LMFDB - Embedded newform 816.2.bq.f.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(49,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))

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

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

chi := DirichletCharacter("816.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bq (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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 466x^{12} + 2956x^{10} + 10049x^{8} + 18032x^{6} + 14800x^{4} + 3200x^{2} + 64 $ x^16 + 36x^14 + 466x^12 + 2956x^10 + 10049x^8 + 18032x^6 + 14800x^4 + 3200*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.2
Root			$-4.11290i$ of defining polynomial
Character	$\chi$	$=$	816.145
Dual form			816.2.bq.f.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{3} +(1.19125 - 2.87594i) q^{5} +(0.497533 + 1.20115i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{3} +(1.19125 - 2.87594i) q^{5} +(0.497533 + 1.20115i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.951637 - 0.394181i) q^{11} -6.68521i q^{13} +(-2.20115 + 2.20115i) q^{15} +(0.866078 + 4.03112i) q^{17} +(0.0370155 - 0.0370155i) q^{19} -1.30012i q^{21} +(2.25820 - 0.935377i) q^{23} +(-3.31643 - 3.31643i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(0.444609 - 1.07338i) q^{29} +(-6.92831 - 2.86980i) q^{31} -1.03004 q^{33} +4.04713 q^{35} +(3.94211 + 1.63287i) q^{37} +(-2.55832 + 6.17632i) q^{39} +(-0.992710 - 2.39661i) q^{41} +(-8.25427 - 8.25427i) q^{43} +(2.87594 - 1.19125i) q^{45} -7.75431i q^{47} +(3.75452 - 3.75452i) q^{49} +(0.742490 - 4.05570i) q^{51} +(-6.10592 + 6.10592i) q^{53} -3.20642i q^{55} +(-0.0483631 + 0.0200326i) q^{57} +(5.46426 + 5.46426i) q^{59} +(-2.67733 - 6.46364i) q^{61} +(-0.497533 + 1.20115i) q^{63} +(-19.2263 - 7.96378i) q^{65} +0.660863 q^{67} -2.44426 q^{69} +(-6.88351 - 2.85124i) q^{71} +(0.530414 - 1.28053i) q^{73} +(1.79484 + 4.33312i) q^{75} +(0.946942 + 0.946942i) q^{77} +(15.4018 - 6.37962i) q^{79} +1.00000i q^{81} +(4.99100 - 4.99100i) q^{83} +(12.6250 + 2.31130i) q^{85} +(-0.821530 + 0.821530i) q^{87} +18.5036i q^{89} +(8.02995 - 3.32611i) q^{91} +(5.30270 + 5.30270i) q^{93} +(-0.0623596 - 0.150549i) q^{95} +(2.87551 - 6.94209i) q^{97} +(0.951637 + 0.394181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{11} - 8 q^{15} + 8 q^{19} + 8 q^{23} - 8 q^{25} + 32 q^{29} - 8 q^{31} - 8 q^{33} - 16 q^{35} + 8 q^{37} + 8 q^{39} + 40 q^{41} + 24 q^{43} + 8 q^{45} + 24 q^{49} - 8 q^{51} - 24 q^{53} - 8 q^{57} + 16 q^{59} - 64 q^{65} - 8 q^{69} + 16 q^{71} + 24 q^{73} + 96 q^{79} - 32 q^{85} - 16 q^{87} + 24 q^{93} + 8 q^{95} + 56 q^{97} + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 - 8 * q^15 + 8 * q^19 + 8 * q^23 - 8 * q^25 + 32 * q^29 - 8 * q^31 - 8 * q^33 - 16 * q^35 + 8 * q^37 + 8 * q^39 + 40 * q^41 + 24 * q^43 + 8 * q^45 + 24 * q^49 - 8 * q^51 - 24 * q^53 - 8 * q^57 + 16 * q^59 - 64 * q^65 - 8 * q^69 + 16 * q^71 + 24 * q^73 + 96 * q^79 - 32 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 56 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$		0			0
$5$	1.19125	−	2.87594i	0.532745	−	1.28616i	−0.396953	−	0.917839i	$-0.629932\pi$
$5$	1.19125	−	2.87594i	0.532745	−	1.28616i	0.929698	−	0.368322i	$-0.120068\pi$
$6$		0			0
$7$	0.497533	+	1.20115i	0.188050	+	0.453993i	0.989584	−	0.143956i	$-0.0459825\pi$
$7$	0.497533	+	1.20115i	0.188050	+	0.453993i	−0.801534	+	0.597949i	$0.795982\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	0.951637	−	0.394181i	0.286929	−	0.118850i	−0.234577	−	0.972098i	$-0.575370\pi$
$11$	0.951637	−	0.394181i	0.286929	−	0.118850i	0.521506	+	0.853248i	$0.325370\pi$
$12$		0			0
$13$		−	6.68521i		−	1.85414i	−0.374885	−	0.927071i	$-0.622318\pi$
$13$		−	6.68521i		−	1.85414i	0.374885	−	0.927071i	$-0.377682\pi$
$14$		0			0
$15$	−2.20115	+	2.20115i	−0.568335	+	0.568335i
$16$		0			0
$17$	0.866078	+	4.03112i	0.210055	+	0.977690i
$17$	0.866078	+	4.03112i	0.210055	+	0.977690i
$18$		0			0
$19$	0.0370155	−	0.0370155i	0.00849193	−	0.00849193i	−0.702848	−	0.711340i	$-0.748089\pi$
$19$	0.0370155	−	0.0370155i	0.00849193	−	0.00849193i	0.711340	+	0.702848i	$0.248089\pi$
$20$		0			0
$21$		−	1.30012i		−	0.283709i
$22$		0			0
$23$	2.25820	−	0.935377i	0.470867	−	0.195040i	−0.134616	−	0.990898i	$-0.542980\pi$
$23$	2.25820	−	0.935377i	0.470867	−	0.195040i	0.605483	+	0.795858i	$0.292980\pi$
$24$		0			0
$25$	−3.31643	−	3.31643i	−0.663286	−	0.663286i
$26$		0			0
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$		0			0
$29$	0.444609	−	1.07338i	0.0825618	−	0.199322i	−0.877208	−	0.480111i	$-0.840596\pi$
$29$	0.444609	−	1.07338i	0.0825618	−	0.199322i	0.959769	+	0.280790i	$0.0905963\pi$
$30$		0			0
$31$	−6.92831	−	2.86980i	−1.24436	−	0.515431i	−0.339286	−	0.940683i	$-0.610185\pi$
$31$	−6.92831	−	2.86980i	−1.24436	−	0.515431i	−0.905075	+	0.425252i	$0.860185\pi$
$32$		0			0
$33$	−1.03004			−0.179308
$34$		0			0
$35$	4.04713			0.684090
$36$		0			0
$37$	3.94211	+	1.63287i	0.648078	+	0.268443i	0.682412	−	0.730968i	$-0.260931\pi$
$37$	3.94211	+	1.63287i	0.648078	+	0.268443i	−0.0343338	+	0.999410i	$0.510931\pi$
$38$		0			0
$39$	−2.55832	+	6.17632i	−0.409659	+	0.989003i
$40$		0			0
$41$	−0.992710	−	2.39661i	−0.155035	−	0.374288i	0.827209	−	0.561894i	$-0.189927\pi$
$41$	−0.992710	−	2.39661i	−0.155035	−	0.374288i	−0.982244	+	0.187606i	$0.939927\pi$
$42$		0			0
$43$	−8.25427	−	8.25427i	−1.25876	−	1.25876i	−0.951684	−	0.307080i	$-0.900648\pi$
$43$	−8.25427	−	8.25427i	−1.25876	−	1.25876i	−0.307080	−	0.951684i	$-0.599352\pi$
$44$		0			0
$45$	2.87594	−	1.19125i	0.428720	−	0.177582i
$46$		0			0
$47$		−	7.75431i		−	1.13108i	−0.824720	−	0.565541i	$-0.808667\pi$
$47$		−	7.75431i		−	1.13108i	0.824720	−	0.565541i	$-0.191333\pi$
$48$		0			0
$49$	3.75452	−	3.75452i	0.536360	−	0.536360i
$50$		0			0
$51$	0.742490	−	4.05570i	0.103969	−	0.567912i
$52$		0			0
$53$	−6.10592	+	6.10592i	−0.838713	+	0.838713i	−0.988690	−	0.149977i	$-0.952080\pi$
$53$	−6.10592	+	6.10592i	−0.838713	+	0.838713i	0.149977	+	0.988690i	$0.452080\pi$
$54$		0			0
$55$		−	3.20642i		−	0.432354i
$56$		0			0
$57$	−0.0483631	+	0.0200326i	−0.00640584	+	0.00265339i
$58$		0			0
$59$	5.46426	+	5.46426i	0.711386	+	0.711386i	0.966825	−	0.255439i	$-0.0822201\pi$
$59$	5.46426	+	5.46426i	0.711386	+	0.711386i	−0.255439	+	0.966825i	$0.582220\pi$
$60$		0			0
$61$	−2.67733	−	6.46364i	−0.342797	−	0.827585i	−0.997431	−	0.0716386i	$-0.977177\pi$
$61$	−2.67733	−	6.46364i	−0.342797	−	0.827585i	0.654634	−	0.755946i	$-0.272823\pi$
$62$		0			0
$63$	−0.497533	+	1.20115i	−0.0626833	+	0.151331i
$64$		0			0
$65$	−19.2263	−	7.96378i	−2.38473	−	0.987786i
$66$		0			0
$67$	0.660863			0.0807373			0.0403687	−	0.999185i	$-0.487147\pi$
