.0690272i
$802$		0			0
$803$	−9.52598	+	3.94579i	−0.336164	+	0.139244i
$804$		0			0
$805$	−1.02052	+	2.46376i	−0.0359687	+	0.0868361i
$806$		0			0
$807$	−0.438013	−	11.6177i	−0.0154188	−	0.408963i
$808$		0			0
$809$	−10.4387	−	10.4387i	−0.367006	−	0.367006i	0.499378	−	0.866384i	$-0.333562\pi$
$809$	−10.4387	−	10.4387i	−0.367006	−	0.367006i	−0.866384	+	0.499378i	$0.833562\pi$
$810$		0			0
$811$	5.74617	−	13.8725i	0.201775	−	0.487129i	−0.790308	−	0.612710i	$-0.790079\pi$
$811$	5.74617	−	13.8725i	0.201775	−	0.487129i	0.992083	+	0.125581i	$0.0400794\pi$
$812$		0			0
$813$	−15.8949	+	42.8756i	−0.557460	+	1.50371i
$814$		0			0
$815$			0.992553i			0.0347676i
$816$		0			0
$817$			0.743472i			0.0260108i
$818$		0			0
$819$	20.9662	+	41.4730i	0.732617	+	1.44919i
$820$		0			0
$821$	−1.81831	+	4.38979i	−0.0634594	+	0.153205i	−0.952428	−	0.304763i	$-0.901423\pi$
$821$	−1.81831	+	4.38979i	−0.0634594	+	0.153205i	0.888969	+	0.457968i	$0.151423\pi$
$822$		0			0
$823$	6.63123	+	6.63123i	0.231150	+	0.231150i	0.813173	−	0.582023i	$-0.197738\pi$
$823$	6.63123	+	6.63123i	0.231150	+	0.231150i	−0.582023	+	0.813173i	$0.697738\pi$
$824$		0			0
$825$	−6.42605	+	0.242276i	−0.223726	+	0.00843496i
$826$		0			0
$827$	4.53700	−	10.9533i	0.157767	−	0.380883i	−0.825155	−	0.564907i	$-0.808912\pi$
$827$	4.53700	−	10.9533i	0.157767	−	0.380883i	0.982922	+	0.184023i	$0.0589122\pi$
$828$		0			0
$829$	23.9460	−	9.91877i	0.831680	−	0.344493i	0.0741124	−	0.997250i	$-0.476388\pi$
$829$	23.9460	−	9.91877i	0.831680	−	0.344493i	0.757568	+	0.652757i	$0.226388\pi$
$830$		0			0
$831$	−15.0563	+	16.2361i	−0.522296	+	0.563223i
$832$		0			0
$833$			6.91947i			0.239745i
$834$		0			0
$835$	−2.98098	−	7.19672i	−0.103161	−	0.249053i
$836$		0			0
$837$	14.4865	+	26.1586i	0.500726	+	0.904173i
$838$		0			0
$839$	20.4190	+	20.4190i	0.704940	+	0.704940i	0.965467	−	0.260526i	$-0.0838961\pi$
$839$	20.4190	+	20.4190i	0.704940	+	0.704940i	−0.260526	+	0.965467i	$0.583896\pi$
$840$		0			0
$841$	0.299407	−	0.299407i	0.0103244	−	0.0103244i
$842$		0			0
$843$	11.1428	+	24.2718i	0.383780	+	0.835967i
$844$		0			0
$845$	6.30393	−	2.61117i	0.216862	−	0.0898271i
$846$		0			0
$847$	−29.6114			−1.01746
$848$		0			0
$849$	−11.2978	+	12.1830i	−0.387738	+	0.418121i
$850$		0			0
$851$	−5.72571	−	13.8231i	−0.196275	−	0.473849i
$852$		0			0
$853$	15.7580	+	6.52717i	0.539543	+	0.223486i	0.635777	−	0.771873i	$-0.280680\pi$
$853$	15.7580	+	6.52717i	0.539543	+	0.223486i	−0.0962340	+	0.995359i	$0.530680\pi$
$854$		0			0
$855$	−0.652237	−	0.560650i	−0.0223060	−	0.0191738i
$856$		0			0
$857$	33.0421	−	33.0421i	1.12870	−	1.12870i	0.138307	−	0.990389i	$-0.455834\pi$
$857$	33.0421	−	33.0421i	1.12870	−	1.12870i	0.990389	−	0.138307i	$-0.0441662\pi$
$858$		0			0
$859$	−29.6597	−	12.2854i	−1.01198	−	0.419174i	−0.185801	−	0.982587i	$-0.559488\pi$
$859$	−29.6597	−	12.2854i	−1.01198	−	0.419174i	−0.826175	+	0.563413i	$0.809488\pi$
$860$		0			0
$861$	−13.3752	+	36.0789i	−0.455827	+	1.22956i
$862$		0			0
