LMFDB - Embedded newform 768.2.o.a.95.3

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			95.3
Character	$\chi$	$=$	768.95
Dual form			768.2.o.a.671.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57410 + 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(-2.01144 - 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +O(q^{10})$	\(q+(-1.57410 + 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(-2.01144 - 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +(-0.709852 + 0.294030i) q^{11} +(-2.08393 + 5.03104i) q^{13} +(-0.482526 + 0.520336i) q^{15} +6.33777 q^{17} +(0.646487 + 0.267784i) q^{19} +(4.61976 + 1.71265i) q^{21} +(1.61798 + 1.61798i) q^{23} +(-3.41684 + 3.41684i) q^{25} +(-1.43422 + 4.99430i) q^{27} +(2.04571 - 4.93879i) q^{29} +5.75464i q^{31} +(0.904897 - 0.975803i) q^{33} +(-1.07674 - 0.446001i) q^{35} +(2.50232 + 6.04113i) q^{37} +(-0.355354 - 9.42529i) q^{39} +(-5.52228 + 5.52228i) q^{41} +(-0.406593 - 0.981601i) q^{43} +(0.383525 - 1.16775i) q^{45} +10.4826i q^{47} +1.09178i q^{49} +(-9.97628 + 4.57996i) q^{51} +(0.674566 + 1.62855i) q^{53} +(-0.222593 + 0.222593i) q^{55} +(-1.21115 + 0.0456628i) q^{57} +(3.35082 + 8.08960i) q^{59} +(-4.14715 - 1.71781i) q^{61} +(-8.50959 + 0.642573i) q^{63} +2.23109i q^{65} +(-2.65183 + 6.40208i) q^{67} +(-3.71607 - 1.37763i) q^{69} +(-1.97014 + 1.97014i) q^{71} +(9.48914 + 9.48914i) q^{73} +(2.90928 - 7.84760i) q^{75} +(2.01925 + 0.836400i) q^{77} +8.75751 q^{79} +(-1.35150 - 8.89795i) q^{81} +(6.60293 - 15.9409i) q^{83} +(2.39898 - 0.993689i) q^{85} +(0.348838 + 9.25246i) q^{87} +(-6.11535 - 6.11535i) q^{89} +(14.3113 - 5.92795i) q^{91} +(-4.15856 - 9.05837i) q^{93} +0.286694 q^{95} -5.09195 q^{97} +(-0.719237 + 2.18993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.57410	+	0.722645i	−0.908806	+	0.417219i
$3$	−1.57410	+	0.722645i	−0.908806	+	0.417219i
$4$		0			0
$5$	0.378520	−	0.156788i	0.169279	−	0.0701179i	−0.296434	−	0.955053i	$-0.595798\pi$
$5$	0.378520	−	0.156788i	0.169279	−	0.0701179i	0.465714	+	0.884935i	$0.345798\pi$
$6$		0			0
$7$	−2.01144	−	2.01144i	−0.760253	−	0.760253i	0.216115	−	0.976368i	$-0.430661\pi$
$7$	−2.01144	−	2.01144i	−0.760253	−	0.760253i	−0.976368	+	0.216115i	$0.930661\pi$
$8$		0			0
$9$	1.95557	−	2.27503i	0.651856	−	0.758343i
$10$		0			0
$11$	−0.709852	+	0.294030i	−0.214028	+	0.0886534i	−0.487122	−	0.873334i	$-0.661953\pi$
$11$	−0.709852	+	0.294030i	−0.214028	+	0.0886534i	0.273093	+	0.961988i	$0.411953\pi$
$12$		0			0
$13$	−2.08393	+	5.03104i	−0.577977	+	1.39536i	0.316648	+	0.948543i	$0.397443\pi$
$13$	−2.08393	+	5.03104i	−0.577977	+	1.39536i	−0.894625	+	0.446817i	$0.852557\pi$
$14$		0			0
$15$	−0.482526	+	0.520336i	−0.124588	+	0.134350i
$16$		0			0
$17$	6.33777			1.53714			0.768568	−	0.639768i	$-0.220970\pi$
$17$	6.33777			1.53714			0.768568	+	0.639768i	$0.220970\pi$
$18$		0			0
$19$	0.646487	+	0.267784i	0.148314	+	0.0614338i	0.455606	−	0.890182i	$-0.349423\pi$
$19$	0.646487	+	0.267784i	0.148314	+	0.0614338i	−0.307291	+	0.951615i	$0.599423\pi$
$20$		0			0
$21$	4.61976	+	1.71265i	1.00811	+	0.373730i
$22$		0			0
$23$	1.61798	+	1.61798i	0.337371	+	0.337371i	0.855377	−	0.518006i	$-0.173325\pi$
$23$	1.61798	+	1.61798i	0.337371	+	0.337371i	−0.518006	+	0.855377i	$0.673325\pi$
$24$		0			0
$25$	−3.41684	+	3.41684i	−0.683368	+	0.683368i
$26$		0			0
$27$	−1.43422	+	4.99430i	−0.276016	+	0.961153i
$28$		0			0
$29$	2.04571	−	4.93879i	0.379879	−	0.917110i	−0.612108	−	0.790774i	$-0.709678\pi$
$29$	2.04571	−	4.93879i	0.379879	−	0.917110i	0.991988	−	0.126336i	$-0.0403217\pi$
$30$		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	0.984768	+	0.173873i	$0.0556282\pi$
$37$	2.50232	+	6.04113i	0.411379	+	0.993156i	−0.573389	+	0.819283i	$0.694372\pi$
$38$		0			0
$39$	−0.355354	−	9.42529i	−0.0569021	−	1.50925i
$40$		0			0
$41$	−5.52228	+	5.52228i	−0.862435	+	0.862435i	−0.991620	−	0.129185i	$-0.958764\pi$
$41$	−5.52228	+	5.52228i	−0.862435	+	0.862435i	0.129185	+	0.991620i	$0.458764\pi$
$42$		0			0
$43$	−0.406593	−	0.981601i	−0.0620048	−	0.149693i	0.889840	−	0.456272i	$-0.150816\pi$
$43$	−0.406593	−	0.981601i	−0.0620048	−	0.149693i	−0.951845	+	0.306579i	$0.900816\pi$
$44$		0			0
$45$	0.383525	−	1.16775i	0.0571725	−	0.174079i
$46$		0			0
$47$			10.4826i			1.52904i	0.644597	+	0.764522i	$0.277025\pi$
$47$			10.4826i			1.52904i	−0.644597	+	0.764522i	$0.722975\pi$
$48$		0			0
$49$			1.09178i			0.155969i
$50$		0			0
$51$	−9.97628	+	4.57996i	−1.39696	+	0.641323i
$52$		0			0
$53$	0.674566	+	1.62855i	0.0926588	+	0.223698i	0.963413	−	0.268020i	$-0.0863692\pi$
$53$	0.674566	+	1.62855i	0.0926588	+	0.223698i	−0.870755	+	0.491718i	$0.836369\pi$
$54$		0			0
$55$	−0.222593	+	0.222593i	−0.0300144	+	0.0300144i
$56$		0			0
$57$	−1.21115	+	0.0456628i	−0.160420	+	0.00604819i
$58$		0			0
$59$	3.35082	+	8.08960i	0.436240	+	1.05318i	0.977237	+	0.212152i	$0.0680472\pi$
$59$	3.35082	+	8.08960i	0.436240	+	1.05318i	−0.540997	+	0.841025i	$0.681953\pi$
$60$		0			0
$61$	−4.14715	−	1.71781i	−0.530988	−	0.219943i	0.101048	−	0.994882i	$-0.467781\pi$
$61$	−4.14715	−	1.71781i	−0.530988	−	0.219943i	−0.632036	+	0.774939i	$0.717781\pi$
$62$		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	0.675043	+	0.737778i	$0.264125\pi$
$67$	−2.65183	+	6.40208i	−0.323972	+	0.782138i	−0.999016	+	0.0443601i	$0.985875\pi$
$68$		0			0
$69$	−3.71607	−	1.37763i	−0.447363	−	0.165847i
$70$		0			0
