LMFDB - Embedded newform 882.3.s.e.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,3,Mod(557,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("882.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.s (of order $6$, degree $2$, 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:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.2
Root			$2.23256 + 1.28897i$ of defining polynomial
Character	$\chi$	$=$	882.557
Dual form			882.3.s.e.863.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +(-6.29150 + 10.8972i) q^{10} +(-15.4110 - 8.89753i) q^{11} +2.58301 q^{13} +(-2.00000 - 3.46410i) q^{16} +(22.4024 + 12.9340i) q^{17} +(-10.0000 - 17.3205i) q^{19} -17.7951i q^{20} +25.1660 q^{22} +(15.4110 - 8.89753i) q^{23} +(27.0830 - 46.9091i) q^{25} +(-3.16352 + 1.82646i) q^{26} +11.9034i q^{29} +(8.58301 - 14.8662i) q^{31} +(4.89898 + 2.82843i) q^{32} -36.5830 q^{34} +(-19.0000 - 32.9090i) q^{37} +(24.4949 + 14.1421i) q^{38} +(12.5830 + 21.7944i) q^{40} -15.7338i q^{41} -43.4980 q^{43} +(-30.8219 + 17.7951i) q^{44} +(-12.5830 + 21.7944i) q^{46} +(-14.6969 + 8.48528i) q^{47} +76.6023i q^{50} +(2.58301 - 4.47390i) q^{52} +(74.0947 + 42.7786i) q^{53} -158.332 q^{55} +(-8.41699 - 14.5787i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-50.1660 - 86.8901i) q^{61} +24.2764i q^{62} -8.00000 q^{64} +(19.9033 - 11.4912i) q^{65} +(-18.3320 + 31.7520i) q^{67} +(44.8048 - 25.8681i) q^{68} +17.7951i q^{71} +(-14.4575 + 25.0411i) q^{73} +(46.5403 + 26.8701i) q^{74} -40.0000 q^{76} +(-59.1660 - 102.479i) q^{79} +(-30.8219 - 17.7951i) q^{80} +(11.1255 + 19.2699i) q^{82} -120.443i q^{83} +230.162 q^{85} +(53.2740 - 30.7578i) q^{86} +(25.1660 - 43.5888i) q^{88} +(-120.789 + 69.7374i) q^{89} -35.5901i q^{92} +(12.0000 - 20.7846i) q^{94} +(-154.110 - 88.9753i) q^{95} +44.4131 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^10 - 64 * q^13 - 16 * q^16 - 80 * q^19 + 32 * q^22 + 132 * q^25 - 16 * q^31 - 208 * q^34 - 152 * q^37 + 16 * q^40 + 160 * q^43 - 16 * q^46 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 + 96 * q^73 - 320 * q^76 - 304 * q^79 + 216 * q^82 + 656 * q^85 + 32 * q^88 + 96 * q^94 - 576 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	7.70549	−	4.44876i	1.54110	−	0.889753i	0.542327	−	0.840167i	$-0.317543\pi$
$5$	7.70549	−	4.44876i	1.54110	−	0.889753i	0.998770	−	0.0495855i	$-0.0157900\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−6.29150	+	10.8972i	−0.629150	+	1.08972i
$11$	−15.4110	−	8.89753i	−1.40100	−	0.808866i	−0.406502	−	0.913650i	$-0.633252\pi$
$11$	−15.4110	−	8.89753i	−1.40100	−	0.808866i	−0.994495	+	0.104784i	$0.966585\pi$
$12$		0			0
$13$	2.58301			0.198693			0.0993464	−	0.995053i	$-0.468325\pi$
$13$	2.58301			0.198693			0.0993464	+	0.995053i	$0.468325\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	22.4024	+	12.9340i	1.31779	+	0.760826i	0.983373	−	0.181599i	$-0.0581273\pi$
$17$	22.4024	+	12.9340i	1.31779	+	0.760826i	0.334417	+	0.942425i	$0.391461\pi$
$18$		0			0