$67$	0.660863			0.0807373			0.0403687	+	0.999185i	$0.487147\pi$
$68$		0			0
$69$	−2.44426			−0.294254
$70$		0			0
$71$	−6.88351	−	2.85124i	−0.816923	−	0.338380i	−0.0652104	−	0.997872i	$-0.520772\pi$
$71$	−6.88351	−	2.85124i	−0.816923	−	0.338380i	−0.751712	+	0.659491i	$0.770772\pi$
$72$		0			0
$73$	0.530414	−	1.28053i	0.0620802	−	0.149875i	−0.889795	−	0.456360i	$-0.849153\pi$
$73$	0.530414	−	1.28053i	0.0620802	−	0.149875i	0.951875	+	0.306485i	$0.0991529\pi$
$74$		0			0
$75$	1.79484	+	4.33312i	0.207250	+	0.500346i
$76$		0			0
$77$	0.946942	+	0.946942i	0.107914	+	0.107914i
$78$		0			0
$79$	15.4018	−	6.37962i	1.73284	−	0.717764i	0.733563	−	0.679622i	$-0.237856\pi$
$79$	15.4018	−	6.37962i	1.73284	−	0.717764i	0.999272	−	0.0381421i	$-0.0121440\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	4.99100	−	4.99100i	0.547833	−	0.547833i	−0.377980	−	0.925814i	$-0.623381\pi$
$83$	4.99100	−	4.99100i	0.547833	−	0.547833i	0.925814	+	0.377980i	$0.123381\pi$
$84$		0			0
$85$	12.6250	+	2.31130i	1.36937	+	0.250695i
$86$		0			0
$87$	−0.821530	+	0.821530i	−0.0880772	+	0.0880772i
$88$		0			0
$89$			18.5036i			1.96138i	0.195579	+	0.980688i	$0.437341\pi$
$89$			18.5036i			1.96138i	−0.195579	+	0.980688i	$0.562659\pi$
$90$		0			0
$91$	8.02995	−	3.32611i	0.841767	−	0.348671i
$92$		0			0
$93$	5.30270	+	5.30270i	0.549864	+	0.549864i
$94$		0			0
$95$	−0.0623596	−	0.150549i	−0.00639796	−	0.0154460i
$96$		0			0
$97$	2.87551	−	6.94209i	0.291964	−	0.704862i	−0.708036	−	0.706177i	$-0.750418\pi$
$97$	2.87551	−	6.94209i	0.291964	−	0.704862i	0.999999	+	0.00131446i	$0.000418406\pi$
$98$		0			0
$99$	0.951637	+	0.394181i	0.0956431	+	0.0396167i
$100$		0			0
$101$	9.34462			0.929825			0.464912	−	0.885357i	$-0.346086\pi$
$101$	9.34462			0.929825			0.464912	+	0.885357i	$0.346086\pi$
$102$		0			0
$103$	5.52226			0.544125			0.272062	−	0.962280i	$-0.412294\pi$
$103$	5.52226			0.544125			0.272062	+	0.962280i	$0.412294\pi$
$104$		0			0
$105$	−3.73906	−	1.54877i	−0.364895	−	0.151145i
$106$		0			0
$107$	2.19624	−	5.30219i	0.212318	−	0.512582i	−0.781460	−	0.623955i	$-0.785525\pi$
$107$	2.19624	−	5.30219i	0.212318	−	0.512582i	0.993779	+	0.111373i	$0.0355248\pi$
$108$		0			0
$109$	1.30453	+	3.14942i	0.124952	+	0.301660i	0.973960	−	0.226719i	$-0.0728000\pi$
$109$	1.30453	+	3.14942i	0.124952	+	0.301660i	−0.849009	+	0.528379i	$0.822800\pi$
$110$		0			0
$111$	−3.01716	−	3.01716i	−0.286376	−	0.286376i
$112$		0			0
$113$	−13.4849	+	5.58561i	−1.26855	+	0.525450i	−0.912523	−	0.409026i	$-0.865868\pi$
$113$	−13.4849	+	5.58561i	−1.26855	+	0.525450i	−0.356026	+	0.934476i	$0.615868\pi$
$114$		0			0
$115$		−	7.60873i		−	0.709517i
$116$		0			0
$117$	4.72715	−	4.72715i	0.437026	−	0.437026i
$118$		0			0
$119$	−4.41108	+	3.04591i	−0.404363	+	0.279218i
$120$		0			0
$121$	−7.02794	+	7.02794i	−0.638904	+	0.638904i
$122$		0			0
$123$			2.59407i			0.233900i
$124$		0			0
$125$	0.891145	−	0.369124i	0.0797064	−	0.0330155i
$126$		0			0
$127$	13.5710	+	13.5710i	1.20423	+	1.20423i	0.972867	+	0.231364i	$0.0743187\pi$
$127$	13.5710	+	13.5710i	1.20423	+	1.20423i	0.231364	+	0.972867i	$0.425681\pi$
$128$		0			0
$129$	4.46718	+	10.7847i	0.393313	+	0.949542i
$130$		0			0
$131$	−7.39702	+	17.8580i	−0.646281	+	1.56026i	0.171785	+	0.985134i	$0.445047\pi$
$131$	−7.39702	+	17.8580i	−0.646281	+	1.56026i	−0.818066	+	0.575125i	$0.804953\pi$
$132$		0			0
$133$	0.0628777	+	0.0260448i	0.00545218	+	0.00225837i
$134$		0			0
$135$	−3.11290			−0.267916
$136$		0			0
$137$	−0.386209			−0.0329961			−0.0164980	−	0.999864i	$-0.505252\pi$
$137$	−0.386209			−0.0329961			−0.0164980	+	0.999864i	$0.505252\pi$
$138$		0			0
$139$	−13.5179	−	5.59930i	−1.14657	−	0.474926i	−0.273190	−	0.961960i	$-0.588079\pi$
$139$	−13.5179	−	5.59930i	−1.14657	−	0.474926i	−0.873383	+	0.487034i	$0.838079\pi$
$140$		0			0
$141$	−2.96745	+	7.16405i	−0.249904	+	0.603322i
$142$		0			0
$143$	−2.63518	−	6.36189i	−0.220365	−	0.532008i
$144$		0			0
$145$	−2.55734	−	2.55734i	−0.212375	−	0.212375i
$146$		0			0
$147$	−4.90552	+	2.03193i	−0.404600	+	0.167591i
$148$		0			0
$149$			14.8965i			1.22037i	0.792260	+	0.610184i	$0.208905\pi$
$149$			14.8965i			1.22037i	−0.792260	+	0.610184i	$0.791095\pi$
$150$		0			0
$151$	−11.6525	+	11.6525i	−0.948266	+	0.948266i	−0.998726	−	0.0504602i	$-0.983931\pi$
$151$	−11.6525	+	11.6525i	−0.948266	+	0.948266i	0.0504602	+	0.998726i	$0.483931\pi$
$152$		0			0
$153$	−2.23802	+	3.46284i	−0.180933	+	0.279954i
$154$		0			0
$155$	−16.5068	+	16.5068i	−1.32585	+	1.32585i
$156$		0			0
$157$			2.21102i			0.176459i	0.996100	+	0.0882294i	$0.0281208\pi$
$157$			2.21102i			0.176459i	−0.996100	+	0.0882294i	$0.971879\pi$
$158$		0			0
$159$	7.97777	−	3.30450i	0.632678	−	0.262064i
$160$		0			0
$161$	2.24706	+	2.24706i	0.177093	+	0.177093i
$162$		0			0
$163$	0.440482	+	1.06342i	0.0345012	+	0.0832933i	0.940191	−	0.340648i	$-0.110646\pi$
$163$	0.440482	+	1.06342i	0.0345012	+	0.0832933i	−0.905690	+	0.423941i	$0.860646\pi$
$164$		0			0
$165$	−1.22705	+	2.96235i	−0.0955253	+	0.230619i
$166$		0			0
$167$	13.2193	+	5.47562i	1.02294	+	0.423716i	0.830160	−	0.557525i	$-0.188249\pi$
$167$	13.2193	+	5.47562i	1.02294	+	0.423716i	0.192782	+	0.981242i	$0.438249\pi$
$168$		0			0
$169$	−31.6920			−2.43784
$170$		0			0
$171$	0.0523478			0.00400314
$172$		0			0
$173$	11.3238	+	4.69047i	0.860933	+	0.356610i	0.769072	−	0.639162i	$-0.220719\pi$
$173$	11.3238	+	4.69047i	0.860933	+	0.356610i	0.0918605	+	0.995772i	$0.470719\pi$
$174$		0			0
$175$	2.33350	−	5.63357i	0.176396	−	0.425858i
$176$		0			0
$177$	−2.95724	−	7.13940i	−0.222279	−	0.536630i
$178$		0			0
$179$	13.4350	+	13.4350i	1.00418	+	1.00418i	0.999991	+	0.00418615i	$0.00133250\pi$
$179$	13.4350	+	13.4350i	1.00418	+	1.00418i	0.00418615	+	0.999991i	$0.498668\pi$
$180$		0			0
$181$	22.7466	−	9.42196i	1.69074	−	0.700329i	0.690998	−	0.722857i	$-0.257171\pi$
$181$	22.7466	−	9.42196i	1.69074	−	0.700329i	0.999746	+	0.0225276i	$0.00717138\pi$
$182$		0			0
$183$			6.99620i			0.517174i
$184$		0			0
$185$	9.39211	−	9.39211i	0.690521	−	0.690521i
$186$		0			0
$187$	2.41318	+	3.49477i	0.176469	+	0.255563i
$188$		0			0
$189$	0.919322	−	0.919322i	0.0668708	−	0.0668708i
$190$		0			0
$191$		−	2.98494i		−	0.215983i	−0.994152	−	0.107991i	$-0.965558\pi$
$191$		−	2.98494i		−	0.215983i	0.994152	−	0.107991i	$-0.0344419\pi$
$192$		0			0
$193$	8.02218	−	3.32289i	0.577449	−	0.239187i	−0.0747916	−	0.997199i	$-0.523829\pi$
$193$	8.02218	−	3.32289i	0.577449	−	0.239187i	0.652241	+	0.758012i	$0.273829\pi$
$194$		0			0
$195$	14.7152	+	14.7152i	1.05377	+	1.05377i
$196$		0			0
$197$	0.380960	+	0.919719i	0.0271423	+	0.0655273i	0.936870	−	0.349679i	$-0.113709\pi$
$197$	0.380960	+	0.919719i	0.0271423	+	0.0655273i	−0.909727	+	0.415206i	$0.863709\pi$