$71$	−1.97014	+	1.97014i	−0.233813	+	0.233813i	−0.814282	−	0.580469i	$-0.802869\pi$
$71$	−1.97014	+	1.97014i	−0.233813	+	0.233813i	0.580469	+	0.814282i	$0.302869\pi$
$72$		0			0
$73$	9.48914	+	9.48914i	1.11062	+	1.11062i	0.993067	+	0.117554i	$0.0375052\pi$
$73$	9.48914	+	9.48914i	1.11062	+	1.11062i	0.117554	+	0.993067i	$0.462495\pi$
$74$		0			0
$75$	2.90928	−	7.84760i	0.335934	−	0.906163i
$76$		0			0
$77$	2.01925	+	0.836400i	0.230115	+	0.0953166i
$78$		0			0
$79$	8.75751			0.985297			0.492649	−	0.870228i	$-0.336029\pi$
$79$	8.75751			0.985297			0.492649	+	0.870228i	$0.336029\pi$
$80$		0			0
$81$	−1.35150	−	8.89795i	−0.150167	−	0.988661i
$82$		0			0
$83$	6.60293	−	15.9409i	0.724766	−	1.74974i	0.0654719	−	0.997854i	$-0.479145\pi$
$83$	6.60293	−	15.9409i	0.724766	−	1.74974i	0.659294	−	0.751885i	$-0.270855\pi$
$84$		0			0
$85$	2.39898	−	0.993689i	0.260206	−	0.107781i
$86$		0			0
$87$	0.348838	+	9.25246i	0.0373993	+	0.991968i
$88$		0			0
$89$	−6.11535	−	6.11535i	−0.648226	−	0.648226i	0.304338	−	0.952564i	$-0.401565\pi$
$89$	−6.11535	−	6.11535i	−0.648226	−	0.648226i	−0.952564	+	0.304338i	$0.901565\pi$
$90$		0			0
$91$	14.3113	−	5.92795i	1.50024	−	0.621418i
$92$		0			0
$93$	−4.15856	−	9.05837i	−0.431223	−	0.939310i
$94$		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
$99$	−0.719237	+	2.18993i	−0.0722860	+	0.220096i
$100$		0			0
$101$	2.33659	−	0.967847i	0.232499	−	0.0963044i	−0.263392	−	0.964689i	$-0.584841\pi$
$101$	2.33659	−	0.967847i	0.232499	−	0.0963044i	0.495892	+	0.868384i	$0.334841\pi$
$102$		0			0
$103$	6.15411	+	6.15411i	0.606383	+	0.606383i	0.941999	−	0.335616i	$-0.108945\pi$
$103$	6.15411	+	6.15411i	0.606383	+	0.606383i	−0.335616	+	0.941999i	$0.608945\pi$
$104$		0			0
$105$	2.01720	−	0.0760526i	0.196858	−	0.00742198i
$106$		0			0
$107$	1.19264	−	0.494009i	0.115297	−	0.0477576i	−0.324289	−	0.945958i	$-0.605125\pi$
$107$	1.19264	−	0.494009i	0.115297	−	0.0477576i	0.439586	+	0.898200i	$0.355125\pi$
$108$		0			0
$109$	0.933827	−	2.25446i	0.0894444	−	0.215938i	−0.872827	−	0.488030i	$-0.837716\pi$
$109$	0.933827	−	2.25446i	0.0894444	−	0.215938i	0.962271	+	0.272092i	$0.0877156\pi$
$110$		0			0
$111$	−8.30449	−	7.70104i	−0.788227	−	0.730951i
$112$		0			0
$113$	7.02329			0.660696			0.330348	−	0.943859i	$-0.392834\pi$
$113$	7.02329			0.660696			0.330348	+	0.943859i	$0.392834\pi$
$114$		0			0
$115$	0.866116	+	0.358757i	0.0807657	+	0.0334543i
$116$		0			0
$117$	7.37050	+	14.5795i	0.681403	+	1.34788i
$118$		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
$123$	4.70196	−	12.6833i	0.423962	−	1.14361i
$124$		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	−0.268412	−	0.963304i	$-0.586499\pi$
$131$	−13.0406	−	5.40161i	−1.13937	−	0.471941i	−0.870955	+	0.491363i	$0.836499\pi$
$132$		0			0
$133$	−0.761739	−	1.83900i	−0.0660512	−	0.159462i
$134$		0			0
$135$	0.240166	+	2.11531i	0.0206702	+	0.182057i
$136$		0			0
$137$	−5.19191	+	5.19191i	−0.443575	+	0.443575i	−0.893211	−	0.449637i	$-0.851553\pi$
$137$	−5.19191	+	5.19191i	−0.443575	+	0.443575i	0.449637	+	0.893211i	$0.351553\pi$
$138$		0			0
$139$	2.91660	+	7.04129i	0.247383	+	0.597234i	0.997980	−	0.0635252i	$-0.0202343\pi$
$139$	2.91660	+	7.04129i	0.247383	+	0.597234i	−0.750598	+	0.660759i	$0.770234\pi$
$140$		0			0
$141$	−7.57520	−	16.5006i	−0.637947	−	1.38960i
$142$		0			0
$143$		−	4.18403i		−	0.349886i
$144$		0			0
$145$		−	2.19018i		−	0.181884i
$146$		0			0
$147$	−0.788970	−	1.71857i	−0.0650732	−	0.141745i
$148$		0			0
$149$	−7.55828	−	18.2473i	−0.619199	−	1.49488i	−0.852636	−	0.522506i	$-0.824997\pi$
$149$	−7.55828	−	18.2473i	−0.619199	−	1.49488i	0.233437	−	0.972372i	$-0.425003\pi$
$150$		0			0
$151$	8.19627	−	8.19627i	0.667003	−	0.667003i	−0.290018	−	0.957021i	$-0.593661\pi$
$151$	8.19627	−	8.19627i	0.667003	−	0.667003i	0.957021	+	0.290018i	$0.0936613\pi$
$152$		0			0
$153$	12.3940	−	14.4186i	1.00199	−	1.16568i
$154$		0			0
$155$	0.902261	+	2.17825i	0.0724713	+	0.174961i
$156$		0			0
$157$	1.42476	+	0.590154i	0.113708	+	0.0470994i	0.438812	−	0.898579i	$-0.355399\pi$
$157$	1.42476	+	0.590154i	0.113708	+	0.0470994i	−0.325104	+	0.945678i	$0.605399\pi$
$158$		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	$-0.844755\pi$
$163$	0.927085	−	2.23818i	0.0726149	−	0.175308i	0.956019	+	0.293303i	$0.0947546\pi$
$164$		0			0
$165$	0.189527	−	0.511239i	0.0147547	−	0.0397999i
$166$		0			0
$167$	13.4441	−	13.4441i	1.04033	−	1.04033i	0.0411813	−	0.999152i	$-0.486888\pi$
$167$	13.4441	−	13.4441i	1.04033	−	1.04033i	0.999152	−	0.0411813i	$-0.0131121\pi$
$168$		0			0
$169$	−11.7763	−	11.7763i	−0.905866	−	0.905866i
$170$		0			0
$171$	1.87347	−	0.947107i	0.143268	−	0.0724271i
$172$		0			0
$173$	5.11484	+	2.11864i	0.388874	+	0.161077i	0.568550	−	0.822649i	$-0.307505\pi$
$173$	5.11484	+	2.11864i	0.388874	+	0.161077i	−0.179675	+	0.983726i	$0.557505\pi$
$174$		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	−0.981247	−	0.192756i	$-0.938257\pi$
$179$	−2.02160	+	4.88057i	−0.151101	+	0.364791i	0.830145	+	0.557547i	$0.188257\pi$
$180$		0			0
$181$	−8.06344	+	3.33999i	−0.599351	+	0.248259i	−0.661668	−	0.749797i	$-0.730151\pi$
$181$	−8.06344	+	3.33999i	−0.599351	+	0.248259i	0.0623171	+	0.998056i	$0.480151\pi$
$182$		0			0
$183$	7.76939	−	0.292922i	0.574330	−	0.0216535i
$184$		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
$189$	12.9306	−	7.16089i	0.940561	−	0.520878i
$190$		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