$19$	−10.0000	−	17.3205i	−0.526316	−	0.911606i	−0.999530	−	0.0306583i	$-0.990240\pi$
$19$	−10.0000	−	17.3205i	−0.526316	−	0.911606i	0.473214	−	0.880947i	$-0.343094\pi$
$20$		−	17.7951i		−	0.889753i
$21$		0			0
$22$	25.1660			1.14391
$23$	15.4110	−	8.89753i	0.670042	−	0.386849i	−0.126050	−	0.992024i	$-0.540230\pi$
$23$	15.4110	−	8.89753i	0.670042	−	0.386849i	0.796093	+	0.605175i	$0.206897\pi$
$24$		0			0
$25$	27.0830	−	46.9091i	1.08332	−	1.87637i
$26$	−3.16352	+	1.82646i	−0.121674	+	0.0702485i
$27$		0			0
$28$		0			0
$29$			11.9034i			0.410463i	0.978713	+	0.205232i	$0.0657947\pi$
$29$			11.9034i			0.410463i	−0.978713	+	0.205232i	$0.934205\pi$
$30$		0			0
$31$	8.58301	−	14.8662i	0.276871	−	0.479555i	−0.693734	−	0.720231i	$-0.744036\pi$
$31$	8.58301	−	14.8662i	0.276871	−	0.479555i	0.970605	+	0.240676i	$0.0773692\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	−36.5830			−1.07597
$35$		0			0
$36$		0			0
$37$	−19.0000	−	32.9090i	−0.513514	−	0.889431i	−0.999877	−	0.0156750i	$-0.995010\pi$
$37$	−19.0000	−	32.9090i	−0.513514	−	0.889431i	0.486364	−	0.873757i	$-0.338323\pi$
$38$	24.4949	+	14.1421i	0.644603	+	0.372161i
$39$		0			0
$40$	12.5830	+	21.7944i	0.314575	+	0.544860i
$41$		−	15.7338i		−	0.383752i	−0.981419	−	0.191876i	$-0.938543\pi$
$41$		−	15.7338i		−	0.383752i	0.981419	−	0.191876i	$-0.0614571\pi$
$42$		0			0
$43$	−43.4980			−1.01158			−0.505791	−	0.862656i	$-0.668799\pi$
$43$	−43.4980			−1.01158			−0.505791	+	0.862656i	$0.668799\pi$
$44$	−30.8219	+	17.7951i	−0.700499	+	0.404433i
$45$		0			0
$46$	−12.5830	+	21.7944i	−0.273544	+	0.473791i
$47$	−14.6969	+	8.48528i	−0.312701	+	0.180538i	−0.648134	−	0.761526i	$-0.724451\pi$
$47$	−14.6969	+	8.48528i	−0.312701	+	0.180538i	0.335434	+	0.942064i	$0.391117\pi$
$48$		0			0
$49$		0			0
$50$			76.6023i			1.53205i
$51$		0			0
$52$	2.58301	−	4.47390i	0.0496732	−	0.0860365i
$53$	74.0947	+	42.7786i	1.39801	+	0.807143i	0.994184	−	0.107692i	$-0.0343461\pi$
$53$	74.0947	+	42.7786i	1.39801	+	0.807143i	0.403828	+	0.914835i	$0.367679\pi$
$54$		0			0
$55$	−158.332			−2.87876
$56$		0			0
$57$		0			0
$58$	−8.41699	−	14.5787i	−0.145121	−	0.251356i
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	0.487849	−	0.872928i	$-0.337782\pi$
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	−0.512053	+	0.858954i	$0.671115\pi$
$60$		0			0
$61$	−50.1660	−	86.8901i	−0.822394	−	1.42443i	−0.903895	−	0.427754i	$-0.859305\pi$
$61$	−50.1660	−	86.8901i	−0.822394	−	1.42443i	0.0815014	−	0.996673i	$-0.474028\pi$
$62$			24.2764i			0.391555i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	19.9033	−	11.4912i	0.306205	−	0.176787i
$66$		0			0
$67$	−18.3320	+	31.7520i	−0.273612	+	0.473910i	−0.969784	−	0.243965i	$-0.921552\pi$
$67$	−18.3320	+	31.7520i	−0.273612	+	0.473910i	0.696172	+	0.717875i	$0.254885\pi$
$68$	44.8048	−	25.8681i	0.658895	−	0.380413i
$69$		0			0
$70$		0			0
$71$			17.7951i			0.250635i	0.992117	+	0.125317i	$0.0399949\pi$
$71$			17.7951i			0.250635i	−0.992117	+	0.125317i	$0.960005\pi$
$72$		0			0