$198$		0			0
$199$	−6.42828	+	15.5192i	−0.455689	+	1.10013i	0.514437	+	0.857528i	$0.328001\pi$
$199$	−6.42828	+	15.5192i	−0.455689	+	1.10013i	−0.970126	+	0.242602i	$0.921999\pi$
$200$		0			0
$201$	−0.610558	−	0.252901i	−0.0430654	−	0.0178383i
$202$		0			0
$203$	1.51050			0.106016
$204$		0			0
$205$	−8.07509			−0.563989
$206$		0			0
$207$	2.25820	+	0.935377i	0.156956	+	0.0650132i
$208$		0			0
$209$	0.0206345	−	0.0498161i	0.00142732	−	0.00344585i
$210$		0			0
$211$	−3.02853	−	7.31152i	−0.208493	−	0.503346i	0.784694	−	0.619884i	$-0.212820\pi$
$211$	−3.02853	−	7.31152i	−0.208493	−	0.503346i	−0.993186	+	0.116538i	$0.962820\pi$
$212$		0			0
$213$	5.26841	+	5.26841i	0.360986	+	0.360986i
$214$		0			0
$215$	−33.5717	+	13.9059i	−2.28957	+	0.948372i
$216$		0			0
$217$		−	9.74977i		−	0.661857i
$218$		0			0
$219$	−0.980077	+	0.980077i	−0.0662275	+	0.0662275i
$220$		0			0
$221$	26.9488	−	5.78991i	1.81278	−	0.389471i
$222$		0			0
$223$	9.80371	−	9.80371i	0.656505	−	0.656505i	−0.298047	−	0.954551i	$-0.596335\pi$
$223$	9.80371	−	9.80371i	0.656505	−	0.656505i	0.954551	+	0.298047i	$0.0963351\pi$
$224$		0			0
$225$		−	4.69014i		−	0.312676i
$226$		0			0
$227$	4.24331	−	1.75764i	0.281639	−	0.116659i	−0.237393	−	0.971414i	$-0.576293\pi$
$227$	4.24331	−	1.75764i	0.281639	−	0.116659i	0.519031	+	0.854755i	$0.326293\pi$
$228$		0			0
$229$	11.2603	+	11.2603i	0.744103	+	0.744103i	0.973365	−	0.229262i	$-0.0736312\pi$
$229$	11.2603	+	11.2603i	0.744103	+	0.744103i	−0.229262	+	0.973365i	$0.573631\pi$
$230$		0			0
$231$	−0.512481	−	1.23724i	−0.0337188	−	0.0814044i
$232$		0			0
$233$	7.59957	−	18.3470i	0.497864	−	1.20195i	−0.452767	−	0.891629i	$-0.649563\pi$
$233$	7.59957	−	18.3470i	0.497864	−	1.20195i	0.950632	−	0.310322i	$-0.100437\pi$
$234$		0			0
$235$	−22.3010	−	9.23736i	−1.45475	−	0.602579i
$236$		0			0
$237$	−16.6708			−1.08288
$238$		0			0
$239$	−5.45935			−0.353136			−0.176568	−	0.984288i	$-0.556500\pi$
$239$	−5.45935			−0.353136			−0.176568	+	0.984288i	$0.556500\pi$
$240$		0			0
$241$	2.35121	+	0.973903i	0.151455	+	0.0627346i	0.457123	−	0.889403i	$-0.348880\pi$
$241$	2.35121	+	0.973903i	0.151455	+	0.0627346i	−0.305668	+	0.952138i	$0.598880\pi$
$242$		0			0
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$		0			0
$245$	−6.32520	−	15.2704i	−0.404102	−	0.975589i
$246$		0			0
$247$	−0.247456	−	0.247456i	−0.0157453	−	0.0157453i
$248$		0			0
$249$	−6.52105	+	2.70111i	−0.413255	+	0.171176i
$250$		0			0
$251$			5.68072i			0.358564i	0.983798	+	0.179282i	$0.0573774\pi$
$251$			5.68072i			0.358564i	−0.983798	+	0.179282i	$0.942623\pi$
$252$		0			0
$253$	1.78028	−	1.78028i	0.111925	−	0.111925i
$254$		0			0
$255$	−10.7795	−	6.96673i	−0.675037	−	0.436274i
$256$		0			0
$257$	5.96917	−	5.96917i	0.372347	−	0.372347i	−0.495985	−	0.868331i	$-0.665193\pi$
$257$	5.96917	−	5.96917i	0.372347	−	0.372347i	0.868331	+	0.495985i	$0.165193\pi$
$258$		0			0
$259$			5.54748i			0.344704i
$260$		0			0
$261$	1.07338	−	0.444609i	0.0664406	−	0.0275206i
$262$		0			0
$263$	17.1500	+	17.1500i	1.05751	+	1.05751i	0.998242	+	0.0592712i	$0.0188777\pi$
$263$	17.1500	+	17.1500i	1.05751	+	1.05751i	0.0592712	+	0.998242i	$0.481122\pi$
$264$		0			0
$265$	10.2866	+	24.8340i	0.631899	+	1.52554i
$266$		0			0
$267$	7.08101	−	17.0951i	0.433351	−	1.04620i
$268$		0			0
$269$	−4.75784	−	1.97076i	−0.290090	−	0.120159i	0.232893	−	0.972502i	$-0.425181\pi$
$269$	−4.75784	−	1.97076i	−0.290090	−	0.120159i	−0.522983	+	0.852343i	$0.675181\pi$
$270$		0			0
$271$	15.6193			0.948808			0.474404	−	0.880307i	$-0.342664\pi$
$271$	15.6193			0.948808			0.474404	+	0.880307i	$0.342664\pi$
$272$		0			0
$273$	−8.69155			−0.526037
$274$		0			0
$275$	−4.46331	−	1.84876i	−0.269148	−	0.111485i
$276$		0			0
$277$	−0.124780	+	0.301246i	−0.00749732	+	0.0181001i	−0.927584	−	0.373615i	$-0.878118\pi$
$277$	−0.124780	+	0.301246i	−0.00749732	+	0.0181001i	0.920087	+	0.391715i	$0.128118\pi$
$278$		0			0
$279$	−2.86980	−	6.92831i	−0.171810	−	0.414787i
$280$		0			0
$281$	19.7997	+	19.7997i	1.18115	+	1.18115i	0.979446	+	0.201705i	$0.0646481\pi$
$281$	19.7997	+	19.7997i	1.18115	+	1.18115i	0.201705	+	0.979446i	$0.435352\pi$
$282$		0			0
$283$	−14.5211	+	6.01482i	−0.863188	+	0.357544i	−0.769953	−	0.638100i	$-0.779721\pi$
$283$	−14.5211	+	6.01482i	−0.863188	+	0.357544i	−0.0932345	+	0.995644i	$0.529721\pi$
$284$		0			0
$285$			0.162953i			0.00965253i
$286$		0			0
$287$	2.38479	−	2.38479i	0.140770	−	0.140770i
$288$		0			0
$289$	−15.4998	+	6.98252i	−0.911754	+	0.410737i
$290$		0			0
$291$	−5.31324	+	5.31324i	−0.311468	+	0.311468i
$292$		0			0
$293$		−	17.3226i		−	1.01200i	−0.862535	−	0.505998i	$-0.831124\pi$
$293$		−	17.3226i		−	1.01200i	0.862535	−	0.505998i	$-0.168876\pi$
$294$		0			0
$295$	22.2242	−	9.20557i	1.29394	−	0.535969i
$296$		0			0
$297$	−0.728351	−	0.728351i	−0.0422632	−	0.0422632i
$298$		0			0
$299$	−6.25319	−	15.0965i	−0.361631	−	0.873055i
$300$		0			0
$301$	5.80785	−	14.0214i	0.334759	−	0.808180i
$302$		0			0
$303$	−8.63330	−	3.57603i	−0.495970	−	0.205438i
$304$		0			0
$305$	−21.7785			−1.24703
$306$		0			0
$307$	18.5111			1.05649			0.528244	−	0.849093i	$-0.322851\pi$
$307$	18.5111			1.05649			0.528244	+	0.849093i	$0.322851\pi$
$308$		0			0
$309$	−5.10191	−	2.11328i	−0.290237	−	0.120220i
$310$		0			0
$311$	10.4069	−	25.1245i	0.590121	−	1.42468i	−0.293265	−	0.956031i	$-0.594742\pi$
$311$	10.4069	−	25.1245i	0.590121	−	1.42468i	0.883386	−	0.468646i	$-0.155258\pi$
$312$		0			0
$313$	−1.43309	−	3.45979i	−0.0810031	−	0.195559i	0.878189	−	0.478314i	$-0.158752\pi$
$313$	−1.43309	−	3.45979i	−0.0810031	−	0.195559i	−0.959192	+	0.282755i	$0.908752\pi$
$314$		0			0
$315$	2.86176	+	2.86176i	0.161242	+	0.161242i
$316$		0			0
$317$	12.2064	−	5.05606i	0.685581	−	0.283977i	−0.0125770	−	0.999921i	$-0.504003\pi$
$317$	12.2064	−	5.05606i	0.685581	−	0.283977i	0.698158	+	0.715944i	$0.254003\pi$
$318$		0			0
$319$		−	1.19672i		−	0.0670037i
$320$		0			0
$321$	−4.05812	+	4.05812i	−0.226502	+	0.226502i
$322$		0			0
$323$	0.181272	+	0.117155i	0.0100862	+	0.00651871i
$324$		0			0
$325$	−22.1710	+	22.1710i	−1.22983	+	1.22983i
$326$		0			0
$327$		−	3.40891i		−	0.188513i
$328$		0			0
$329$	9.31410	−	3.85803i	0.513503	−	0.212700i
$330$		0			0
$331$	−3.21190	−	3.21190i	−0.176542	−	0.176542i	0.613305	−	0.789847i	$-0.289840\pi$
$331$	−3.21190	−	3.21190i	−0.176542	−	0.176542i	−0.789847	+	0.613305i	$0.789840\pi$
$332$		0			0
$333$	1.63287	+	3.94211i	0.0894810	+	0.216026i
$334$		0			0
$335$	0.787257	−	1.90061i	0.0430124	−	0.103841i
$336$		0			0
$337$	0.885943	+	0.366970i	0.0482604	+	0.0199901i	0.406683	−	0.913569i	$-0.366685\pi$
$337$	0.885943	+	0.366970i	0.0482604	+	0.0199901i	−0.358423	+	0.933559i	$0.616685\pi$