$195$	−1.61228	−	3.51195i	−0.115458	−	0.251496i
$196$		0			0
$197$	−19.4552	+	8.05861i	−1.38613	+	0.574152i	−0.946112	−	0.323839i	$-0.895026\pi$
$197$	−19.4552	+	8.05861i	−1.38613	+	0.574152i	−0.440014	+	0.897991i	$0.645026\pi$
$198$		0			0
$199$	−1.63519	−	1.63519i	−0.115916	−	0.115916i	0.646770	−	0.762685i	$-0.276120\pi$
$199$	−1.63519	−	1.63519i	−0.115916	−	0.115916i	−0.762685	+	0.646770i	$0.776120\pi$
$200$		0			0
$201$	−0.452193	−	11.9938i	−0.0318952	−	0.845979i
$202$		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	$-0.208089\pi$
$211$	13.4379	+	5.56618i	0.925106	+	0.383192i	0.131286	+	0.991344i	$0.458089\pi$
$212$		0			0
$213$	1.67748	−	4.52491i	0.114939	−	0.310041i
$214$		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
$219$	−21.7941	−	8.07956i	−1.47271	−	0.545966i
$220$		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	0.948681	−	0.316233i	$-0.102418\pi$
$227$	21.0312	+	8.71141i	1.39589	+	0.578196i	0.447208	+	0.894430i	$0.352418\pi$
$228$		0			0
$229$	1.56199	+	3.77098i	0.103219	+	0.249193i	0.967049	−	0.254591i	$-0.0819407\pi$
$229$	1.56199	+	3.77098i	0.103219	+	0.249193i	−0.863830	+	0.503784i	$0.831941\pi$
$230$		0			0
$231$	−3.78291	+	0.142624i	−0.248898	+	0.00938397i
$232$		0			0
$233$	−4.47635	+	4.47635i	−0.293255	+	0.293255i	−0.838365	−	0.545110i	$-0.816488\pi$
$233$	−4.47635	+	4.47635i	−0.293255	+	0.293255i	0.545110	+	0.838365i	$0.316488\pi$
$234$		0			0
$235$	1.64355	+	3.96788i	0.107213	+	0.258836i
$236$		0			0
$237$	−13.7852	+	6.32857i	−0.895444	+	0.411085i
$238$		0			0
$239$		−	8.68031i		−	0.561483i	−0.959783	−	0.280741i	$-0.909420\pi$
$239$		−	8.68031i		−	0.561483i	0.959783	−	0.280741i	$-0.0905803\pi$
$240$		0			0
$241$			4.55656i			0.293514i	0.989173	+	0.146757i	$0.0468835\pi$
$241$			4.55656i			0.293514i	−0.989173	+	0.146757i	$0.953117\pi$
$242$		0			0
$243$	8.55745	+	13.0296i	0.548961	+	0.835848i
$244$		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
$249$	1.12594	+	29.8641i	0.0713536	+	1.89256i
$250$		0			0
$251$	−0.750992	−	1.81305i	−0.0474022	−	0.114439i	0.898405	−	0.439168i	$-0.144727\pi$
$251$	−0.750992	−	1.81305i	−0.0474022	−	0.114439i	−0.945807	+	0.324729i	$0.894727\pi$
$252$		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
$261$	−7.23535	−	14.3122i	−0.447857	−	0.885903i
$262$		0			0
$263$	−18.7027	+	18.7027i	−1.15326	+	1.15326i	−0.167359	+	0.985896i	$0.553524\pi$
$263$	−18.7027	+	18.7027i	−1.15326	+	1.15326i	−0.985896	+	0.167359i	$0.946476\pi$
$264$		0			0
$265$	0.510674	+	0.510674i	0.0313705	+	0.0313705i
$266$		0			0
$267$	14.0454	+	5.20693i	0.859564	+	0.318659i
$268$		0			0
$269$	6.20132	+	2.56867i	0.378101	+	0.156615i	0.563636	−	0.826023i	$-0.309402\pi$
$269$	6.20132	+	2.56867i	0.378101	+	0.156615i	−0.185535	+	0.982638i	$0.559402\pi$
$270$		0			0
$271$	−26.4006			−1.60372			−0.801860	−	0.597512i	$-0.796156\pi$
$271$	−26.4006			−1.60372			−0.801860	+	0.597512i	$0.796156\pi$
$272$		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	0.00149230	−	0.999999i	$-0.499525\pi$
$277$	11.8110	−	4.89227i	0.709654	−	0.293948i	0.708161	+	0.706051i	$0.249525\pi$
$278$		0			0
$279$	13.0920	+	11.2536i	0.783796	+	0.673736i
$280$		0			0
$281$	−10.9033	−	10.9033i	−0.650433	−	0.650433i	0.302664	−	0.953097i	$-0.402124\pi$
$281$	−10.9033	−	10.9033i	−0.650433	−	0.650433i	−0.953097	+	0.302664i	$0.902124\pi$
$282$		0			0
$283$	−8.86260	+	3.67101i	−0.526827	+	0.218219i	−0.630213	−	0.776423i	$-0.717032\pi$
$283$	−8.86260	+	3.67101i	−0.526827	+	0.218219i	0.103386	+	0.994641i	$0.467032\pi$
$284$		0			0
$285$	−0.451284	+	0.207178i	−0.0267318	+	0.0122722i
$286$		0			0
$287$	22.2155			1.31134
$288$		0			0
$289$	23.1674			1.36279
$290$		0			0
$291$	8.01523	−	3.67967i	0.469861	−	0.215706i
$292$		0			0
$293$	20.0666	−	8.31184i	1.17230	−	0.485583i	0.290348	−	0.956921i	$-0.406229\pi$
$293$	20.0666	−	8.31184i	1.17230	−	0.485583i	0.881952	+	0.471338i	$0.156229\pi$
$294$		0			0
$295$	2.53671	+	2.53671i	0.147693	+	0.147693i
$296$		0			0
$297$	−0.450392	−	3.96691i	−0.0261344	−	0.230184i
$298$		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	$-0.369605\pi$
$307$	0.548682	+	0.227272i	0.0313149	+	0.0129711i	−0.366971	+	0.930232i	$0.619605\pi$
$308$		0			0
$309$	−14.1344	−	5.23994i	−0.804079	−	0.298090i
$310$		0			0
$311$	−8.31914	−	8.31914i	−0.471735	−	0.471735i	0.430741	−	0.902476i	$-0.358252\pi$
$311$	−8.31914	−	8.31914i	−0.471735	−	0.471735i	−0.902476	+	0.430741i	$0.858252\pi$
$312$		0			0
$313$	5.90243	−	5.90243i	0.333625	−	0.333625i	−0.520336	−	0.853961i	$-0.674193\pi$
$313$	5.90243	−	5.90243i	0.333625	−	0.333625i	0.853961	+	0.520336i	$0.174193\pi$
$314$		0			0
$315$	−3.12031	+	1.57743i	−0.175809	+	0.0888782i
$316$		0			0
$317$	−0.432895	+	1.04510i	−0.0243138	+	0.0586987i	−0.935570	−	0.353141i	$-0.885114\pi$
$317$	−0.432895	+	1.04510i	−0.0243138	+	0.0586987i	0.911256	+	0.411840i	$0.135114\pi$
$318$		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
$327$	0.159237	+	4.22356i	0.00880584	+	0.233564i
$328$		0			0
$329$	21.0851	−	21.0851i	1.16246	−	1.16246i
$330$		0			0
$331$	−6.16978	−	14.8952i	−0.339122	−	0.818713i	−0.997801	−	0.0662882i	$-0.978884\pi$
$331$	−6.16978	−	14.8952i	−0.339122	−	0.818713i	0.658679	−	0.752424i	$-0.271116\pi$
$332$		0			0
$333$	18.6372	+	6.12100i	1.02131	+	0.335429i
$334$		0			0
$335$			2.83909i			0.155116i
$336$		0			0
$337$			17.2474i			0.939527i	0.882792	+	0.469763i	$0.155661\pi$