$863$	−36.6539			−1.24771			−0.623856	−	0.781539i	$-0.714435\pi$
$863$	−36.6539			−1.24771			−0.623856	+	0.781539i	$0.714435\pi$
$864$		0			0
$865$	2.26825			0.0771228
$866$		0			0
$867$	−13.9483	+	37.6248i	−0.473711	+	1.27781i
$868$		0			0
$869$	6.21654	+	2.57497i	0.210882	+	0.0873500i
$870$		0			0
$871$	26.6829	−	26.6829i	0.904116	−	0.904116i
$872$		0			0
$873$	11.5843	+	9.95766i	0.392070	+	0.337016i
$874$		0			0
$875$	10.5867	+	4.38514i	0.357895	+	0.148245i
$876$		0			0
$877$	−17.7546	−	42.8634i	−0.599531	−	1.44740i	−0.874060	−	0.485817i	$-0.838522\pi$
$877$	−17.7546	−	42.8634i	−0.599531	−	1.44740i	0.274529	−	0.961579i	$-0.411478\pi$
$878$		0			0
$879$	25.5802	−	27.5846i	0.862799	−	0.930407i
$880$		0			0
$881$	30.9787			1.04370			0.521850	−	0.853038i	$-0.325242\pi$
$881$	30.9787			1.04370			0.521850	+	0.853038i	$0.325242\pi$
$882$		0			0
$883$	27.3679	−	11.3361i	0.921002	−	0.381492i	0.128744	−	0.991678i	$-0.458905\pi$
$883$	27.3679	−	11.3361i	0.921002	−	0.381492i	0.792258	+	0.610186i	$0.208905\pi$
$884$		0			0
$885$	−2.59245	−	5.64700i	−0.0871443	−	0.189822i
$886$		0			0
$887$	2.37216	−	2.37216i	0.0796492	−	0.0796492i	−0.666160	−	0.745809i	$-0.732063\pi$
$887$	2.37216	−	2.37216i	0.0796492	−	0.0796492i	0.745809	+	0.666160i	$0.232063\pi$
$888$		0			0
$889$	−10.3047	−	10.3047i	−0.345610	−	0.345610i
$890$		0			0
$891$	1.65690	−	6.71360i	0.0555082	−	0.224914i
$892$		0			0
$893$	2.80707	+	6.77687i	0.0939350	+	0.226779i
$894$		0			0
$895$			2.16436i			0.0723465i
$896$		0			0
$897$	14.6749	−	15.8248i	0.489982	−	0.528376i
$898$		0			0
$899$	28.4210	−	11.7724i	0.947893	−	0.392630i
$900$		0			0
$901$	4.27525	−	10.3214i	0.142429	−	0.343854i
$902$		0			0
$903$	5.23111	−	0.197224i	0.174080	−	0.00656321i
$904$		0			0
$905$	2.52850	+	2.52850i	0.0840503	+	0.0840503i
$906$		0			0
$907$	13.3336	−	32.1901i	0.442734	−	1.06885i	−0.532252	−	0.846586i	$-0.678654\pi$
$907$	13.3336	−	32.1901i	0.442734	−	1.06885i	0.974986	−	0.222268i	$-0.0713459\pi$
$908$		0			0
$909$	3.42312	+	6.77124i	0.113538	+	0.224588i
$910$		0			0
$911$		−	11.2111i		−	0.371441i	−0.982603	−	0.185721i	$-0.940538\pi$
$911$		−	11.2111i		−	0.371441i	0.982603	−	0.185721i	$-0.0594620\pi$
$912$		0			0
$913$		−	13.2571i		−	0.438747i
$914$		0			0
$915$	−1.10727	+	2.98680i	−0.0366053	+	0.0987405i
$916$		0			0
$917$	−15.3655	+	37.0955i	−0.507412	+	1.22500i
$918$		0			0
$919$	−9.86384	−	9.86384i	−0.325378	−	0.325378i	0.525448	−	0.850826i	$-0.323898\pi$
$919$	−9.86384	−	9.86384i	−0.325378	−	0.325378i	−0.850826	+	0.525448i	$0.823898\pi$
$920$		0			0
$921$	−0.0387546	−	1.02792i	−0.00127701	−	0.0338710i
$922$		0			0
$923$	−5.80623	+	14.0175i	−0.191115	+	0.461391i
$924$		0			0
$925$	−29.1916	+	12.0916i	−0.959814	+	0.397568i
$926$		0			0
$927$	26.0356	−	1.96599i	0.855120	−	0.0645715i
$928$		0			0
$929$			6.97392i			0.228807i	0.993434	+	0.114403i	$0.0364956\pi$
$929$			6.97392i			0.228807i	−0.993434	+	0.114403i	$0.963504\pi$
$930$		0			0
$931$	0.292361	+	0.705823i	0.00958176	+	0.0231324i