$338$		0			0
$339$	14.5959			0.792741
$340$		0			0
$341$	−7.72445			−0.418302
$342$		0			0
$343$	14.7858	+	6.12448i	0.798359	+	0.330691i
$344$		0			0
$345$	−2.91173	+	7.02955i	−0.156762	+	0.378458i
$346$		0			0
$347$	−2.56881	−	6.20165i	−0.137901	−	0.332922i	0.839809	−	0.542881i	$-0.182667\pi$
$347$	−2.56881	−	6.20165i	−0.137901	−	0.332922i	−0.977710	+	0.209960i	$0.932667\pi$
$348$		0			0
$349$	−25.7173	−	25.7173i	−1.37661	−	1.37661i	−0.850275	−	0.526338i	$-0.823565\pi$
$349$	−25.7173	−	25.7173i	−1.37661	−	1.37661i	−0.526338	−	0.850275i	$-0.676435\pi$
$350$		0			0
$351$	−6.17632	+	2.55832i	−0.329668	+	0.136553i
$352$		0			0
$353$			14.0435i			0.747460i	0.927538	+	0.373730i	$0.121921\pi$
$353$			14.0435i			0.747460i	−0.927538	+	0.373730i	$0.878079\pi$
$354$		0			0
$355$	−16.4000	+	16.4000i	−0.870424	+	0.870424i
$356$		0			0
$357$	5.24093	−	1.12600i	0.277379	−	0.0595944i
$358$		0			0
$359$	−21.4184	+	21.4184i	−1.13042	+	1.13042i	−0.140313	+	0.990107i	$0.544811\pi$
$359$	−21.4184	+	21.4184i	−1.13042	+	1.13042i	−0.990107	+	0.140313i	$0.955189\pi$
$360$		0			0
$361$			18.9973i			0.999856i
$362$		0			0
$363$	9.18245	−	3.80349i	0.481953	−	0.199632i
$364$		0			0
$365$	−3.05088	−	3.05088i	−0.159690	−	0.159690i
$366$		0			0
$367$	−7.71162	−	18.6175i	−0.402543	−	0.971825i	−0.987047	−	0.160434i	$-0.948711\pi$
$367$	−7.71162	−	18.6175i	−0.402543	−	0.971825i	0.584503	−	0.811391i	$-0.301289\pi$
$368$		0			0
$369$	0.992710	−	2.39661i	0.0516784	−	0.124763i
$370$		0			0
$371$	−10.3720	−	4.29624i	−0.538489	−	0.223050i
$372$		0			0
$373$	−21.6908			−1.12311			−0.561553	−	0.827441i	$-0.689796\pi$
$373$	−21.6908			−1.12311			−0.561553	+	0.827441i	$0.689796\pi$
$374$		0			0
$375$	−0.964568			−0.0498101
$376$		0			0
$377$	−7.17577	−	2.97230i	−0.369571	−	0.153081i
$378$		0			0
$379$	5.98489	−	14.4488i	0.307423	−	0.742185i	−0.692364	−	0.721549i	$-0.743431\pi$
$379$	5.98489	−	14.4488i	0.307423	−	0.742185i	0.999787	−	0.0206367i	$-0.00656935\pi$
$380$		0			0
$381$	−7.34457	−	17.7314i	−0.376274	−	0.908405i
$382$		0			0
$383$	−6.95101	−	6.95101i	−0.355180	−	0.355180i	0.506853	−	0.862033i	$-0.330809\pi$
$383$	−6.95101	−	6.95101i	−0.355180	−	0.355180i	−0.862033	+	0.506853i	$0.830809\pi$
$384$		0			0
$385$	3.85140	−	1.59530i	0.196286	−	0.0813042i
$386$		0			0
$387$		−	11.6733i		−	0.593387i
$388$		0			0
$389$	−7.37138	+	7.37138i	−0.373744	+	0.373744i	−0.868839	−	0.495095i	$-0.835133\pi$
$389$	−7.37138	+	7.37138i	−0.373744	+	0.373744i	0.495095	+	0.868839i	$0.335133\pi$
$390$		0			0
$391$	5.72639	+	8.29296i	0.289596	+	0.419393i
$392$		0			0
$393$	13.6679	−	13.6679i	0.689455	−	0.689455i
$394$		0			0
$395$		−	51.8944i		−	2.61109i
$396$		0			0
$397$	−21.3163	+	8.82952i	−1.06984	+	0.443141i	−0.846933	−	0.531700i	$-0.821553\pi$
$397$	−21.3163	+	8.82952i	−1.06984	+	0.443141i	−0.222903	+	0.974841i	$0.571553\pi$
$398$		0			0
$399$	−0.0481245	−	0.0481245i	−0.00240924	−	0.00240924i
$400$		0			0
$401$	6.99523	+	16.8880i	0.349325	+	0.843345i	0.996700	+	0.0811737i	$0.0258669\pi$
$401$	6.99523	+	16.8880i	0.349325	+	0.843345i	−0.647375	+	0.762172i	$0.724133\pi$
$402$		0			0
$403$	−19.1852	+	46.3171i	−0.955682	+	2.30722i
$404$		0			0
$405$	2.87594	+	1.19125i	0.142907	+	0.0591939i
$406$		0			0
$407$	4.39510			0.217857
$408$		0			0
$409$	11.9639			0.591574			0.295787	−	0.955254i	$-0.404418\pi$
$409$	11.9639			0.591574			0.295787	+	0.955254i	$0.404418\pi$
$410$		0			0
$411$	0.356811	+	0.147796i	0.0176002	+	0.00729023i
$412$		0			0
$413$	−3.84475	+	9.28205i	−0.189188	+	0.456740i
$414$		0			0
$415$	−8.40828	−	20.2994i	−0.412746	−	0.996457i
$416$		0			0
$417$	10.3462	+	10.3462i	0.506653	+	0.506653i
$418$		0			0
$419$	15.8630	−	6.57066i	0.774958	−	0.320998i	0.0400789	−	0.999197i	$-0.487239\pi$
$419$	15.8630	−	6.57066i	0.774958	−	0.320998i	0.734879	+	0.678199i	$0.237239\pi$
$420$		0			0
$421$		−	22.0942i		−	1.07680i	−0.842688	−	0.538402i	$-0.819028\pi$
$421$		−	22.0942i		−	1.07680i	0.842688	−	0.538402i	$-0.180972\pi$
$422$		0			0
$423$	5.48313	−	5.48313i	0.266599	−	0.266599i
$424$		0			0
$425$	10.4966	−	16.2412i	0.509161	−	0.787814i
$426$		0			0
$427$	6.43176	−	6.43176i	0.311255	−	0.311255i
$428$		0			0
$429$			6.88606i			0.332462i
$430$		0			0
$431$	−37.1429	+	15.3851i	−1.78911	+	0.741073i	−0.798902	+	0.601461i	$0.794586\pi$
$431$	−37.1429	+	15.3851i	−1.78911	+	0.741073i	−0.990206	+	0.139612i	$0.955414\pi$
$432$		0			0
$433$	3.99293	+	3.99293i	0.191888	+	0.191888i	0.796511	−	0.604623i	$-0.206676\pi$
$433$	3.99293	+	3.99293i	0.191888	+	0.191888i	−0.604623	+	0.796511i	$0.706676\pi$
$434$		0			0
$435$	1.38402	+	3.34132i	0.0663588	+	0.160204i
$436$		0			0
$437$	0.0489649	−	0.118212i	0.00234231	−	0.00565484i
$438$		0			0
$439$	27.0721	+	11.2136i	1.29208	+	0.535197i	0.919605	−	0.392845i	$-0.128509\pi$
$439$	27.0721	+	11.2136i	1.29208	+	0.535197i	0.372476	+	0.928042i	$0.378509\pi$
$440$		0			0
$441$	5.30969			0.252843
$442$		0			0
$443$	32.1170			1.52592			0.762962	−	0.646443i	$-0.223744\pi$
$443$	32.1170			1.52592			0.762962	+	0.646443i	$0.223744\pi$
$444$		0			0
$445$	53.2153	+	22.0425i	2.52265	+	1.04491i
$446$		0			0
$447$	5.70064	−	13.7626i	0.269631	−	0.650947i
$448$		0			0
$449$	−12.8408	−	31.0005i	−0.605996	−	1.46300i	−0.867319	−	0.497752i	$-0.834159\pi$
$449$	−12.8408	−	31.0005i	−0.605996	−	1.46300i	0.261324	−	0.965251i	$-0.415841\pi$
$450$		0			0
$451$	−1.88940	−	1.88940i	−0.0889683	−	0.0889683i
$452$		0			0
$453$	15.2247	−	6.30628i	0.715319	−	0.296295i
$454$		0			0
$455$		−	27.0559i		−	1.26840i
$456$		0			0
$457$	−26.7952	+	26.7952i	−1.25343	+	1.25343i	−0.299253	+	0.954174i	$0.596737\pi$
$457$	−26.7952	+	26.7952i	−1.25343	+	1.25343i	−0.954174	+	0.299253i	$0.903263\pi$
$458$		0			0
$459$	3.39283	−	2.34279i	0.158364	−	0.109352i
$460$		0			0
$461$	−3.84146	+	3.84146i	−0.178915	+	0.178915i	−0.790883	−	0.611968i	$-0.790378\pi$
$461$	−3.84146	+	3.84146i	−0.178915	+	0.178915i	0.611968	+	0.790883i	$0.290378\pi$
$462$		0			0
$463$		−	22.0011i		−	1.02248i	−0.859439	−	0.511239i	$-0.829187\pi$
$463$		−	22.0011i		−	1.02248i	0.859439	−	0.511239i	$-0.170813\pi$
$464$		0			0
$465$	21.5671	−	8.93339i	1.00015	−	0.414276i
$466$		0			0
$467$	7.25522	+	7.25522i	0.335732	+	0.335732i	0.854758	−	0.519026i	$-0.173705\pi$
$467$	7.25522	+	7.25522i	0.335732	+	0.335732i	−0.519026	+	0.854758i	$0.673705\pi$
$468$		0			0
$469$	0.328802	+	0.793797i	0.0151826	+	0.0366541i
$470$		0			0
$471$	0.846121	−	2.04272i	0.0389872	−	0.0941235i
$472$		0			0
$473$	−11.1087	−	4.60139i	−0.510780	−	0.211572i
$474$		0			0
$475$	−0.245518			−0.0112652
$476$		0			0
$477$	−8.63508			−0.395373
$478$		0			0
$479$	10.3143	+	4.27231i	0.471271	+	0.195207i	0.605663	−	0.795722i	$-0.292908\pi$