$73$	−14.4575	+	25.0411i	−0.198048	+	0.343029i	−0.947895	−	0.318581i	$-0.896794\pi$
$73$	−14.4575	+	25.0411i	−0.198048	+	0.343029i	0.749847	+	0.661611i	$0.230127\pi$
$74$	46.5403	+	26.8701i	0.628923	+	0.363109i
$75$		0			0
$76$	−40.0000			−0.526316
$77$		0			0
$78$		0			0
$79$	−59.1660	−	102.479i	−0.748937	−	1.29720i	−0.948333	−	0.317278i	$-0.897231\pi$
$79$	−59.1660	−	102.479i	−0.748937	−	1.29720i	0.199396	−	0.979919i	$-0.436102\pi$
$80$	−30.8219	−	17.7951i	−0.385274	−	0.222438i
$81$		0			0
$82$	11.1255	+	19.2699i	0.135677	+	0.234999i
$83$		−	120.443i		−	1.45112i	−0.688159	−	0.725560i	$-0.741581\pi$
$83$		−	120.443i		−	1.45112i	0.688159	−	0.725560i	$-0.258419\pi$
$84$		0			0
$85$	230.162			2.70779
$86$	53.2740	−	30.7578i	0.619465	−	0.357648i
$87$		0			0
$88$	25.1660	−	43.5888i	0.285977	−	0.495327i
$89$	−120.789	+	69.7374i	−1.35718	+	0.783566i	−0.989242	−	0.146286i	$-0.953268\pi$
$89$	−120.789	+	69.7374i	−1.35718	+	0.783566i	−0.367934	+	0.929852i	$0.619935\pi$
$90$		0			0
$91$		0			0
$92$		−	35.5901i		−	0.386849i
$93$		0			0
$94$	12.0000	−	20.7846i	0.127660	−	0.221113i
$95$	−154.110	−	88.9753i	−1.62221	−	0.936582i
$96$		0			0
$97$	44.4131			0.457867			0.228933	−	0.973442i	$-0.426476\pi$
$97$	44.4131			0.457867			0.228933	+	0.973442i	$0.426476\pi$
$98$		0			0
$99$		0			0
$100$	−54.1660	−	93.8183i	−0.541660	−	0.938183i
$101$	−27.6088	−	15.9399i	−0.273354	−	0.157821i	0.357057	−	0.934083i	$-0.383780\pi$
$101$	−27.6088	−	15.9399i	−0.273354	−	0.157821i	−0.630411	+	0.776261i	$0.717114\pi$
$102$		0			0
$103$	−2.25098	−	3.89882i	−0.0218542	−	0.0378526i	0.854891	−	0.518807i	$-0.173624\pi$
$103$	−2.25098	−	3.89882i	−0.0218542	−	0.0378526i	−0.876746	+	0.480954i	$0.840290\pi$
$104$			7.30584i			0.0702485i
$105$		0			0
$106$	−120.996			−1.14147
$107$	149.111	−	86.0896i	1.39357	−	0.804575i	0.399857	−	0.916577i	$-0.369060\pi$
$107$	149.111	−	86.0896i	1.39357	−	0.804575i	0.993708	+	0.112002i	$0.0357263\pi$
$108$		0			0
$109$	88.9150	−	154.005i	0.815734	−	1.41289i	−0.0930653	−	0.995660i	$-0.529667\pi$
$109$	88.9150	−	154.005i	0.815734	−	1.41289i	0.908800	−	0.417233i	$-0.137000\pi$
$110$	193.916	−	111.958i	1.76288	−	1.01780i
$111$		0			0
$112$		0			0
$113$			31.3475i			0.277411i	0.990334	+	0.138706i	$0.0442942\pi$
$113$			31.3475i			0.277411i	−0.990334	+	0.138706i	$0.955706\pi$
$114$		0			0
$115$	79.1660	−	137.120i	0.688400	−	1.19234i
$116$	20.6173	+	11.9034i	0.177736	+	0.102616i
$117$		0			0
$118$	2.33202			0.0197629
$119$		0			0
$120$		0			0
$121$	97.8320	+	169.450i	0.808529	+	1.40041i
$122$	122.881	+	70.9455i	1.00722	+	0.581520i
$123$		0			0
$124$	−17.1660	−	29.7324i	−0.138436	−	0.239777i
$125$		−	259.505i		−	2.07604i
$126$		0			0
$127$	214.332			1.68765			0.843827	−	0.536616i	$-0.180297\pi$
$127$	214.332			1.68765			0.843827	+	0.536616i	$0.180297\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−16.2510	+	28.1475i	−0.125008	+	0.216519i
$131$	79.1970	−	45.7244i	0.604557	−	0.349041i	−0.166275	−	0.986079i	$-0.553174\pi$