$932$		0			0
$933$	−8.50194	−	18.5193i	−0.278341	−	0.606295i
$934$		0			0
$935$	−1.41074	−	1.41074i	−0.0461362	−	0.0461362i
$936$		0			0
$937$	32.9019	−	32.9019i	1.07486	−	1.07486i	0.0778973	−	0.996961i	$-0.475179\pi$
$937$	32.9019	−	32.9019i	1.07486	−	1.07486i	0.996961	−	0.0778973i	$-0.0248206\pi$
$938$		0			0
$939$	−13.1395	+	6.03213i	−0.428790	+	0.196851i
$940$		0			0
$941$	−1.67400	+	0.693394i	−0.0545709	+	0.0226040i	−0.409802	−	0.912175i	$-0.634402\pi$
$941$	−1.67400	+	0.693394i	−0.0545709	+	0.0226040i	0.355231	+	0.934779i	$0.384402\pi$
$942$		0			0
$943$	17.8698			0.581922
$944$		0			0
$945$	−3.77174	+	4.73790i	−0.122695	+	0.154124i
$946$		0			0
$947$	−5.82625	−	14.0658i	−0.189328	−	0.457078i	0.800503	−	0.599329i	$-0.204566\pi$
$947$	−5.82625	−	14.0658i	−0.189328	−	0.457078i	−0.989831	+	0.142251i	$0.954566\pi$
$948$		0			0
$949$	−67.5150	−	27.9656i	−2.19163	−	0.907802i
$950$		0			0
$951$	−1.95792	+	0.0738178i	−0.0634899	+	0.00239371i
$952$		0			0
$953$	−30.1975	+	30.1975i	−0.978193	+	0.978193i	−0.999767	−	0.0215739i	$-0.993132\pi$
$953$	−30.1975	+	30.1975i	−0.978193	+	0.978193i	0.0215739	+	0.999767i	$0.493132\pi$
$954$		0			0
$955$	−4.09053	−	1.69435i	−0.132366	−	0.0548279i
$956$		0			0
$957$	−6.67044	−	2.47288i	−0.215625	−	0.0799369i
$958$		0			0
$959$	20.8864			0.674458
$960$		0			0
$961$	−2.11594			−0.0682560
$962$		0			0
$963$	−1.74723	−	3.45618i	−0.0563036	−	0.111374i
$964$		0			0
$965$	2.20435	+	0.913071i	0.0709605	+	0.0293928i
$966$		0			0
$967$	−19.7575	+	19.7575i	−0.635360	+	0.635360i	−0.949407	−	0.314047i	$-0.898315\pi$
$967$	−19.7575	+	19.7575i	−0.635360	+	0.635360i	0.314047	+	0.949407i	$0.398315\pi$
$968$		0			0
$969$	0.289401	+	7.67598i	0.00929689	+	0.246588i
$970$		0			0
$971$	12.7822	+	5.29454i	0.410199	+	0.169910i	0.578234	−	0.815871i	$-0.303742\pi$
$971$	12.7822	+	5.29454i	0.410199	+	0.169910i	−0.168035	+	0.985781i	$0.553742\pi$
$972$		0			0
$973$	8.29657	+	20.0297i	0.265976	+	0.642122i
$974$		0			0
$975$	−33.4189	−	30.9905i	−1.07026	−	0.992491i
$976$		0			0
$977$	−38.6385			−1.23615			−0.618077	−	0.786117i	$-0.712088\pi$
$977$	−38.6385			−1.23615			−0.618077	+	0.786117i	$0.712088\pi$
$978$		0			0
$979$	−6.13909	+	2.54289i	−0.196206	+	0.0812713i
$980$		0			0
$981$	2.28426	−	6.95512i	0.0729309	−	0.222060i
$982$		0			0
$983$	20.6692	−	20.6692i	0.659244	−	0.659244i	−0.295957	−	0.955201i	$-0.595639\pi$
$983$	20.6692	−	20.6692i	0.659244	−	0.659244i	0.955201	+	0.295957i	$0.0956386\pi$
$984$		0			0
$985$	−6.10069	−	6.10069i	−0.194384	−	0.194384i
$986$		0			0
$987$	46.9378	−	21.5485i	1.49405	−	0.685895i
$988$		0			0
$989$	−0.930350	−	2.24606i	−0.0295834	−	0.0714206i
$990$		0			0
$991$		−	37.7543i		−	1.19931i	−0.800260	−	0.599653i	$-0.795305\pi$
$991$		−	37.7543i		−	1.19931i	0.800260	−	0.599653i	$-0.204695\pi$
$992$		0			0
$993$	20.4758	+	18.9879i	0.649779	+	0.602563i
$994$		0			0
$995$	−0.875334	+	0.362575i	−0.0277499	+	0.0114944i
$996$		0			0