$479$	10.3143	+	4.27231i	0.471271	+	0.195207i	−0.134392	+	0.990928i	$0.542908\pi$
$480$		0			0
$481$	10.9161	−	26.3538i	0.497731	−	1.20163i
$482$		0			0
$483$	−1.21610	−	2.93592i	−0.0553345	−	0.133589i
$484$		0			0
$485$	−16.5396	−	16.5396i	−0.751024	−	0.751024i
$486$		0			0
$487$	28.6591	−	11.8710i	1.29867	−	0.537925i	0.377110	−	0.926169i	$-0.376918\pi$
$487$	28.6591	−	11.8710i	1.29867	−	0.537925i	0.921557	+	0.388243i	$0.126918\pi$
$488$		0			0
$489$		−	1.15104i		−	0.0520516i
$490$		0			0
$491$	−2.40605	+	2.40605i	−0.108583	+	0.108583i	−0.759311	−	0.650728i	$-0.774464\pi$
$491$	−2.40605	+	2.40605i	−0.108583	+	0.108583i	0.650728	+	0.759311i	$0.274464\pi$
$492$		0			0
$493$	4.71199	+	0.862639i	0.212217	+	0.0388513i
$494$		0			0
$495$	2.26728	−	2.26728i	0.101907	−	0.101907i
$496$		0			0
$497$		−	9.68673i		−	0.434509i
$498$		0			0
$499$	−34.8488	+	14.4349i	−1.56005	+	0.646193i	−0.985098	−	0.171995i	$-0.944979\pi$
$499$	−34.8488	+	14.4349i	−1.56005	+	0.646193i	−0.574951	+	0.818188i	$0.694979\pi$
$500$		0			0
$501$	−10.1176	−	10.1176i	−0.452022	−	0.452022i
$502$		0			0
$503$	16.8808	+	40.7538i	0.752676	+	1.81712i	0.543882	+	0.839161i	$0.316954\pi$
$503$	16.8808	+	40.7538i	0.752676	+	1.81712i	0.208794	+	0.977960i	$0.433046\pi$
$504$		0			0
$505$	11.1318	−	26.8746i	0.495360	−	1.19590i
$506$		0			0
$507$	29.2796	+	12.1280i	1.30035	+	0.538623i
$508$		0			0
$509$	−19.4799			−0.863431			−0.431716	−	0.902010i	$-0.642092\pi$
$509$	−19.4799			−0.863431			−0.431716	+	0.902010i	$0.642092\pi$
$510$		0			0
$511$	1.80201			0.0797163
$512$		0			0
$513$	−0.0483631	−	0.0200326i	−0.00213528	−	0.000884462i
$514$		0			0
$515$	6.57842	−	15.8817i	0.289880	−	0.699832i
$516$		0			0
$517$	−3.05660	−	7.37929i	−0.134429	−	0.324541i
$518$		0			0
$519$	−8.66686	−	8.66686i	−0.380433	−	0.380433i
$520$		0			0
$521$	2.02983	−	0.840785i	0.0889287	−	0.0368355i	−0.337776	−	0.941227i	$-0.609675\pi$
$521$	2.02983	−	0.840785i	0.0889287	−	0.0368355i	0.426704	+	0.904391i	$0.359675\pi$
$522$		0			0
$523$		−	28.7418i		−	1.25679i	−0.777895	−	0.628395i	$-0.783712\pi$
$523$		−	28.7418i		−	1.25679i	0.777895	−	0.628395i	$-0.216288\pi$
$524$		0			0
$525$	−4.31175	+	4.31175i	−0.188180	+	0.188180i
$526$		0			0
$527$	5.56804	−	30.4143i	0.242548	−	1.32487i
$528$		0			0
$529$	−12.0389	+	12.0389i	−0.523431	+	0.523431i
$530$		0			0
$531$			7.72763i			0.335351i
$532$		0			0
$533$	−16.0218	+	6.63647i	−0.693983	+	0.287457i
$534$		0			0
$535$	−12.6325	−	12.6325i	−0.546151	−	0.546151i
$536$		0			0
$537$	−7.27096	−	17.5536i	−0.313765	−	0.757496i
$538$		0			0
$539$	2.09298	−	5.05290i	0.0901511	−	0.217644i
$540$		0			0
$541$	11.9441	+	4.94742i	0.513518	+	0.212706i	0.624367	−	0.781131i	$-0.285357\pi$
$541$	11.9441	+	4.94742i	0.513518	+	0.212706i	−0.110849	+	0.993837i	$0.535357\pi$
$542$		0			0
$543$	−24.6208			−1.05658
$544$		0			0
$545$	10.6116			0.454551
$546$		0			0
$547$	−1.93331	−	0.800804i	−0.0826624	−	0.0342399i	0.340969	−	0.940075i	$-0.389245\pi$
$547$	−1.93331	−	0.800804i	−0.0826624	−	0.0342399i	−0.423632	+	0.905835i	$0.639245\pi$
$548$		0			0
$549$	2.67733	−	6.46364i	0.114266	−	0.275862i
$550$		0			0
$551$	−0.0232743	−	0.0561891i	−0.000991518	−	0.00239374i
$552$		0			0
$553$	15.3258	+	15.3258i	0.651719	+	0.651719i
$554$		0			0
$555$	−12.2714	+	5.08297i	−0.520891	+	0.215760i
$556$		0			0
$557$		−	15.7425i		−	0.667029i	−0.942745	−	0.333515i	$-0.891765\pi$
$557$		−	15.7425i		−	0.667029i	0.942745	−	0.333515i	$-0.108235\pi$
$558$		0			0
$559$	−55.1815	+	55.1815i	−2.33393	+	2.33393i
$560$		0			0
$561$	−0.892099	−	4.15223i	−0.0376644	−	0.175307i
$562$		0			0
$563$	6.86293	−	6.86293i	0.289238	−	0.289238i	−0.547541	−	0.836779i	$-0.684436\pi$
$563$	6.86293	−	6.86293i	0.289238	−	0.289238i	0.836779	+	0.547541i	$0.184436\pi$
$564$		0			0
$565$			45.4356i			1.91149i
$566$		0			0
$567$	−1.20115	+	0.497533i	−0.0504436	+	0.0208944i
$568$		0			0
$569$	−3.54867	−	3.54867i	−0.148768	−	0.148768i	0.628800	−	0.777567i	$-0.283547\pi$
$569$	−3.54867	−	3.54867i	−0.148768	−	0.148768i	−0.777567	+	0.628800i	$0.783547\pi$
$570$		0			0
$571$	8.67431	+	20.9416i	0.363009	+	0.876380i	0.994857	+	0.101288i	$0.0322964\pi$
$571$	8.67431	+	20.9416i	0.363009	+	0.876380i	−0.631849	+	0.775092i	$0.717704\pi$
$572$		0			0
$573$	−1.14229	+	2.75773i	−0.0477198	+	0.115206i
$574$		0			0
$575$	−10.5913	−	4.38705i	−0.441686	−	0.182953i
$576$		0			0
$577$	17.0022			0.707810			0.353905	−	0.935281i	$-0.384854\pi$
$577$	17.0022			0.707810			0.353905	+	0.935281i	$0.384854\pi$
$578$		0			0
$579$	−8.68314			−0.360859
$580$		0			0
$581$	8.47814	+	3.51176i	0.351732	+	0.145692i
$582$		0			0
$583$	−3.40378	+	8.21746i	−0.140970	+	0.340332i
$584$		0			0
$585$	−7.96378	−	19.2263i	−0.329262	−	0.794908i
$586$		0			0
$587$	−11.3612	−	11.3612i	−0.468929	−	0.468929i	0.432639	−	0.901567i	$-0.357583\pi$
$587$	−11.3612	−	11.3612i	−0.468929	−	0.468929i	−0.901567	+	0.432639i	$0.857583\pi$
$588$		0			0
$589$	−0.362682	+	0.150228i	−0.0149440	+	0.00619002i
$590$		0			0
$591$		−	0.995496i		−	0.0409493i
$592$		0			0
$593$	−18.0376	+	18.0376i	−0.740714	+	0.740714i	−0.972715	−	0.232001i	$-0.925473\pi$
$593$	−18.0376	+	18.0376i	−0.740714	+	0.740714i	0.232001	+	0.972715i	$0.425473\pi$
$594$		0			0
$595$	3.50513	+	16.3145i	0.143696	+	0.668828i
$596$		0			0
$597$	11.8779	−	11.8779i	0.486131	−	0.486131i
$598$		0			0
$599$			2.88098i			0.117714i	0.998266	+	0.0588568i	$0.0187455\pi$
$599$			2.88098i			0.117714i	−0.998266	+	0.0588568i	$0.981254\pi$
$600$		0			0
$601$	24.3881	−	10.1019i	0.994811	−	0.412064i	0.174919	−	0.984583i	$-0.444034\pi$
$601$	24.3881	−	10.1019i	0.994811	−	0.412064i	0.819892	+	0.572518i	$0.194034\pi$
$602$		0			0
$603$	0.467301	+	0.467301i	0.0190300	+	0.0190300i
$604$		0			0
$605$	11.8399	+	28.5840i	0.481360	+	1.16211i
$606$		0			0
$607$	−7.16567	+	17.2995i	−0.290845	+	0.702163i	−0.999996	−	0.00289420i	$-0.999079\pi$
$607$	−7.16567	+	17.2995i	−0.290845	+	0.702163i	0.709150	+	0.705057i	$0.249079\pi$
$608$		0			0
$609$	−1.39552	−	0.578043i	−0.0565493	−	0.0234235i
$610$		0			0
$611$	−51.8392			−2.09719
$612$		0			0
$613$	−2.20627			−0.0891105			−0.0445552	−	0.999007i	$-0.514187\pi$
$613$	−2.20627			−0.0891105			−0.0445552	+	0.999007i	$0.514187\pi$
$614$		0			0
$615$	7.46041	+	3.09020i	0.300833	+	0.124609i
$616$		0			0
$617$	11.5165	−	27.8032i	0.463635	−	1.11931i	−0.503258	−	0.864136i	$-0.667866\pi$
$617$	11.5165	−	27.8032i	0.463635	−	1.11931i	0.966894	−	0.255179i	$-0.0821344\pi$
$618$		0			0
$619$	−4.38632	−	10.5895i	−0.176301	−	0.425628i	0.810884	−	0.585207i	$-0.198987\pi$
$619$	−4.38632	−	10.5895i	−0.176301	−	0.425628i	−0.987185	+	0.159578i	$0.948987\pi$
$620$		0			0
$621$	−1.72835	−	1.72835i	−0.0693564	−	0.0693564i