$131$	79.1970	−	45.7244i	0.604557	−	0.349041i	0.770832	+	0.637038i	$0.219841\pi$
$132$		0			0
$133$		0			0
$134$		−	51.8508i		−	0.386946i
$135$		0			0
$136$	−36.5830	+	63.3636i	−0.268993	+	0.465909i
$137$	92.5699	+	53.4453i	0.675693	+	0.390111i	0.798230	−	0.602353i	$-0.205770\pi$
$137$	92.5699	+	53.4453i	0.675693	+	0.390111i	−0.122537	+	0.992464i	$0.539103\pi$
$138$		0			0
$139$	−121.328			−0.872864			−0.436432	−	0.899737i	$-0.643758\pi$
$139$	−121.328			−0.872864			−0.436432	+	0.899737i	$0.643758\pi$
$140$		0			0
$141$		0			0
$142$	−12.5830	−	21.7944i	−0.0886127	−	0.153482i
$143$	−39.8066	−	22.9824i	−0.278368	−	0.160716i
$144$		0			0
$145$	52.9555	+	91.7217i	0.365211	+	0.632563i
$146$		−	40.8920i		−	0.280082i
$147$		0			0
$148$	−76.0000			−0.513514
$149$	−15.3069	+	8.83744i	−0.102731	+	0.0593117i	−0.550485	−	0.834845i	$-0.685557\pi$
$149$	−15.3069	+	8.83744i	−0.102731	+	0.0593117i	0.447754	+	0.894157i	$0.352224\pi$
$150$		0			0
$151$	25.4170	−	44.0235i	0.168324	−	0.291547i	−0.769506	−	0.638639i	$-0.779498\pi$
$151$	25.4170	−	44.0235i	0.168324	−	0.291547i	0.937831	+	0.347093i	$0.112831\pi$
$152$	48.9898	−	28.2843i	0.322301	−	0.186081i
$153$		0			0
$154$		0			0
$155$		−	152.735i		−	0.985388i
$156$		0			0
$157$	−34.4980	+	59.7523i	−0.219733	+	0.380588i	−0.954726	−	0.297486i	$-0.903852\pi$
$157$	−34.4980	+	59.7523i	−0.219733	+	0.380588i	0.734994	+	0.678074i	$0.237185\pi$
$158$	144.927	+	83.6734i	0.917257	+	0.529578i
$159$		0			0
$160$	50.3320			0.314575
$161$		0			0
$162$		0			0
$163$	83.4980	+	144.623i	0.512258	+	0.887257i	0.999899	+	0.0142125i	$0.00452412\pi$
$163$	83.4980	+	144.623i	0.512258	+	0.887257i	−0.487641	+	0.873044i	$0.662143\pi$
$164$	−27.2518	−	15.7338i	−0.166169	−	0.0959379i
$165$		0			0
$166$	85.1660	+	147.512i	0.513048	+	0.888626i
$167$			120.443i			0.721215i	0.932718	+	0.360608i	$0.117431\pi$
$167$			120.443i			0.721215i	−0.932718	+	0.360608i	$0.882569\pi$
$168$		0			0
$169$	−162.328			−0.960521
$170$	−281.890	+	162.749i	−1.65818	+	0.957348i
$171$		0			0
$172$	−43.4980	+	75.3408i	−0.252896	+	0.438028i
$173$	−79.5540	+	45.9305i	−0.459850	+	0.265494i	−0.711981	−	0.702199i	$-0.752202\pi$
$173$	−79.5540	+	45.9305i	−0.459850	+	0.265494i	0.252131	+	0.967693i	$0.418868\pi$
$174$		0			0
$175$		0			0
$176$			71.1802i			0.404433i
$177$		0			0
$178$	98.6235	−	170.821i	0.554065	−	0.959668i
$179$	−115.433	−	66.6455i	−0.644879	−	0.372321i	0.141612	−	0.989922i	$-0.454771\pi$
$179$	−115.433	−	66.6455i	−0.644879	−	0.372321i	−0.786492	+	0.617601i	$0.788105\pi$
$180$		0			0
$181$	83.0850			0.459033			0.229517	−	0.973305i	$-0.426286\pi$
$181$	83.0850			0.459033			0.229517	+	0.973305i	$0.426286\pi$
$182$		0			0
$183$		0			0
$184$	25.1660	+	43.5888i	0.136772	+	0.236896i
$185$	−292.808	−	169.053i	−1.58275	−	0.913800i
$186$		0			0
$187$	−230.162	−	398.652i	−1.23081	−	2.13183i
$188$			33.9411i			0.180538i
$189$		0			0
$190$	251.660			1.32453
$191$	35.8202	−	20.6808i	0.187540	−	0.108276i	−0.403290	−	0.915072i	$-0.632134\pi$
$191$	35.8202	−	20.6808i	0.187540	−	0.108276i	0.590830	+	0.806796i	$0.298800\pi$