$337$			17.2474i			0.939527i	−0.882792	+	0.469763i	$0.844339\pi$
$338$		0			0
$339$	−11.0553	+	5.07535i	−0.600444	+	0.275655i
$340$		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
$345$	−1.62261	+	0.0611757i	−0.0873581	+	0.00329359i
$346$		0			0
$347$	3.34246	+	8.06942i	0.179433	+	0.433189i	0.987848	−	0.155424i	$-0.0496743\pi$
$347$	3.34246	+	8.06942i	0.179433	+	0.433189i	−0.808415	+	0.588613i	$0.799674\pi$
$348$		0			0
$349$	22.7745	+	9.43351i	1.21909	+	0.504964i	0.897121	−	0.441785i	$-0.145655\pi$
$349$	22.7745	+	9.43351i	1.21909	+	0.504964i	0.321971	+	0.946750i	$0.395655\pi$
$350$		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
$357$	29.2790	+	10.8544i	1.54961	+	0.574474i
$358$		0			0
$359$	−17.9832	+	17.9832i	−0.949116	+	0.949116i	−0.998767	−	0.0496509i	$-0.984189\pi$
$359$	−17.9832	+	17.9832i	−0.949116	+	0.949116i	0.0496509	+	0.998767i	$0.484189\pi$
$360$		0			0
$361$	−13.0888	−	13.0888i	−0.688884	−	0.688884i
$362$		0			0
$363$	6.26732	−	16.9057i	0.328949	−	0.887320i
$364$		0			0
$365$	5.07962	+	2.10405i	0.265879	+	0.110131i
$366$		0			0
$367$	−9.28729			−0.484792			−0.242396	−	0.970177i	$-0.577933\pi$
$367$	−9.28729			−0.484792			−0.242396	+	0.970177i	$0.577933\pi$
$368$		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	−0.996541	−	0.0830975i	$-0.973519\pi$
$373$	−31.7209	+	13.1392i	−1.64244	+	0.680323i	−0.645902	+	0.763420i	$0.723519\pi$
$374$		0			0
$375$	−0.262869	−	6.97227i	−0.0135745	−	0.360046i
$376$		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	$-0.909789\pi$
$379$	−28.0588	+	11.6223i	−1.44128	+	0.596999i	−0.481174	+	0.876625i	$0.659789\pi$
$380$		0			0
$381$	3.70216	+	8.06421i	0.189667	+	0.413142i
$382$		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
$387$	−3.02829	−	0.994579i	−0.153937	−	0.0505573i
$388$		0			0
$389$	20.0435	−	8.30227i	1.01624	−	0.420942i	0.188515	−	0.982070i	$-0.439633\pi$
$389$	20.0435	−	8.30227i	1.01624	−	0.420942i	0.827729	+	0.561128i	$0.189633\pi$
$390$		0			0
$391$	10.2544	+	10.2544i	0.518585	+	0.518585i
$392$		0			0
$393$	24.4307	−	0.921090i	1.23237	−	0.0464628i
$394$		0			0
$395$	3.31490	−	1.37308i	0.166791	−	0.0690869i
$396$		0			0
$397$	2.65193	−	6.40233i	0.133097	−	0.321323i	−0.843255	−	0.537514i	$-0.819363\pi$
$397$	2.65193	−	6.40233i	0.133097	−	0.321323i	0.976351	+	0.216191i	$0.0693634\pi$
$398$		0			0
$399$	2.52800	+	2.34430i	0.126558	+	0.117362i
$400$		0			0
$401$	5.61080			0.280190			0.140095	−	0.990138i	$-0.455259\pi$
$401$	5.61080			0.280190			0.140095	+	0.990138i	$0.455259\pi$
$402$		0			0
$403$	−28.9519	−	11.9923i	−1.44220	−	0.597377i
$404$		0			0
$405$	−1.90666	−	3.15615i	−0.0947429	−	0.156831i
$406$		0			0
$407$	−3.55255	−	3.55255i	−0.176093	−	0.176093i
$408$		0			0
$409$	−0.683364	+	0.683364i	−0.0337902	+	0.0337902i	−0.723800	−	0.690010i	$-0.757606\pi$
$409$	−0.683364	+	0.683364i	−0.0337902	+	0.0337902i	0.690010	+	0.723800i	$0.257606\pi$
$410$		0			0
$411$	4.42067	−	11.9245i	0.218055	−	0.588191i
$412$		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	0.754724	−	0.656042i	$-0.227771\pi$
$419$	16.8772	+	6.99075i	0.824503	+	0.341521i	0.0697790	+	0.997562i	$0.477771\pi$
$420$		0			0
$421$	7.36473	+	17.7800i	0.358935	+	0.866546i	0.995450	+	0.0952818i	$0.0303752\pi$
$421$	7.36473	+	17.7800i	0.358935	+	0.866546i	−0.636515	+	0.771264i	$0.719625\pi$
$422$		0			0
$423$	23.8482	+	20.4994i	1.15954	+	0.996717i
$424$		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
$429$	3.02357	+	6.58608i	0.145979	+	0.317979i
$430$		0			0
$431$		−	18.7398i		−	0.902664i	−0.892356	−	0.451332i	$-0.850949\pi$
$431$		−	18.7398i		−	0.902664i	0.892356	−	0.451332i	$-0.149051\pi$
$432$		0			0
$433$		−	2.88137i		−	0.138470i	−0.997600	−	0.0692349i	$-0.977944\pi$
$433$		−	2.88137i		−	0.138470i	0.997600	−	0.0692349i	$-0.0220558\pi$
$434$		0			0
$435$	1.58272	+	3.44755i	0.0758856	+	0.165297i
$436$		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	$-0.820887\pi$
$439$	−6.54440	+	6.54440i	−0.312347	+	0.312347i	0.533471	+	0.845818i	$0.320887\pi$
$440$		0			0
$441$	2.48383	+	2.13505i	0.118278	+	0.101669i
$442$		0			0
$443$	−5.97491	−	14.4247i	−0.283877	−	0.685339i	0.716042	−	0.698057i	$-0.245952\pi$
$443$	−5.97491	−	14.4247i	−0.283877	−	0.685339i	−0.999919	+	0.0127177i	$0.995952\pi$
$444$		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
$453$	−6.97874	+	18.8247i	−0.327890	+	0.884463i
$454$		0			0
$455$	4.48770	−	4.48770i	0.210387	−	0.210387i
$456$		0			0
$457$	26.6180	+	26.6180i	1.24514	+	1.24514i	0.957842	+	0.287295i	$0.0927560\pi$
$457$	26.6180	+	26.6180i	1.24514	+	1.24514i	0.287295	+	0.957842i	$0.407244\pi$
$458$		0			0
$459$	−9.08976	+	31.6527i	−0.424274	+	1.47742i
$460$		0			0
$461$	16.9365	+	7.01532i	0.788810	+	0.326736i	0.740465	−	0.672095i	$-0.234605\pi$
$461$	16.9365	+	7.01532i	0.788810	+	0.326736i	0.0483450	+	0.998831i	$0.484605\pi$
$462$		0			0
$463$	−22.1078			−1.02744			−0.513719	−	0.857959i	$-0.671732\pi$
$463$	−22.1078			−1.02744			−0.513719	+	0.857959i	$0.671732\pi$
$464$		0			0
$465$	−2.99435	−	2.77677i	−0.138860	−	0.128769i
$466$		0			0
$467$	−11.0935	+	26.7822i	−0.513348	+	1.23933i	0.428577	+	0.903505i	$0.359015\pi$
$467$	−11.0935	+	26.7822i	−0.513348	+	1.23933i	−0.941924	+	0.335825i	$0.890985\pi$
$468$		0			0
$469$	18.2114	−	7.54340i	0.840923	−	0.348322i
$470$		0			0
$471$	−2.66918	+	0.100634i	−0.122989	+	0.00463696i
$472$		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