$997$	11.1744	−	26.9773i	0.353896	−	0.854381i	−0.642235	−	0.766507i	$-0.721993\pi$
$997$	11.1744	−	26.9773i	0.353896	−	0.854381i	0.996132	−	0.0878737i	$-0.0280072\pi$
$998$		0			0
$999$	−3.83302	−	33.7601i	−0.121271	−	1.06812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.671.6		56
3.2	odd	2	inner	768.2.o.b.671.12		56
4.3	odd	2		768.2.o.a.671.9		56
8.3	odd	2		384.2.o.a.335.6		56
8.5	even	2		96.2.o.a.11.4	✓	56
12.11	even	2		768.2.o.a.671.3		56
24.5	odd	2		96.2.o.a.11.11	yes	56
24.11	even	2		384.2.o.a.335.12		56
32.3	odd	8	inner	768.2.o.b.95.12		56
32.13	even	8		384.2.o.a.47.12		56
32.19	odd	8		96.2.o.a.35.11	yes	56
32.29	even	8		768.2.o.a.95.3		56
96.29	odd	8		768.2.o.a.95.9		56
96.35	even	8	inner	768.2.o.b.95.6		56
96.77	odd	8		384.2.o.a.47.6		56
96.83	even	8		96.2.o.a.35.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.4	✓	56	8.5	even	2
96.2.o.a.11.11	yes	56	24.5	odd	2
96.2.o.a.35.4	yes	56	96.83	even	8
96.2.o.a.35.11	yes	56	32.19	odd	8
384.2.o.a.47.6		56	96.77	odd	8
384.2.o.a.47.12		56	32.13	even	8
384.2.o.a.335.6		56	8.3	odd	2
384.2.o.a.335.12		56	24.11	even	2
768.2.o.a.95.3		56	32.29	even	8
768.2.o.a.95.9		56	96.29	odd	8
768.2.o.a.671.3		56	12.11	even	2
768.2.o.a.671.9		56	4.3	odd	2
768.2.o.b.95.6		56	96.35	even	8	inner
768.2.o.b.95.12		56	32.3	odd	8	inner
768.2.o.b.671.6		56	1.1	even	1	trivial
768.2.o.b.671.12		56	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.602068 + 1.62404i) q^{3} +(-0.378520 - 0.156788i) q^{5} +(2.01144 - 2.01144i) q^{7} +(-2.27503 - 1.95557i) q^{9} +O(q^{10})\)	\(q+(-0.602068 + 1.62404i) q^{3} +(-0.378520 - 0.156788i) q^{5} +(2.01144 - 2.01144i) q^{7} +(-2.27503 - 1.95557i) q^{9} +(-0.709852 - 0.294030i) q^{11} +(-2.08393 - 5.03104i) q^{13} +(0.482526 - 0.520336i) q^{15} -6.33777 q^{17} +(-0.646487 + 0.267784i) q^{19} +(2.05564 + 4.47769i) q^{21} +(1.61798 - 1.61798i) q^{23} +(-3.41684 - 3.41684i) q^{25} +(4.54565 - 2.51736i) q^{27} +(-2.04571 - 4.93879i) q^{29} +5.75464i q^{31} +(0.904897 - 0.975803i) q^{33} +(-1.07674 + 0.446001i) q^{35} +(2.50232 - 6.04113i) q^{37} +(9.42529 - 0.355354i) q^{39} +(5.52228 + 5.52228i) q^{41} +(0.406593 - 0.981601i) q^{43} +(0.554534 + 1.09692i) q^{45} -10.4826i q^{47} -1.09178i q^{49} +(3.81577 - 10.2928i) q^{51} +(-0.674566 + 1.62855i) q^{53} +(0.222593 + 0.222593i) q^{55} +(-0.0456628 - 1.21115i) q^{57} +(3.35082 - 8.08960i) q^{59} +(-4.14715 + 1.71781i) q^{61} +(-8.50959 + 0.642573i) q^{63} +2.23109i q^{65} +(2.65183 + 6.40208i) q^{67} +(1.65353 + 3.60179i) q^{69} +(-1.97014 - 1.97014i) q^{71} +(9.48914 - 9.48914i) q^{73} +(7.60626 - 3.49192i) q^{75} +(-2.01925 + 0.836400i) q^{77} -8.75751 q^{79} +(1.35150 + 8.89795i) q^{81} +(6.60293 + 15.9409i) q^{83} +(2.39898 + 0.993689i) q^{85} +(9.25246 - 0.348838i) q^{87} +(6.11535 - 6.11535i) q^{89} +(-14.3113 - 5.92795i) q^{91} +(-9.34579 - 3.46469i) q^{93} +0.286694 q^{95} -5.09195 q^{97} +(1.03994 + 2.05709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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