$192$		0			0
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	−0.985742	−	0.168264i	$-0.946184\pi$
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	0.638592	+	0.769546i	$0.279517\pi$
$194$	−54.3947	+	31.4048i	−0.280385	+	0.161880i
$195$		0			0
$196$		0			0
$197$		−	68.8269i		−	0.349375i	−0.984624	−	0.174688i	$-0.944108\pi$
$197$		−	68.8269i		−	0.349375i	0.984624	−	0.174688i	$-0.0558916\pi$
$198$		0			0
$199$	139.247	−	241.183i	0.699734	−	1.21197i	−0.268825	−	0.963189i	$-0.586635\pi$
$199$	139.247	−	241.183i	0.699734	−	1.21197i	0.968559	−	0.248786i	$-0.0800314\pi$
$200$	132.679	+	76.6023i	0.663395	+	0.383012i
$201$		0			0
$202$	45.0850			0.223193
$203$		0			0
$204$		0			0
$205$	−69.9961	−	121.237i	−0.341444	−	0.591399i
$206$	5.51376	+	3.18337i	0.0267658	+	0.0154533i
$207$		0			0
$208$	−5.16601	−	8.94779i	−0.0248366	−	0.0430182i
$209$			355.901i			1.70288i
$210$		0			0
$211$	−211.498			−1.00236			−0.501180	−	0.865343i	$-0.667101\pi$
$211$	−211.498			−1.00236			−0.501180	+	0.865343i	$0.667101\pi$
$212$	148.189	−	85.5571i	0.699006	−	0.403571i
$213$		0			0
$214$	−121.749	+	210.875i	−0.568921	+	0.985399i
$215$	−335.173	+	193.512i	−1.55895	+	0.900058i
$216$		0			0
$217$		0			0
$218$			251.490i			1.15362i
$219$		0			0
$220$	−158.332	+	274.239i	−0.719691	+	1.24654i
$221$	57.8656	+	33.4087i	0.261835	+	0.151171i
$222$		0			0
$223$	222.494			0.997731			0.498866	−	0.866679i	$-0.333750\pi$
$223$	222.494			0.997731			0.498866	+	0.866679i	$0.333750\pi$
$224$		0			0
$225$		0			0
$226$	−22.1660	−	38.3927i	−0.0980797	−	0.169879i
$227$	−88.1816	−	50.9117i	−0.388465	−	0.224281i	0.293030	−	0.956103i	$-0.405337\pi$
$227$	−88.1816	−	50.9117i	−0.388465	−	0.224281i	−0.681495	+	0.731823i	$0.738670\pi$
$228$		0			0
$229$	81.5425	+	141.236i	0.356081	+	0.616750i	0.987302	−	0.158853i	$-0.0507795\pi$
$229$	81.5425	+	141.236i	0.356081	+	0.616750i	−0.631222	+	0.775603i	$0.717446\pi$
$230$			223.915i			0.973545i
$231$		0			0
$232$	−33.6680			−0.145121
$233$	314.244	−	181.429i	1.34869	−	0.778664i	0.360623	−	0.932712i	$-0.382564\pi$
$233$	314.244	−	181.429i	1.34869	−	0.778664i	0.988063	+	0.154047i	$0.0492308\pi$
$234$		0			0
$235$	−75.4980	+	130.766i	−0.321268	+	0.556453i
$236$	−2.85613	+	1.64899i	−0.0121022	+	0.00698724i
$237$		0			0
$238$		0			0
$239$		−	177.126i		−	0.741113i	−0.928810	−	0.370557i	$-0.879167\pi$
$239$		−	177.126i		−	0.741113i	0.928810	−	0.370557i	$-0.120833\pi$
$240$		0			0
$241$	−76.3765	+	132.288i	−0.316915	+	0.548913i	−0.979843	−	0.199771i	$-0.935980\pi$
$241$	−76.3765	+	132.288i	−0.316915	+	0.548913i	0.662928	+	0.748683i	$0.269314\pi$
$242$	−239.639	−	138.355i	−0.990242	−	0.571716i
$243$		0			0
$244$	−200.664			−0.822394
$245$		0			0
$246$		0			0
$247$	−25.8301	−	44.7390i	−0.104575	−	0.181129i
$248$	42.0480	+	24.2764i	0.169548	+	0.0978887i
$249$		0			0
$250$	183.498	+	317.828i	0.733992	+	1.27131i
$251$			356.382i			1.41985i	0.704278	+	0.709924i	$0.251271\pi$