$477$	5.02415	+	1.65008i	0.230040	+	0.0755519i
$478$		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
$483$	4.70364	+	10.2457i	0.214023	+	0.466194i
$484$		0			0
$485$	−1.92741	+	0.798358i	−0.0875190	+	0.0362516i
$486$		0			0
$487$	−24.3533	−	24.3533i	−1.10355	−	1.10355i	−0.993979	−	0.109575i	$-0.965051\pi$
$487$	−24.3533	−	24.3533i	−1.10355	−	1.10355i	−0.109575	−	0.993979i	$-0.534949\pi$
$488$		0			0
$489$	0.158088	+	4.19307i	0.00714897	+	0.189617i
$490$		0			0
$491$	−13.2408	+	5.48453i	−0.597550	+	0.247513i	−0.660895	−	0.750478i	$-0.729823\pi$
$491$	−13.2408	+	5.48453i	−0.597550	+	0.247513i	0.0633450	+	0.997992i	$0.479823\pi$
$492$		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	$-0.427675\pi$
$499$	−6.79930	−	2.81636i	−0.304378	−	0.126078i	−0.529645	+	0.848220i	$0.677675\pi$
$500$		0			0
$501$	−11.4470	+	30.8776i	−0.511414	+	1.37951i
$502$		0			0
$503$	20.7317	+	20.7317i	0.924383	+	0.924383i	0.997335	−	0.0729527i	$-0.0232422\pi$
$503$	20.7317	+	20.7317i	0.924383	+	0.924383i	−0.0729527	+	0.997335i	$0.523242\pi$
$504$		0			0
$505$	0.732700	−	0.732700i	0.0326047	−	0.0326047i
$506$		0			0
$507$	27.0470	+	10.0269i	1.20120	+	0.445312i
$508$		0			0
$509$	−7.27710	+	17.5685i	−0.322552	+	0.778708i	0.676553	+	0.736394i	$0.263473\pi$
$509$	−7.27710	+	17.5685i	−0.322552	+	0.778708i	−0.999104	+	0.0423143i	$0.986527\pi$
$510$		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
$519$	−9.58229	+	0.361273i	−0.420616	+	0.0158581i
$520$		0			0
$521$	12.9964	−	12.9964i	0.569382	−	0.569382i	−0.362573	−	0.931955i	$-0.618102\pi$
$521$	12.9964	−	12.9964i	0.569382	−	0.569382i	0.931955	+	0.362573i	$0.118102\pi$
$522$		0			0
$523$	−13.8611	−	33.4638i	−0.606105	−	1.46327i	−0.867203	−	0.497955i	$-0.834084\pi$
$523$	−13.8611	−	33.4638i	−0.606105	−	1.46327i	0.261097	−	0.965313i	$-0.415916\pi$
$524$		0			0
$525$	−21.6368	+	9.93314i	−0.944308	+	0.433518i
$526$		0			0
$527$			36.4716i			1.58873i
$528$		0			0
$529$		−	17.7643i		−	0.772361i
$530$		0			0
$531$	24.9568	+	8.19656i	1.08303	+	0.355700i
$532$		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
$537$	−0.344725	−	9.14339i	−0.0148760	−	0.394566i
$538$		0			0
$539$	−0.321017	−	0.775003i	−0.0138272	−	0.0333817i
$540$		0			0
$541$	−0.814609	−	0.337422i	−0.0350228	−	0.0145069i	0.365103	−	0.930967i	$-0.381034\pi$
$541$	−0.814609	−	0.337422i	−0.0350228	−	0.0145069i	−0.400126	+	0.916460i	$0.631034\pi$
$542$		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	0.455356	+	0.890310i	$0.349512\pi$
$547$	−11.6045	+	28.0158i	−0.496173	+	1.19787i	−0.951529	+	0.307559i	$0.900488\pi$
$548$		0			0
$549$	−12.0181	+	6.07560i	−0.512920	+	0.259300i
$550$		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
$555$	−4.35085	−	1.61296i	−0.184683	−	0.0684662i
$556$		0			0
$557$	−9.67547	−	4.00771i	−0.409963	−	0.169812i	0.168164	−	0.985759i	$-0.446216\pi$
$557$	−9.67547	−	4.00771i	−0.409963	−	0.169812i	−0.578127	+	0.815947i	$0.696216\pi$
$558$		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	−0.675758	−	0.737124i	$-0.736183\pi$
$563$	7.67115	−	18.5198i	0.323300	−	0.780516i	0.999058	−	0.0433923i	$-0.0138165\pi$
$564$		0			0
$565$	2.65846	−	1.10117i	0.111842	−	0.0463266i
$566$		0			0
$567$	−15.1792	+	20.6162i	−0.637467	+	0.865797i
$568$		0			0
$569$	−3.36174	−	3.36174i	−0.140932	−	0.140932i	0.633121	−	0.774053i	$-0.281773\pi$
$569$	−3.36174	−	3.36174i	−0.140932	−	0.140932i	−0.774053	+	0.633121i	$0.781773\pi$
$570$		0			0
$571$	14.6718	−	6.07726i	0.613996	−	0.254325i	−0.0539402	−	0.998544i	$-0.517178\pi$
$571$	14.6718	−	6.07726i	0.613996	−	0.254325i	0.667936	+	0.744219i	$0.267178\pi$
$572$		0			0
$573$	−17.0107	+	7.80935i	−0.710631	+	0.326240i
$574$		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
$579$	9.16691	−	4.20839i	0.380964	−	0.174895i
$580$		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
$585$	5.07579	+	4.36305i	0.209858	+	0.180390i
$586$		0			0
$587$	31.3098	−	12.9689i	1.29229	−	0.535286i	0.372625	−	0.927982i	$-0.378458\pi$
$587$	31.3098	−	12.9689i	1.29229	−	0.535286i	0.919668	+	0.392696i	$0.128458\pi$
$588$		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	$-0.641955\pi$
$593$	−21.0070			−0.862656			−0.431328	+	0.902195i	$0.641955\pi$
$594$		0			0
$595$	−6.82414	−	2.82665i	−0.279763	−	0.115881i
$596$		0			0
$597$	3.75562	+	1.39229i	0.153707	+	0.0569827i
$598$		0			0
$599$	4.73031	+	4.73031i	0.193275	+	0.193275i	0.797110	−	0.603835i	$-0.206361\pi$
$599$	4.73031	+	4.73031i	0.193275	+	0.193275i	−0.603835	+	0.797110i	$0.706361\pi$
$600$		0			0
$601$	22.8135	−	22.8135i	0.930581	−	0.930581i	−0.0671615	−	0.997742i	$-0.521394\pi$
$601$	22.8135	−	22.8135i	0.930581	−	0.930581i	0.997742	+	0.0671615i	$0.0213943\pi$
$602$		0			0
$603$	9.37907	+	18.5527i	0.381945	+	0.755523i
$604$		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	0.957638	−	0.287974i	$-0.0929818\pi$
$613$	1.90289	+	4.59399i	0.0768571	+	0.185550i	−0.880781	+	0.473524i	$0.842982\pi$
$614$		0			0
$615$	−0.208798	−	5.53808i	−0.00841953	−	0.223317i
$616$		0			0
$617$	−2.85391	+	2.85391i	−0.114894	+	0.114894i	−0.762216	−	0.647322i	$-0.775889\pi$
$617$	−2.85391	+	2.85391i	−0.114894	+	0.114894i	0.647322	+	0.762216i	$0.275889\pi$
$618$		0			0
$619$	12.0551	+	29.1035i	0.484534	+	1.16977i	0.957434	+	0.288652i	$0.0932070\pi$
$619$	12.0551	+	29.1035i	0.484534	+	1.16977i	−0.472901	+	0.881116i	$0.656793\pi$
$620$		0			0
$621$	−10.4012	+	5.76012i	−0.417385	+	0.231146i