$622$		0			0
$623$	−22.2256	+	9.20615i	−0.890450	+	0.368837i
$624$		0			0
$625$		−	26.4533i		−	1.05813i
$626$		0			0
$627$	−0.0381276	+	0.0381276i	−0.00152267	+	0.00152267i
$628$		0			0
$629$	−3.16814	+	17.3053i	−0.126322	+	0.690007i
$630$		0			0
$631$	−25.8448	+	25.8448i	−1.02886	+	1.02886i	−0.0292941	+	0.999571i	$0.509326\pi$
$631$	−25.8448	+	25.8448i	−1.02886	+	1.02886i	−0.999571	+	0.0292941i	$0.990674\pi$
$632$		0			0
$633$			7.91393i			0.314550i
$634$		0			0
$635$	55.1959	−	22.8629i	2.19038	−	0.907287i
$636$		0			0
$637$	−25.0997	−	25.0997i	−0.994488	−	0.994488i
$638$		0			0
$639$	−2.85124	−	6.88351i	−0.112793	−	0.272308i
$640$		0			0
$641$	5.80355	−	14.0110i	0.229226	−	0.553401i	−0.766857	−	0.641818i	$-0.778181\pi$
$641$	5.80355	−	14.0110i	0.229226	−	0.553401i	0.996084	+	0.0884165i	$0.0281806\pi$
$642$		0			0
$643$	−40.7984	−	16.8992i	−1.60893	−	0.666441i	−0.616288	−	0.787521i	$-0.711364\pi$
$643$	−40.7984	−	16.8992i	−1.60893	−	0.666441i	−0.992643	+	0.121080i	$0.961364\pi$
$644$		0			0
$645$	36.3378			1.43080
$646$		0			0
$647$	40.4822			1.59152			0.795759	−	0.605613i	$-0.207072\pi$
$647$	40.4822			1.59152			0.795759	+	0.605613i	$0.207072\pi$
$648$		0			0
$649$	7.35390	+	3.04608i	0.288666	+	0.119569i
$650$		0			0
$651$	−3.73107	+	9.00761i	−0.146232	+	0.353036i
$652$		0			0
$653$	−3.51730	−	8.49152i	−0.137643	−	0.332299i	0.839995	−	0.542594i	$-0.182558\pi$
$653$	−3.51730	−	8.49152i	−0.137643	−	0.332299i	−0.977638	+	0.210295i	$0.932558\pi$
$654$		0			0
$655$	42.5468	+	42.5468i	1.66244	+	1.66244i
$656$		0			0
$657$	1.28053	−	0.530414i	0.0499583	−	0.0206934i
$658$		0			0
$659$			41.6886i			1.62396i	0.583686	+	0.811979i	$0.301610\pi$
$659$			41.6886i			1.62396i	−0.583686	+	0.811979i	$0.698390\pi$
$660$		0			0
$661$	−25.4496	+	25.4496i	−0.989876	+	0.989876i	−0.999949	−	0.0100728i	$-0.996794\pi$
$661$	−25.4496	+	25.4496i	−0.989876	+	0.989876i	0.0100728	+	0.999949i	$0.496794\pi$
$662$		0			0
$663$	−27.1132	−	4.96370i	−1.05299	−	0.192774i
$664$		0			0
$665$	0.149807	−	0.149807i	0.00580925	−	0.00580925i
$666$		0			0
$667$		−	2.83978i		−	0.109957i
$668$		0			0
$669$	−12.8092	+	5.30573i	−0.495231	+	0.205131i
$670$		0			0
$671$	−5.09569	−	5.09569i	−0.196717	−	0.196717i
$672$		0			0
$673$	−14.0171	−	33.8403i	−0.540319	−	1.30445i	−0.924498	−	0.381188i	$-0.875515\pi$
$673$	−14.0171	−	33.8403i	−0.540319	−	1.30445i	0.384178	−	0.923259i	$-0.374485\pi$
$674$		0			0
$675$	−1.79484	+	4.33312i	−0.0690834	+	0.166782i
$676$		0			0
$677$	−19.9147	−	8.24892i	−0.765382	−	0.317032i	−0.0343820	−	0.999409i	$-0.510946\pi$
$677$	−19.9147	−	8.24892i	−0.765382	−	0.317032i	−0.731000	+	0.682377i	$0.760946\pi$
$678$		0			0
$679$	9.76916			0.374906
$680$		0			0
$681$	−4.59293			−0.176001
$682$		0			0
$683$	33.4534	+	13.8569i	1.28006	+	0.530218i	0.916007	−	0.401161i	$-0.131393\pi$
$683$	33.4534	+	13.8569i	1.28006	+	0.530218i	0.364051	+	0.931379i	$0.381393\pi$
$684$		0			0
$685$	−0.460073	+	1.11072i	−0.0175785	+	0.0424383i
$686$		0			0
$687$	−6.09404	−	14.7123i	−0.232502	−	0.561310i
$688$		0			0
$689$	40.8193	+	40.8193i	1.55509	+	1.55509i
$690$		0			0
$691$	2.54578	−	1.05450i	0.0968462	−	0.0401150i	−0.333734	−	0.942667i	$-0.608309\pi$
$691$	2.54578	−	1.05450i	0.0968462	−	0.0401150i	0.430581	+	0.902552i	$0.358309\pi$
$692$		0			0
$693$			1.33918i			0.0508712i
$694$		0			0
$695$	−32.2065	+	32.2065i	−1.22166	+	1.22166i
$696$		0			0
$697$	8.80126	−	6.07738i	0.333372	−	0.230197i
$698$		0			0
$699$	−14.0422	+	14.0422i	−0.531124	+	0.531124i
$700$		0			0
$701$		−	8.81001i		−	0.332750i	−0.986063	−	0.166375i	$-0.946794\pi$
$701$		−	8.81001i		−	0.332750i	0.986063	−	0.166375i	$-0.0532062\pi$
$702$		0			0
$703$	0.206361	−	0.0854774i	0.00778304	−	0.00322384i
$704$		0			0
$705$	17.0684	+	17.0684i	0.642834	+	0.642834i
$706$		0			0
$707$	4.64926	+	11.2243i	0.174853	+	0.422134i
$708$		0			0
$709$	−15.4637	+	37.3326i	−0.580751	+	1.40206i	0.311383	+	0.950285i	$0.399208\pi$
$709$	−15.4637	+	37.3326i	−0.580751	+	1.40206i	−0.892134	+	0.451772i	$0.850792\pi$
$710$		0			0
$711$	15.4018	+	6.37962i	0.577612	+	0.239255i
$712$		0			0
$713$	−18.3298			−0.686458
$714$		0			0
$715$	−21.4356			−0.801646
$716$		0			0
$717$	5.04378	+	2.08920i	0.188363	+	0.0780227i
$718$		0			0
$719$	5.99086	−	14.4632i	0.223421	−	0.539387i	−0.771929	−	0.635709i	$-0.780708\pi$
$719$	5.99086	−	14.4632i	0.223421	−	0.539387i	0.995350	+	0.0963222i	$0.0307079\pi$
$720$		0			0
$721$	2.74751	+	6.63308i	0.102323	+	0.247029i
$722$		0			0
$723$	−1.79954	−	1.79954i	−0.0669255	−	0.0669255i
$724$		0			0
$725$	−5.03430	+	2.08528i	−0.186969	+	0.0774452i
$726$		0			0
$727$			28.5009i			1.05704i	0.848920	+	0.528521i	$0.177253\pi$
$727$			28.5009i			1.05704i	−0.848920	+	0.528521i	$0.822747\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	26.1251	−	40.4228i	0.966271	−	1.49509i
$732$		0			0
$733$	−12.3553	+	12.3553i	−0.456352	+	0.456352i	−0.897456	−	0.441104i	$-0.854587\pi$
$733$	−12.3553	+	12.3553i	−0.456352	+	0.456352i	0.441104	+	0.897456i	$0.354587\pi$
$734$		0			0
$735$			16.5285i			0.609664i
$736$		0			0
$737$	0.628902	−	0.260500i	0.0231659	−	0.00959563i
$738$		0			0
$739$	29.8120	+	29.8120i	1.09665	+	1.09665i	0.994799	+	0.101854i	$0.0324775\pi$
$739$	29.8120	+	29.8120i	1.09665	+	1.09665i	0.101854	+	0.994799i	$0.467523\pi$
$740$		0			0
$741$	0.133922	+	0.323317i	0.00491976	+	0.0118773i
$742$		0			0
$743$	9.82649	−	23.7232i	0.360499	−	0.870321i	−0.634728	−	0.772735i	$-0.718888\pi$
$743$	9.82649	−	23.7232i	0.360499	−	0.870321i	0.995227	−	0.0975858i	$-0.0311121\pi$
$744$		0			0
$745$	42.8415	+	17.7455i	1.56959	+	0.650146i
$746$		0			0
$747$	7.05834			0.258251
$748$		0			0
$749$	7.46144			0.272635
$750$		0			0
$751$	−21.6108	−	8.95147i	−0.788588	−	0.326644i	−0.0482124	−	0.998837i	$-0.515352\pi$
$751$	−21.6108	−	8.95147i	−0.788588	−	0.326644i	−0.740376	+	0.672193i	$0.765352\pi$
$752$		0			0
$753$	2.17392	−	5.24830i	0.0792220	−	0.191259i
$754$		0			0
$755$	19.6308	+	47.3930i	0.714438	+	1.72481i
$756$		0			0
$757$	−25.6060	−	25.6060i	−0.930664	−	0.930664i	0.0670830	−	0.997747i	$-0.478631\pi$
$757$	−25.6060	−	25.6060i	−0.930664	−	0.930664i	−0.997747	+	0.0670830i	$0.978631\pi$
$758$		0			0
$759$	−2.32605	+	0.963480i	−0.0844301	+	0.0349721i
$760$		0			0
$761$			6.19717i			0.224647i	0.993672	+	0.112324i	$0.0358293\pi$
$761$			6.19717i			0.224647i	−0.993672	+	0.112324i	$0.964171\pi$
$762$		0			0
$763$	−3.13388	+	3.13388i	−0.113454	+	0.113454i
$764$		0			0
$765$	7.29288	+	10.5615i	0.263675	+	0.381854i
$766$		0			0
$767$	36.5297	−	36.5297i	1.31901	−	1.31901i
$768$		0			0
$769$			28.8712i			1.04112i	0.853825	+	0.520561i	$0.174277\pi$
$769$			28.8712i			1.04112i	−0.853825	+	0.520561i	$0.825723\pi$
$770$		0			0