$251$			356.382i			1.41985i	−0.704278	+	0.709924i	$0.748729\pi$
$252$		0			0
$253$	−316.664			−1.25164
$254$	−262.502	+	151.556i	−1.03347	+	0.596676i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	51.5882	−	29.7844i	0.200732	−	0.115893i	−0.396265	−	0.918136i	$-0.629694\pi$
$257$	51.5882	−	29.7844i	0.200732	−	0.115893i	0.596997	+	0.802244i	$0.296360\pi$
$258$		0			0
$259$		0			0
$260$		−	45.9647i		−	0.176787i
$261$		0			0
$262$	−64.6640	+	112.001i	−0.246809	+	0.427486i
$263$	6.42629	+	3.71022i	0.0244346	+	0.0141073i	0.512168	−	0.858886i	$-0.328843\pi$
$263$	6.42629	+	3.71022i	0.0244346	+	0.0141073i	−0.487733	+	0.872993i	$0.662176\pi$
$264$		0			0
$265$	761.247			2.87263
$266$		0			0
$267$		0			0
$268$	36.6640	+	63.5040i	0.136806	+	0.236955i
$269$	372.571	+	215.104i	1.38502	+	0.799642i	0.992749	−	0.120207i	$-0.0383559\pi$
$269$	372.571	+	215.104i	1.38502	+	0.799642i	0.392272	+	0.919849i	$0.371689\pi$
$270$		0			0
$271$	20.5830	+	35.6508i	0.0759520	+	0.131553i	0.901500	−	0.432779i	$-0.142467\pi$
$271$	20.5830	+	35.6508i	0.0759520	+	0.131553i	−0.825548	+	0.564332i	$0.809134\pi$
$272$		−	103.472i		−	0.380413i
$273$		0			0
$274$	−151.166			−0.551701
$275$	−834.751	+	481.944i	−3.03546	+	1.75252i
$276$		0			0
$277$	−16.0000	+	27.7128i	−0.0577617	+	0.100046i	−0.893460	−	0.449142i	$-0.851730\pi$
$277$	−16.0000	+	27.7128i	−0.0577617	+	0.100046i	0.835699	+	0.549188i	$0.185063\pi$
$278$	148.596	−	85.7919i	0.534518	−	0.308604i
$279$		0			0
$280$		0			0
$281$			17.0907i			0.0608211i	0.999537	+	0.0304106i	$0.00968147\pi$
$281$			17.0907i			0.0608211i	−0.999537	+	0.0304106i	$0.990319\pi$
$282$		0			0
$283$	−219.830	+	380.757i	−0.776785	+	1.34543i	0.157001	+	0.987598i	$0.449817\pi$
$283$	−219.830	+	380.757i	−0.776785	+	1.34543i	−0.933786	+	0.357832i	$0.883516\pi$
$284$	30.8219	+	17.7951i	0.108528	+	0.0626587i
$285$		0			0
$286$	65.0039			0.227286
$287$		0			0
$288$		0			0
$289$	190.079	+	329.227i	0.657713	+	1.13919i
$290$	−129.714	−	74.8904i	−0.447290	−	0.258243i
$291$		0			0
$292$	28.9150	+	50.0823i	0.0990241	+	0.171515i
$293$		−	394.377i		−	1.34600i	−0.739644	−	0.672998i	$-0.765006\pi$
$293$		−	394.377i		−	1.34600i	0.739644	−	0.672998i	$-0.234994\pi$
$294$		0			0
$295$	−14.6719			−0.0497353
$296$	93.0806	−	53.7401i	0.314462	−	0.181554i
$297$		0			0
$298$	12.4980	−	21.6472i	0.0419397	−	0.0726417i
$299$	39.8066	−	22.9824i	0.133133	−	0.0768641i
$300$		0			0
$301$		0			0
$302$			71.8901i			0.238047i
$303$		0			0
$304$	−40.0000	+	69.2820i	−0.131579	+	0.227901i
$305$	−773.107	−	446.353i	−2.53478	−	1.46345i
$306$		0			0
$307$	−23.3360			−0.0760129			−0.0380064	−	0.999277i	$-0.512101\pi$
$307$	−23.3360			−0.0760129			−0.0380064	+	0.999277i	$0.512101\pi$
$308$		0			0
$309$		0			0
$310$	108.000	+	187.061i	0.348387	+	0.603424i
$311$	456.617	+	263.628i	1.46822	+	0.847678i	0.999366	−	0.0355970i	$-0.0113333\pi$
$311$	456.617	+	263.628i	1.46822	+	0.847678i	0.468855	+	0.883275i	$0.344667\pi$
$312$		0			0
$313$	147.664	+	255.762i	0.471770	+	0.817130i	0.999478	−	0.0322959i	$-0.0102819\pi$