$622$		0			0
$623$			24.6013i			0.985631i
$624$		0			0
$625$		−	22.5103i		−	0.900411i
$626$		0			0
$627$	0.846308	−	0.388528i	0.0337983	−	0.0155163i
$628$		0			0
$629$	15.8591	+	38.2873i	0.632345	+	1.52662i
$630$		0			0
$631$	27.3014	−	27.3014i	1.08685	−	1.08685i	0.0910003	−	0.995851i	$-0.470994\pi$
$631$	27.3014	−	27.3014i	1.08685	−	1.08685i	0.995851	−	0.0910003i	$-0.0290064\pi$
$632$		0			0
$633$	−25.1750	+	0.949152i	−1.00062	+	0.0377254i
$634$		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	0.571061	+	0.820908i	$0.306532\pi$
$643$	−10.4779	+	25.2960i	−0.413210	+	0.997576i	−0.984270	+	0.176669i	$0.943468\pi$
$644$		0			0
$645$	0.706954	+	0.262083i	0.0278363	+	0.0103195i
$646$		0			0
$647$	26.7097	−	26.7097i	1.05007	−	1.05007i	0.0513899	−	0.998679i	$-0.483635\pi$
$647$	26.7097	−	26.7097i	1.05007	−	1.05007i	0.998679	−	0.0513899i	$-0.0163651\pi$
$648$		0			0
$649$	−4.75718	−	4.75718i	−0.186735	−	0.186735i
$650$		0			0
$651$	−9.85567	+	26.5851i	−0.386274	+	1.04195i
$652$		0			0
$653$	−40.0093	−	16.5724i	−1.56569	−	0.648528i	−0.579620	−	0.814887i	$-0.696799\pi$
$653$	−40.0093	−	16.5724i	−1.56569	−	0.648528i	−0.986065	+	0.166358i	$0.946799\pi$
$654$		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	−0.751129	−	0.660155i	$-0.770491\pi$
$659$	6.33558	−	15.2955i	0.246799	−	0.595826i	0.997929	+	0.0643286i	$0.0204906\pi$
$660$		0			0
$661$	13.2351	−	5.48218i	0.514787	−	0.213232i	−0.110138	−	0.993916i	$-0.535129\pi$
$661$	13.2351	−	5.48218i	0.514787	−	0.213232i	0.624926	+	0.780684i	$0.285129\pi$
$662$		0			0
$663$	−2.25215	−	59.7354i	−0.0874663	−	2.31993i
$664$		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
$669$	0.0770531	+	0.167841i	0.00297905	+	0.00648909i
$670$		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
$675$	−12.1642	−	21.9652i	−0.468201	−	0.845441i
$676$		0			0
$677$	36.6561	−	15.1834i	1.40881	−	0.583547i	0.456785	−	0.889577i	$-0.349001\pi$
$677$	36.6561	−	15.1834i	1.40881	−	0.583547i	0.952022	+	0.306030i	$0.0990009\pi$
$678$		0			0
$679$	10.2422	+	10.2422i	0.393058	+	0.393058i
$680$		0			0
$681$	−39.4004	+	1.48548i	−1.50983	+	0.0569237i
$682$		0			0
$683$	24.0996	−	9.98236i	0.922144	−	0.381965i	0.129451	−	0.991586i	$-0.458678\pi$
$683$	24.0996	−	9.98236i	0.922144	−	0.381965i	0.792693	+	0.609621i	$0.208678\pi$
$684$		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	$-0.284079\pi$
$691$	13.6860	+	5.66894i	0.520641	+	0.215657i	−0.106857	+	0.994274i	$0.534079\pi$
$692$		0			0
$693$	5.85161	−	2.95821i	0.222284	−	0.112373i
$694$		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
$699$	3.81140	−	10.2810i	0.144160	−	0.388864i
$700$		0			0
$701$	15.2498	−	36.8163i	0.575977	−	1.39053i	−0.320419	−	0.947276i	$-0.603824\pi$
$701$	15.2498	−	36.8163i	0.575977	−	1.39053i	0.896396	−	0.443255i	$-0.146176\pi$
$702$		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	−0.977389	−	0.211449i	$-0.932182\pi$
$709$	−11.6037	−	28.0139i	−0.435788	−	1.05209i	0.541601	−	0.840636i	$-0.317818\pi$
$710$		0			0
$711$	17.1259	−	19.9236i	0.642272	−	0.747193i
$712$		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
$717$	6.27278	+	13.6637i	0.234261	+	0.510279i
$718$		0			0
$719$		−	44.6170i		−	1.66393i	−0.554826	−	0.831967i	$-0.687215\pi$
$719$		−	44.6170i		−	1.66393i	0.554826	−	0.831967i	$-0.312785\pi$
$720$		0			0
$721$		−	24.7573i		−	0.922008i
$722$		0			0
$723$	−3.29277	−	7.17247i	−0.122460	−	0.266747i
$724$		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	$-0.883321\pi$
$727$	−15.5081	+	15.5081i	−0.575162	+	0.575162i	0.358405	+	0.933566i	$0.383321\pi$
$728$		0			0
$729$	−22.8860	−	14.3258i	−0.847631	−	0.530587i
$730$		0			0
$731$	−2.57689	−	6.22117i	−0.0953098	−	0.230098i
$732$		0			0
$733$	−43.3401	−	17.9520i	−1.60080	−	0.663074i	−0.609273	−	0.792961i	$-0.708538\pi$
$733$	−43.3401	−	17.9520i	−1.60080	−	0.663074i	−0.991529	+	0.129887i	$0.958538\pi$
$734$		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	−0.130686	−	0.991424i	$-0.541718\pi$
$739$	18.0170	−	43.4968i	0.662765	−	1.60006i	0.793452	−	0.608633i	$-0.208282\pi$
$740$		0			0
$741$	2.29421	−	6.18849i	0.0842799	−	0.227340i
$742$		0			0
$743$	−3.20365	+	3.20365i	−0.117530	+	0.117530i	−0.763426	−	0.645895i	$-0.776484\pi$
$743$	−3.20365	+	3.20365i	−0.117530	+	0.117530i	0.645895	+	0.763426i	$0.276484\pi$
$744$		0			0
$745$	−5.72193	−	5.72193i	−0.209635	−	0.209635i
$746$		0			0
$747$	−23.3535	−	46.1954i	−0.854459	−	1.69020i
$748$		0			0
$749$	−3.39260	−	1.40526i	−0.123963	−	0.0513471i
$750$		0			0
$751$	53.3838			1.94800			0.974001	−	0.226542i	$-0.0727419\pi$
$751$	53.3838			1.94800			0.974001	+	0.226542i	$0.0727419\pi$
$752$		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	0.512941	−	0.858424i	$-0.328556\pi$
$757$	40.7929	−	16.8970i	1.48264	−	0.614130i	0.969701	+	0.244294i	$0.0785560\pi$
$758$		0			0
$759$	3.04293	−	0.114725i	0.110451	−	0.00416425i
$760$		0			0
$761$	2.82203	+	2.82203i	0.102299	+	0.102299i	0.756404	−	0.654105i	$-0.226955\pi$
$761$	2.82203	+	2.82203i	0.102299	+	0.102299i	−0.654105	+	0.756404i	$0.726955\pi$
$762$		0			0
$763$	−6.41304	+	2.65637i	−0.232168	+	0.0961670i
$764$		0			0
$765$	2.43069	−	7.40097i	0.0878819	−	0.267582i
$766$		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
$771$	9.69264	+	21.1130i	0.349072	+	0.760365i
$772$		0			0
$773$	−17.4059	+	7.20975i	−0.626046	+	0.259317i	−0.673072	−	0.739577i	$-0.735026\pi$