$771$	−7.79910	+	3.23049i	−0.280878	+	0.116343i
$772$		0			0
$773$	4.61440	+	4.61440i	0.165968	+	0.165968i	0.785205	−	0.619236i	$-0.212558\pi$
$773$	4.61440	+	4.61440i	0.165968	+	0.165968i	−0.619236	+	0.785205i	$0.712558\pi$
$774$		0			0
$775$	13.4598	+	32.4947i	0.483489	+	1.16724i
$776$		0			0
$777$	2.12293	−	5.12520i	0.0761596	−	0.183866i
$778$		0			0
$779$	−0.125457	−	0.0519662i	−0.00449498	−	0.00186188i
$780$		0			0
$781$	−7.67451			−0.274616
$782$		0			0
$783$	−1.16182			−0.0415200
$784$		0			0
$785$	6.35877	+	2.63389i	0.226954	+	0.0940076i
$786$		0			0
$787$	−3.45953	+	8.35205i	−0.123319	+	0.297718i	−0.973468	−	0.228824i	$-0.926512\pi$
$787$	−3.45953	+	8.35205i	−0.123319	+	0.297718i	0.850149	+	0.526543i	$0.176512\pi$
$788$		0			0
$789$	−9.28150	−	22.4075i	−0.330430	−	0.797729i
$790$		0			0
$791$	−13.4183	−	13.4183i	−0.477101	−	0.477101i
$792$		0			0
$793$	−43.2108	+	17.8985i	−1.53446	+	0.635594i
$794$		0			0
$795$		−	26.8801i		−	0.953340i
$796$		0			0
$797$	3.37796	−	3.37796i	0.119654	−	0.119654i	−0.644745	−	0.764398i	$-0.723036\pi$
$797$	3.37796	−	3.37796i	0.119654	−	0.119654i	0.764398	+	0.644745i	$0.223036\pi$
$798$		0			0
$799$	31.2585	−	6.71584i	1.10585	−	0.237589i
$800$		0			0
$801$	−13.0840	+	13.0840i	−0.462301	+	0.462301i
$802$		0			0
$803$		−	1.42768i		−	0.0503818i
$804$		0			0
$805$	9.13924	−	3.78560i	0.322116	−	0.133425i
$806$		0			0
$807$	3.64149	+	3.64149i	0.128187	+	0.128187i
$808$		0			0
$809$	11.6542	+	28.1357i	0.409740	+	0.989199i	0.985206	+	0.171374i	$0.0548205\pi$
$809$	11.6542	+	28.1357i	0.409740	+	0.989199i	−0.575467	+	0.817825i	$0.695180\pi$
$810$		0			0
$811$	3.61699	−	8.73219i	0.127010	−	0.306629i	−0.847565	−	0.530692i	$-0.821932\pi$
$811$	3.61699	−	8.73219i	0.127010	−	0.306629i	0.974575	+	0.224063i	$0.0719322\pi$
$812$		0			0
$813$	−14.4304	−	5.97727i	−0.506096	−	0.209632i
$814$		0			0
$815$	3.58306			0.125509
$816$		0			0
$817$	−0.611071			−0.0213787
$818$		0			0
$819$	8.02995	+	3.32611i	0.280589	+	0.116224i
$820$		0			0
$821$	9.68739	−	23.3874i	0.338092	−	0.816227i	−0.659807	−	0.751435i	$-0.729362\pi$
$821$	9.68739	−	23.3874i	0.338092	−	0.816227i	0.997899	−	0.0647914i	$-0.0206382\pi$
$822$		0			0
$823$	−2.48711	−	6.00441i	−0.0866951	−	0.209301i	0.874586	−	0.484871i	$-0.161133\pi$
$823$	−2.48711	−	6.00441i	−0.0866951	−	0.209301i	−0.961281	+	0.275570i	$0.911133\pi$
$824$		0			0
$825$	3.41607	+	3.41607i	0.118932	+	0.118932i
$826$		0			0
$827$	−35.3303	+	14.6343i	−1.22855	+	0.508884i	−0.900120	−	0.435643i	$-0.856521\pi$
$827$	−35.3303	+	14.6343i	−1.22855	+	0.508884i	−0.328435	+	0.944527i	$0.606521\pi$
$828$		0			0
$829$			3.18171i			0.110505i	0.998472	+	0.0552526i	$0.0175964\pi$
$829$			3.18171i			0.110505i	−0.998472	+	0.0552526i	$0.982404\pi$
$830$		0			0
$831$	0.230564	−	0.230564i	0.00799817	−	0.00799817i
$832$		0			0
$833$	18.3866	+	11.8832i	0.637059	+	0.411729i
$834$		0			0
$835$	31.4952	−	31.4952i	1.08993	−	1.08993i
$836$		0			0
$837$			7.49914i			0.259208i
$838$		0			0
$839$	12.5803	−	5.21093i	0.434320	−	0.179901i	−0.154802	−	0.987946i	$-0.549474\pi$
$839$	12.5803	−	5.21093i	0.434320	−	0.179901i	0.589122	+	0.808044i	$0.299474\pi$
$840$		0			0
$841$	19.5516	+	19.5516i	0.674194	+	0.674194i
$842$		0			0
$843$	−10.7155	−	25.8696i	−0.369062	−	0.890995i
$844$		0			0
$845$	−37.7532	+	91.1443i	−1.29875	+	3.13546i
$846$		0			0
$847$	−11.9383	−	4.94499i	−0.410203	−	0.169912i
$848$		0			0
$849$	15.7175			0.539423
$850$		0			0
$851$	10.4294			0.357516
$852$		0			0
$853$	49.8673	+	20.6557i	1.70742	+	0.707238i	1.00000		0.000447751i	$0.000142524\pi$
$853$	49.8673	+	20.6557i	1.70742	+	0.707238i	0.707423	+	0.706790i	$0.249857\pi$
$854$		0			0
$855$	0.0623596	−	0.150549i	0.00213265	−	0.00514868i
$856$		0			0
$857$	10.4987	+	25.3461i	0.358629	+	0.865806i	0.995493	+	0.0948308i	$0.0302310\pi$
$857$	10.4987	+	25.3461i	0.358629	+	0.865806i	−0.636865	+	0.770976i	$0.719769\pi$
$858$		0			0
$859$	−22.6761	−	22.6761i	−0.773698	−	0.773698i	0.205053	−	0.978751i	$-0.434263\pi$
$859$	−22.6761	−	22.6761i	−0.773698	−	0.773698i	−0.978751	+	0.205053i	$0.934263\pi$
$860$		0			0
$861$	−3.11588	+	1.29064i	−0.106189	+	0.0439849i
$862$		0			0
$863$		−	5.64442i		−	0.192138i	−0.995375	−	0.0960692i	$-0.969373\pi$
$863$		−	5.64442i		−	0.192138i	0.995375	−	0.0960692i	$-0.0306270\pi$
$864$		0			0
$865$	26.9791	−	26.9791i	0.917316	−	0.917316i
$866$		0			0
$867$	16.9921	−	0.519486i	0.577081	−	0.0176427i
$868$		0			0
$869$	12.1422	−	12.1422i	0.411895	−	0.411895i
$870$		0			0
$871$		−	4.41801i		−	0.149698i
$872$		0			0
$873$	6.94209	−	2.87551i	0.234954	−	0.0973212i
$874$		0			0
$875$	0.886748	+	0.886748i	0.0299776	+	0.0299776i
$876$		0			0
$877$	6.38918	+	15.4249i	0.215747	+	0.520860i	0.994288	−	0.106735i	$-0.0340395\pi$
$877$	6.38918	+	15.4249i	0.215747	+	0.520860i	−0.778540	+	0.627595i	$0.784040\pi$
$878$		0			0
$879$	−6.62906	+	16.0040i	−0.223593	+	0.539801i
$880$		0			0
$881$	42.7318	+	17.7001i	1.43967	+	0.596331i	0.959718	−	0.280964i	$-0.0906541\pi$
$881$	42.7318	+	17.7001i	1.43967	+	0.596331i	0.479952	+	0.877295i	$0.340654\pi$
$882$		0			0
$883$	−16.0530			−0.540227			−0.270114	−	0.962828i	$-0.587061\pi$
$883$	−16.0530			−0.540227			−0.270114	+	0.962828i	$0.587061\pi$
$884$		0			0
$885$	−24.0553			−0.808611
$886$		0			0
$887$	17.1554	+	7.10602i	0.576023	+	0.238597i	0.651625	−	0.758541i	$-0.274088\pi$
$887$	17.1554	+	7.10602i	0.576023	+	0.238597i	−0.0756014	+	0.997138i	$0.524088\pi$
$888$		0			0
$889$	−9.54880	+	23.0528i	−0.320257	+	0.773168i
$890$		0			0
$891$	0.394181	+	0.951637i	0.0132056	+	0.0318810i
$892$		0			0
$893$	−0.287030	−	0.287030i	−0.00960508	−	0.00960508i
$894$		0			0
$895$	54.6427	−	22.6338i	1.82650	−	0.756563i
$896$		0			0
$897$			16.3404i			0.545589i
$898$		0			0
$899$	−6.16077	+	6.16077i	−0.205473	+	0.205473i
$900$		0			0
$901$	−29.9019	−	19.3255i	−0.996176	−	0.643825i
$902$		0			0
$903$	−10.7315	+	10.7315i	−0.357122	+	0.357122i
$904$		0			0
$905$		−	76.6420i		−	2.54767i
$906$		0			0
$907$	27.4248	−	11.3597i	0.910625	−	0.377193i	0.122329	−	0.992490i	$-0.460964\pi$
$907$	27.4248	−	11.3597i	0.910625	−	0.377193i	0.788296	+	0.615297i	$0.210964\pi$
$908$		0			0
$909$	6.60765	+	6.60765i	0.219162	+	0.219162i
$910$		0			0
$911$	−1.13880	−	2.74930i	−0.0377300	−	0.0910883i	0.903891	−	0.427762i	$-0.140698\pi$
$911$	−1.13880	−	2.74930i	−0.0377300	−	0.0910883i	−0.941621	+	0.336674i	$0.890698\pi$
$912$		0			0
$913$	2.78226	−	6.71698i	0.0920794	−	0.222299i
$914$		0			0
$915$	20.1207	+	8.33425i	0.665169	+	0.275522i
$916$		0			0
$917$	−25.1304			−0.829879
$918$		0			0
$919$	−39.7923			−1.31263			−0.656313	−	0.754489i	$-0.727885\pi$
$919$	−39.7923			−1.31263			−0.656313	+	0.754489i	$0.727885\pi$