$313$	147.664	+	255.762i	0.471770	+	0.817130i	−0.527708	+	0.849426i	$0.676949\pi$
$314$		−	97.5752i		−	0.310749i
$315$		0			0
$316$	−236.664			−0.748937
$317$	93.0758	−	53.7373i	0.293614	−	0.169518i	−0.345956	−	0.938251i	$-0.612445\pi$
$317$	93.0758	−	53.7373i	0.293614	−	0.169518i	0.639571	+	0.768732i	$0.279112\pi$
$318$		0			0
$319$	105.911	−	183.443i	0.332010	−	0.575058i
$320$	−61.6439	+	35.5901i	−0.192637	+	0.111219i
$321$		0			0
$322$		0			0
$323$		−	517.362i		−	1.60174i
$324$		0			0
$325$	69.9555	−	121.167i	0.215248	−	0.372820i
$326$	−204.528	−	118.084i	−0.627385	−	0.362221i
$327$		0			0
$328$	44.5020			0.135677
$329$		0			0
$330$		0			0
$331$	136.745	+	236.849i	0.413127	+	0.715557i	0.995230	−	0.0975581i	$-0.0311032\pi$
$331$	136.745	+	236.849i	0.413127	+	0.715557i	−0.582103	+	0.813115i	$0.697770\pi$
$332$	−208.613	−	120.443i	−0.628353	−	0.362780i
$333$		0			0
$334$	−85.1660	−	147.512i	−0.254988	−	0.441652i
$335$			326.219i			0.973789i
$336$		0			0
$337$	−341.166			−1.01236			−0.506181	−	0.862427i	$-0.668943\pi$
$337$	−341.166			−1.01236			−0.506181	+	0.862427i	$0.668943\pi$
$338$	198.810	−	114.783i	0.588197	−	0.339596i
$339$		0			0
$340$	230.162	−	398.652i	0.676947	−	1.17251i
$341$	−264.545	+	152.735i	−0.775791	+	0.447903i
$342$		0			0
$343$		0			0
$344$		−	123.031i		−	0.357648i
$345$		0			0
$346$	64.9555	−	112.506i	0.187733	−	0.325163i
$347$	−100.736	−	58.1602i	−0.290307	−	0.167609i	0.347773	−	0.937579i	$-0.386938\pi$
$347$	−100.736	−	58.1602i	−0.290307	−	0.167609i	−0.638080	+	0.769970i	$0.720271\pi$
$348$		0			0
$349$	−158.324			−0.453651			−0.226825	−	0.973935i	$-0.572835\pi$
$349$	−158.324			−0.453651			−0.226825	+	0.973935i	$0.572835\pi$
$350$		0			0
$351$		0			0
$352$	−50.3320	−	87.1776i	−0.142989	−	0.247664i
$353$	199.480	+	115.170i	0.565098	+	0.326260i	0.755189	−	0.655507i	$-0.227545\pi$
$353$	199.480	+	115.170i	0.565098	+	0.326260i	−0.190091	+	0.981766i	$0.560878\pi$
$354$		0			0
$355$	79.1660	+	137.120i	0.223003	+	0.386252i
$356$			278.949i			0.783566i
$357$		0			0
$358$	188.502			0.526542
$359$	148.695	−	85.8492i	0.414193	−	0.239134i	−0.278397	−	0.960466i	$-0.589803\pi$
$359$	148.695	−	85.8492i	0.414193	−	0.239134i	0.692590	+	0.721332i	$0.256470\pi$
$360$		0			0
$361$	−19.5000	+	33.7750i	−0.0540166	+	0.0935595i
$362$	−101.758	+	58.7499i	−0.281099	+	0.162293i
$363$		0			0
$364$		0			0
$365$			257.272i			0.704856i
$366$		0			0
$367$	−258.745	+	448.160i	−0.705027	+	1.22114i	0.261654	+	0.965162i	$0.415732\pi$
$367$	−258.745	+	448.160i	−0.705027	+	1.22114i	−0.966682	+	0.255982i	$0.917601\pi$
$368$	−61.6439	−	35.5901i	−0.167511	−	0.0967123i
$369$		0			0
$370$	478.154			1.29231
$371$		0			0
$372$		0			0
$373$	116.668	+	202.075i	0.312783	+	0.541756i	0.978964	−	0.204035i	$-0.0654055\pi$
$373$	116.668	+	202.075i	0.312783	+	0.541756i	−0.666181	+	0.745790i	$0.732072\pi$
$374$	563.780	+	325.498i	1.50743	+	0.870316i
$375$		0			0
$376$	−24.0000	−	41.5692i	−0.0638298	−	0.110556i
$377$			30.7466i			0.0815560i