$773$	−17.4059	+	7.20975i	−0.626046	+	0.259317i	0.0470263	+	0.998894i	$0.485026\pi$
$774$		0			0
$775$	−19.6627	−	19.6627i	−0.706305	−	0.706305i
$776$		0			0
$777$	1.21379	+	32.1942i	0.0435444	+	1.15496i
$778$		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	$-0.202823\pi$
$787$	26.6913	+	11.0559i	0.951441	+	0.394100i	0.147669	+	0.989037i	$0.452823\pi$
$788$		0			0
$789$	15.9244	−	42.9552i	0.566925	−	1.52925i
$790$		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
$795$	−1.17289	−	0.434815i	−0.0415980	−	0.0154213i
$796$		0			0
$797$	18.1728	−	43.8730i	0.643714	−	1.55406i	−0.177919	−	0.984045i	$-0.556936\pi$
$797$	18.1728	−	43.8730i	0.643714	−	1.55406i	0.821633	−	0.570017i	$-0.193064\pi$
$798$		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
$807$	−11.6177	+	0.438013i	−0.408963	+	0.0154188i
$808$		0			0
$809$	10.4387	−	10.4387i	0.367006	−	0.367006i	−0.499378	−	0.866384i	$-0.666438\pi$
$809$	10.4387	−	10.4387i	0.367006	−	0.367006i	0.866384	+	0.499378i	$0.166438\pi$
$810$		0			0
$811$	−5.74617	−	13.8725i	−0.201775	−	0.487129i	0.790308	−	0.612710i	$-0.209921\pi$
$811$	−5.74617	−	13.8725i	−0.201775	−	0.487129i	−0.992083	+	0.125581i	$0.959921\pi$
$812$		0			0
$813$	41.5571	−	19.0782i	1.45747	−	0.669103i
$814$		0			0
$815$		−	0.992553i		−	0.0347676i
$816$		0			0
$817$		−	0.743472i		−	0.0260108i
$818$		0			0
$819$	14.5005	−	44.1512i	0.506690	−	1.54277i
$820$		0			0
$821$	1.81831	+	4.38979i	0.0634594	+	0.153205i	0.952428	−	0.304763i	$-0.0985774\pi$
$821$	1.81831	+	4.38979i	0.0634594	+	0.153205i	−0.888969	+	0.457968i	$0.848577\pi$
$822$		0			0
$823$	−6.63123	+	6.63123i	−0.231150	+	0.231150i	−0.813173	−	0.582023i	$-0.802262\pi$
$823$	−6.63123	+	6.63123i	−0.231150	+	0.231150i	0.582023	+	0.813173i	$0.302262\pi$
$824$		0			0
$825$	0.242276	+	6.42605i	0.00843496	+	0.223726i
$826$		0			0
$827$	4.53700	+	10.9533i	0.157767	+	0.380883i	0.982922	−	0.184023i	$-0.0589122\pi$
$827$	4.53700	+	10.9533i	0.157767	+	0.380883i	−0.825155	+	0.564907i	$0.808912\pi$
$828$		0			0
$829$	23.9460	+	9.91877i	0.831680	+	0.344493i	0.757568	−	0.652757i	$-0.226388\pi$
$829$	23.9460	+	9.91877i	0.831680	+	0.344493i	0.0741124	+	0.997250i	$0.476388\pi$
$830$		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
$837$	−28.7404	−	8.25342i	−0.993414	−	0.285280i
$838$		0			0
$839$	20.4190	−	20.4190i	0.704940	−	0.704940i	−0.260526	−	0.965467i	$-0.583896\pi$
$839$	20.4190	−	20.4190i	0.704940	−	0.704940i	0.965467	+	0.260526i	$0.0838961\pi$
$840$		0			0
$841$	0.299407	+	0.299407i	0.0103244	+	0.0103244i
$842$		0			0
$843$	25.0420	+	9.28361i	0.862491	+	0.319744i
$844$		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	−0.0962340	−	0.995359i	$-0.530680\pi$
$853$	15.7580	−	6.52717i	0.539543	−	0.223486i	0.635777	+	0.771873i	$0.280680\pi$
$854$		0			0
$855$	0.560650	−	0.652237i	0.0191738	−	0.0223060i
$856$		0			0
$857$	−33.0421	−	33.0421i	−1.12870	−	1.12870i	−0.990389	−	0.138307i	$-0.955834\pi$
$857$	−33.0421	−	33.0421i	−1.12870	−	1.12870i	−0.138307	−	0.990389i	$-0.544166\pi$
$858$		0			0
$859$	29.6597	−	12.2854i	1.01198	−	0.419174i	0.185801	−	0.982587i	$-0.440512\pi$
$859$	29.6597	−	12.2854i	1.01198	−	0.419174i	0.826175	+	0.563413i	$0.190512\pi$
$860$		0			0
$861$	−34.9693	+	16.0539i	−1.19175	+	0.547115i
$862$		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
$867$	−36.4677	+	16.7418i	−1.23851	+	0.568581i
$868$		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
$873$	−9.95766	+	11.5843i	−0.337016	+	0.392070i
$874$		0			0
$875$	10.5867	−	4.38514i	0.357895	−	0.148245i
$876$		0			0
$877$	−17.7546	+	42.8634i	−0.599531	+	1.44740i	0.274529	+	0.961579i	$0.411478\pi$
$877$	−17.7546	+	42.8634i	−0.599531	+	1.44740i	−0.874060	+	0.485817i	$0.838522\pi$
$878$		0			0
$879$	−25.5802	+	27.5846i	−0.862799	+	0.930407i
$880$		0			0
$881$	−30.9787			−1.04370			−0.521850	−	0.853038i	$-0.674758\pi$
$881$	−30.9787			−1.04370			−0.521850	+	0.853038i	$0.674758\pi$
$882$		0			0
$883$	−27.3679	−	11.3361i	−0.921002	−	0.381492i	−0.128744	−	0.991678i	$-0.541095\pi$
$883$	−27.3679	−	11.3361i	−0.921002	−	0.381492i	−0.792258	+	0.610186i	$0.791095\pi$
$884$		0			0
$885$	−5.82617	−	2.15989i	−0.195845	−	0.0726039i
$886$		0			0
$887$	2.37216	+	2.37216i	0.0796492	+	0.0796492i	0.745809	−	0.666160i	$-0.232063\pi$
$887$	2.37216	+	2.37216i	0.0796492	+	0.0796492i	−0.666160	+	0.745809i	$0.732063\pi$
$888$		0			0
$889$	−10.3047	+	10.3047i	−0.345610	+	0.345610i
$890$		0			0
$891$	3.57563	+	5.91884i	0.119788	+	0.198289i
$892$		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
$903$	−0.197224	−	5.23111i	−0.00656321	−	0.174080i
$904$		0			0
$905$	−2.52850	+	2.52850i	−0.0840503	+	0.0840503i
$906$		0			0
$907$	−13.3336	−	32.1901i	−0.442734	−	1.06885i	−0.974986	−	0.222268i	$-0.928654\pi$
$907$	−13.3336	−	32.1901i	−0.442734	−	1.06885i	0.532252	−	0.846586i	$-0.321346\pi$
$908$		0			0
$909$	2.36748	−	7.20850i	0.0785245	−	0.239091i
$910$		0			0
$911$			11.2111i			0.371441i	0.982603	+	0.185721i	$0.0594620\pi$
$911$			11.2111i			0.371441i	−0.982603	+	0.185721i	$0.940538\pi$
$912$		0			0
$913$			13.2571i			0.438747i
$914$		0			0
$915$	2.89494	−	1.32903i	0.0957039	−	0.0439362i
$916$		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	$-0.676102\pi$
$919$	9.86384	−	9.86384i	0.325378	−	0.325378i	0.850826	+	0.525448i	$0.176102\pi$
$920$		0			0
$921$	−1.02792	+	0.0387546i	−0.0338710	+	0.00127701i
$922$		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