$920$		0			0
$921$	−17.1021	−	7.08391i	−0.563532	−	0.233423i
$922$		0			0
$923$	−19.0612	+	46.0177i	−0.627406	+	1.51469i
$924$		0			0
$925$	−7.65841	−	18.4890i	−0.251807	−	0.607915i
$926$		0			0
$927$	3.90483	+	3.90483i	0.128251	+	0.128251i
$928$		0			0
$929$	−38.1006	+	15.7818i	−1.25004	+	0.517783i	−0.906838	−	0.421479i	$-0.861511\pi$
$929$	−38.1006	+	15.7818i	−1.25004	+	0.517783i	−0.343201	+	0.939262i	$0.611511\pi$
$930$		0			0
$931$		−	0.277951i		−	0.00910947i
$932$		0			0
$933$	−19.2294	+	19.2294i	−0.629543	+	0.629543i
$934$		0			0
$935$	12.9255	−	2.77701i	0.422708	−	0.0908180i
$936$		0			0
$937$	−15.2856	+	15.2856i	−0.499357	+	0.499357i	−0.911238	−	0.411881i	$-0.864872\pi$
$937$	−15.2856	+	15.2856i	−0.499357	+	0.499357i	0.411881	+	0.911238i	$0.364872\pi$
$938$		0			0
$939$			3.74485i			0.122208i
$940$		0			0
$941$	−30.4191	+	12.6000i	−0.991634	+	0.410748i	−0.818723	−	0.574189i	$-0.805317\pi$
$941$	−30.4191	+	12.6000i	−0.991634	+	0.410748i	−0.172911	+	0.984937i	$0.555317\pi$
$942$		0			0
$943$	−4.48347	−	4.48347i	−0.146002	−	0.146002i
$944$		0			0
$945$	−1.54877	−	3.73906i	−0.0503815	−	0.121632i
$946$		0			0
$947$	11.0141	−	26.5904i	0.357911	−	0.864073i	−0.637683	−	0.770299i	$-0.720107\pi$
$947$	11.0141	−	26.5904i	0.357911	−	0.864073i	0.995594	−	0.0937739i	$-0.0298931\pi$
$948$		0			0
$949$	−8.56062	−	3.54593i	−0.277890	−	0.115106i
$950$		0			0
$951$	−13.2121			−0.428433
$952$		0			0
$953$	−49.6066			−1.60692			−0.803458	−	0.595361i	$-0.797009\pi$
$953$	−49.6066			−1.60692			−0.803458	+	0.595361i	$0.797009\pi$
$954$		0			0
$955$	−8.58453	−	3.55583i	−0.277789	−	0.115064i
$956$		0			0
$957$	−0.457967	+	1.10563i	−0.0148040	+	0.0357399i
$958$		0			0
$959$	−0.192152	−	0.463896i	−0.00620491	−	0.0149800i
$960$		0			0
$961$	17.8454	+	17.8454i	0.575657	+	0.575657i
$962$		0			0
$963$	5.30219	−	2.19624i	0.170861	−	0.0707728i
$964$		0			0
$965$		−	27.0297i		−	0.870118i
$966$		0			0
$967$	23.4188	−	23.4188i	0.753097	−	0.753097i	−0.221959	−	0.975056i	$-0.571245\pi$
$967$	23.4188	−	23.4188i	0.753097	−	0.753097i	0.975056	+	0.221959i	$0.0712452\pi$
$968$		0			0
$969$	−0.122640	−	0.177607i	−0.00393977	−	0.00570557i
$970$		0			0
$971$	−43.2866	+	43.2866i	−1.38913	+	1.38913i	−0.561984	+	0.827148i	$0.689962\pi$
$971$	−43.2866	+	43.2866i	−1.38913	+	1.38913i	−0.827148	+	0.561984i	$0.810038\pi$
$972$		0			0
$973$		−	19.0229i		−	0.609846i
$974$		0			0
$975$	28.9678	−	11.9989i	0.927713	−	0.384271i
$976$		0			0
$977$	5.52735	+	5.52735i	0.176836	+	0.176836i	0.789975	−	0.613139i	$-0.210094\pi$
$977$	5.52735	+	5.52735i	0.176836	+	0.176836i	−0.613139	+	0.789975i	$0.710094\pi$
$978$		0			0
$979$	7.29376	+	17.6087i	0.233110	+	0.562776i
$980$		0			0
$981$	−1.30453	+	3.14942i	−0.0416505	+	0.100553i
$982$		0			0
$983$	−20.5607	−	8.51653i	−0.655785	−	0.271635i	0.0298784	−	0.999554i	$-0.490488\pi$
$983$	−20.5607	−	8.51653i	−0.655785	−	0.271635i	−0.685664	+	0.727918i	$0.740488\pi$
$984$		0			0
$985$	3.09888			0.0987385
$986$		0			0
$987$	−10.0815			−0.320898
$988$		0			0
$989$	−26.3606	−	10.9189i	−0.838219	−	0.347202i
$990$		0			0
$991$	6.41970	−	15.4985i	0.203928	−	0.492327i	−0.788517	−	0.615013i	$-0.789151\pi$
$991$	6.41970	−	15.4985i	0.203928	−	0.492327i	0.992446	+	0.122686i	$0.0391508\pi$
$992$		0			0
$993$	1.73827	+	4.19655i	0.0551623	+	0.133174i
$994$		0			0
$995$	36.9747	+	36.9747i	1.17218	+	1.17218i
$996$		0			0
$997$	−38.9013	+	16.1135i	−1.23202	+	0.510318i	−0.901211	−	0.433380i	$-0.857321\pi$
$997$	−38.9013	+	16.1135i	−1.23202	+	0.510318i	−0.330806	+	0.943699i	$0.607321\pi$
$998$		0			0
$999$		−	4.26691i		−	0.134999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bq.f.145.2		16
4.3	odd	2		408.2.ba.a.145.4	yes	16
12.11	even	2		1224.2.bq.e.145.1		16
17.2	even	8	inner	816.2.bq.f.529.2		16
68.11	even	16		6936.2.a.bl.1.8		8
68.19	odd	8		408.2.ba.a.121.4	✓	16
68.23	even	16		6936.2.a.bo.1.1		8
204.155	even	8		1224.2.bq.e.937.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.ba.a.121.4	✓	16	68.19	odd	8
408.2.ba.a.145.4	yes	16	4.3	odd	2
816.2.bq.f.145.2		16	1.1	even	1	trivial
816.2.bq.f.529.2		16	17.2	even	8	inner
1224.2.bq.e.145.1		16	12.11	even	2
1224.2.bq.e.937.1		16	204.155	even	8
6936.2.a.bl.1.8		8	68.11	even	16
6936.2.a.bo.1.1		8	68.23	even	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bq (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{3} +(1.19125 - 2.87594i) q^{5} +(0.497533 + 1.20115i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{3} +(1.19125 - 2.87594i) q^{5} +(0.497533 + 1.20115i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.951637 - 0.394181i) q^{11} -6.68521i q^{13} +(-2.20115 + 2.20115i) q^{15} +(0.866078 + 4.03112i) q^{17} +(0.0370155 - 0.0370155i) q^{19} -1.30012i q^{21} +(2.25820 - 0.935377i) q^{23} +(-3.31643 - 3.31643i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(0.444609 - 1.07338i) q^{29} +(-6.92831 - 2.86980i) q^{31} -1.03004 q^{33} +4.04713 q^{35} +(3.94211 + 1.63287i) q^{37} +(-2.55832 + 6.17632i) q^{39} +(-0.992710 - 2.39661i) q^{41} +(-8.25427 - 8.25427i) q^{43} +(2.87594 - 1.19125i) q^{45} -7.75431i q^{47} +(3.75452 - 3.75452i) q^{49} +(0.742490 - 4.05570i) q^{51} +(-6.10592 + 6.10592i) q^{53} -3.20642i q^{55} +(-0.0483631 + 0.0200326i) q^{57} +(5.46426 + 5.46426i) q^{59} +(-2.67733 - 6.46364i) q^{61} +(-0.497533 + 1.20115i) q^{63} +(-19.2263 - 7.96378i) q^{65} +0.660863 q^{67} -2.44426 q^{69} +(-6.88351 - 2.85124i) q^{71} +(0.530414 - 1.28053i) q^{73} +(1.79484 + 4.33312i) q^{75} +(0.946942 + 0.946942i) q^{77} +(15.4018 - 6.37962i) q^{79} +1.00000i q^{81} +(4.99100 - 4.99100i) q^{83} +(12.6250 + 2.31130i) q^{85} +(-0.821530 + 0.821530i) q^{87} +18.5036i q^{89} +(8.02995 - 3.32611i) q^{91} +(5.30270 + 5.30270i) q^{93} +(-0.0623596 - 0.150549i) q^{95} +(2.87551 - 6.94209i) q^{97} +(0.951637 + 0.394181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{11} - 8 q^{15} + 8 q^{19} + 8 q^{23} - 8 q^{25} + 32 q^{29} - 8 q^{31} - 8 q^{33} - 16 q^{35} + 8 q^{37} + 8 q^{39} + 40 q^{41} + 24 q^{43} + 8 q^{45} + 24 q^{49} - 8 q^{51} - 24 q^{53} - 8 q^{57} + 16 q^{59} - 64 q^{65} - 8 q^{69} + 16 q^{71} + 24 q^{73} + 96 q^{79} - 32 q^{85} - 16 q^{87} + 24 q^{93} + 8 q^{95} + 56 q^{97} + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 - 8 * q^15 + 8 * q^19 + 8 * q^23 - 8 * q^25 + 32 * q^29 - 8 * q^31 - 8 * q^33 - 16 * q^35 + 8 * q^37 + 8 * q^39 + 40 * q^41 + 24 * q^43 + 8 * q^45 + 24 * q^49 - 8 * q^51 - 24 * q^53 - 8 * q^57 + 16 * q^59 - 64 * q^65 - 8 * q^69 + 16 * q^71 + 24 * q^73 + 96 * q^79 - 32 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 56 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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