$933$	19.1069	+	7.08335i	0.625532	+	0.231899i
$934$		0			0
$935$	−1.41074	+	1.41074i	−0.0461362	+	0.0461362i
$936$		0			0
$937$	32.9019	+	32.9019i	1.07486	+	1.07486i	0.996961	+	0.0778973i	$0.0248206\pi$
$937$	32.9019	+	32.9019i	1.07486	+	1.07486i	0.0778973	+	0.996961i	$0.475179\pi$
$938$		0			0
$939$	−5.02564	+	13.5564i	−0.164006	+	0.442395i
$940$		0			0
$941$	1.67400	+	0.693394i	0.0545709	+	0.0226040i	0.409802	−	0.912175i	$-0.365598\pi$
$941$	1.67400	+	0.693394i	0.0545709	+	0.0226040i	−0.355231	+	0.934779i	$0.615598\pi$
$942$		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	−0.989831	−	0.142251i	$-0.954566\pi$
$947$	−5.82625	+	14.0658i	−0.189328	+	0.457078i	0.800503	+	0.599329i	$0.204566\pi$
$948$		0			0
$949$	−67.5150	+	27.9656i	−2.19163	+	0.907802i
$950$		0			0
$951$	−0.0738178	−	1.95792i	−0.00239371	−	0.0634899i
$952$		0			0
$953$	30.1975	+	30.1975i	0.978193	+	0.978193i	0.999767	−	0.0215739i	$-0.00686771\pi$
$953$	30.1975	+	30.1975i	0.978193	+	0.978193i	−0.0215739	+	0.999767i	$0.506868\pi$
$954$		0			0
$955$	4.09053	−	1.69435i	0.132366	−	0.0548279i
$956$		0			0
$957$	−2.96813	−	6.46531i	−0.0959459	−	0.208994i
$958$		0			0
$959$	20.8864			0.674458
$960$		0			0
$961$	−2.11594			−0.0682560
$962$		0			0
$963$	1.20841	−	3.67936i	0.0389405	−	0.118566i
$964$		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	$-0.101685\pi$
$967$	19.7575	+	19.7575i	0.635360	+	0.635360i	−0.314047	+	0.949407i	$0.601685\pi$
$968$		0			0
$969$	−7.67598	+	0.289401i	−0.246588	+	0.00929689i
$970$		0			0
$971$	12.7822	−	5.29454i	0.410199	−	0.169910i	−0.168035	−	0.985781i	$-0.553742\pi$
$971$	12.7822	−	5.29454i	0.410199	−	0.169910i	0.578234	+	0.815871i	$0.303742\pi$
$972$		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	$-0.287912\pi$
$977$	38.6385			1.23615			0.618077	+	0.786117i	$0.287912\pi$
$978$		0			0
$979$	6.13909	+	2.54289i	0.196206	+	0.0812713i
$980$		0			0
$981$	−3.30279	−	6.53323i	−0.105450	−	0.208590i
$982$		0			0
$983$	20.6692	+	20.6692i	0.659244	+	0.659244i	0.955201	−	0.295957i	$-0.0956386\pi$
$983$	20.6692	+	20.6692i	0.659244	+	0.659244i	−0.295957	+	0.955201i	$0.595639\pi$
$984$		0			0
$985$	−6.10069	+	6.10069i	−0.194384	+	0.194384i
$986$		0			0
$987$	−17.9530	+	48.4271i	−0.571450	+	1.54145i
$988$		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	0.996132	+	0.0878737i	$0.0280072\pi$
$997$	11.1744	+	26.9773i	0.353896	+	0.854381i	−0.642235	+	0.766507i	$0.721993\pi$
$998$		0			0
$999$	−33.7601	+	3.83302i	−1.06812	+	0.121271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.95.3		56
3.2	odd	2	inner	768.2.o.a.95.9		56
4.3	odd	2		768.2.o.b.95.12		56
8.3	odd	2		96.2.o.a.35.11	yes	56
8.5	even	2		384.2.o.a.47.12		56
12.11	even	2		768.2.o.b.95.6		56
24.5	odd	2		384.2.o.a.47.6		56
24.11	even	2		96.2.o.a.35.4	yes	56
32.5	even	8		96.2.o.a.11.4	✓	56
32.11	odd	8	inner	768.2.o.a.671.9		56
32.21	even	8		768.2.o.b.671.6		56
32.27	odd	8		384.2.o.a.335.6		56
96.5	odd	8		96.2.o.a.11.11	yes	56
96.11	even	8	inner	768.2.o.a.671.3		56
96.53	odd	8		768.2.o.b.671.12		56
96.59	even	8		384.2.o.a.335.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.4	✓	56	32.5	even	8
96.2.o.a.11.11	yes	56	96.5	odd	8
96.2.o.a.35.4	yes	56	24.11	even	2
96.2.o.a.35.11	yes	56	8.3	odd	2
384.2.o.a.47.6		56	24.5	odd	2
384.2.o.a.47.12		56	8.5	even	2
384.2.o.a.335.6		56	32.27	odd	8
384.2.o.a.335.12		56	96.59	even	8
768.2.o.a.95.3		56	1.1	even	1	trivial
768.2.o.a.95.9		56	3.2	odd	2	inner
768.2.o.a.671.3		56	96.11	even	8	inner
768.2.o.a.671.9		56	32.11	odd	8	inner
768.2.o.b.95.6		56	12.11	even	2
768.2.o.b.95.12		56	4.3	odd	2
768.2.o.b.671.6		56	32.21	even	8
768.2.o.b.671.12		56	96.53	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.57410 + 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(-2.01144 - 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +O(q^{10})\)	\(q+(-1.57410 + 0.722645i) q^{3} +(0.378520 - 0.156788i) q^{5} +(-2.01144 - 2.01144i) q^{7} +(1.95557 - 2.27503i) q^{9} +(-0.709852 + 0.294030i) q^{11} +(-2.08393 + 5.03104i) q^{13} +(-0.482526 + 0.520336i) q^{15} +6.33777 q^{17} +(0.646487 + 0.267784i) q^{19} +(4.61976 + 1.71265i) q^{21} +(1.61798 + 1.61798i) q^{23} +(-3.41684 + 3.41684i) q^{25} +(-1.43422 + 4.99430i) q^{27} +(2.04571 - 4.93879i) q^{29} +5.75464i q^{31} +(0.904897 - 0.975803i) q^{33} +(-1.07674 - 0.446001i) q^{35} +(2.50232 + 6.04113i) q^{37} +(-0.355354 - 9.42529i) q^{39} +(-5.52228 + 5.52228i) q^{41} +(-0.406593 - 0.981601i) q^{43} +(0.383525 - 1.16775i) q^{45} +10.4826i q^{47} +1.09178i q^{49} +(-9.97628 + 4.57996i) q^{51} +(0.674566 + 1.62855i) q^{53} +(-0.222593 + 0.222593i) q^{55} +(-1.21115 + 0.0456628i) q^{57} +(3.35082 + 8.08960i) q^{59} +(-4.14715 - 1.71781i) q^{61} +(-8.50959 + 0.642573i) q^{63} +2.23109i q^{65} +(-2.65183 + 6.40208i) q^{67} +(-3.71607 - 1.37763i) q^{69} +(-1.97014 + 1.97014i) q^{71} +(9.48914 + 9.48914i) q^{73} +(2.90928 - 7.84760i) q^{75} +(2.01925 + 0.836400i) q^{77} +8.75751 q^{79} +(-1.35150 - 8.89795i) q^{81} +(6.60293 - 15.9409i) q^{83} +(2.39898 - 0.993689i) q^{85} +(0.348838 + 9.25246i) q^{87} +(-6.11535 - 6.11535i) q^{89} +(14.3113 - 5.92795i) q^{91} +(-4.15856 - 9.05837i) q^{93} +0.286694 q^{95} -5.09195 q^{97} +(-0.719237 + 2.18993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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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