$378$		0			0
$379$	441.166			1.16403			0.582013	−	0.813179i	$-0.302265\pi$
$379$	441.166			1.16403			0.582013	+	0.813179i	$0.302265\pi$
$380$	−308.219	+	177.951i	−0.811104	+	0.468291i
$381$		0			0
$382$	−29.2470	+	50.6574i	−0.0765630	+	0.132611i
$383$	−184.515	+	106.530i	−0.481763	+	0.278146i	−0.721151	−	0.692778i	$-0.756387\pi$
$383$	−184.515	+	106.530i	−0.481763	+	0.278146i	0.239388	+	0.970924i	$0.423053\pi$
$384$		0			0
$385$		0			0
$386$		−	189.505i		−	0.490945i
$387$		0			0
$388$	44.4131	−	76.9257i	0.114467	−	0.198262i
$389$	489.387	+	282.548i	1.25806	+	0.726344i	0.972698	−	0.232074i	$-0.0745512\pi$
$389$	489.387	+	282.548i	1.25806	+	0.726344i	0.285367	+	0.958418i	$0.407885\pi$
$390$		0			0
$391$	460.324			1.17730
$392$		0			0
$393$		0			0
$394$	48.6680	+	84.2954i	0.123523	+	0.213948i
$395$	−911.806	−	526.431i	−2.30837	−	1.33274i
$396$		0			0
$397$	−249.162	−	431.561i	−0.627612	−	1.08706i	−0.988029	−	0.154265i	$-0.950699\pi$
$397$	−249.162	−	431.561i	−0.627612	−	1.08706i	0.360417	−	0.932791i	$-0.382634\pi$
$398$			393.850i			0.989573i
$399$		0			0
$400$	−216.664			−0.541660
$401$	−167.483	+	96.6962i	−0.417662	+	0.241138i	−0.694077	−	0.719901i	$-0.744187\pi$
$401$	−167.483	+	96.6962i	−0.417662	+	0.241138i	0.276414	+	0.961039i	$0.410854\pi$
$402$		0			0
$403$	22.1699	−	38.3995i	0.0550123	−	0.0952841i
$404$	−55.2176	+	31.8799i	−0.136677	+	0.0789106i
$405$		0			0
$406$		0			0
$407$			676.212i			1.66145i
$408$		0			0
$409$	227.122	−	393.386i	0.555309	−	0.961824i	−0.442570	−	0.896734i	$-0.645933\pi$
$409$	227.122	−	393.386i	0.555309	−	0.961824i	0.997879	−	0.0650902i	$-0.0207335\pi$
$410$	171.455	+	98.9894i	0.418182	+	0.241438i
$411$		0			0
$412$	−9.00394			−0.0218542
$413$		0			0
$414$		0			0
$415$	−535.822	−	928.071i	−1.29114	−	2.23632i
$416$	12.6541	+	7.30584i	0.0304185	+	0.0175621i
$417$		0			0
$418$	−251.660	−	435.888i	−0.602058	−	1.04279i
$419$			339.411i			0.810051i	0.914305	+	0.405025i	$0.132737\pi$
$419$			339.411i			0.810051i	−0.914305	+	0.405025i	$0.867263\pi$
$420$		0			0
$421$	247.320			0.587459			0.293729	−	0.955889i	$-0.405104\pi$
$421$	247.320			0.587459			0.293729	+	0.955889i	$0.405104\pi$
$422$	259.031	−	149.552i	0.613818	−	0.354388i
$423$		0			0
$424$	−120.996	+	209.571i	−0.285368	+	0.494272i
$425$	1213.45	−	700.586i	2.85518	−	1.64844i
$426$		0			0
$427$		0			0
$428$		−	344.358i		−	0.804575i
$429$		0			0
$430$	273.668	−	474.007i	0.636437	−	1.10234i
$431$	395.271	+	228.210i	0.917101	+	0.529489i	0.882709	−	0.469920i	$-0.155717\pi$
$431$	395.271	+	228.210i	0.917101	+	0.529489i	0.0343923	+	0.999408i	$0.489050\pi$
$432$		0			0
$433$	−637.984			−1.47340			−0.736702	−	0.676217i	$-0.763618\pi$
$433$	−637.984			−1.47340			−0.736702	+	0.676217i	$0.763618\pi$
$434$		0			0
$435$		0			0
$436$	−177.830	−	308.011i	−0.407867	−	0.706447i
$437$	−308.219	−	177.951i	−0.705308	−	0.407210i
$438$		0			0
$439$	392.073	+	679.091i	0.893105	+	1.54690i	0.836132	+	0.548528i	$0.184812\pi$
$439$	392.073	+	679.091i	0.893105	+	1.54690i	0.0569728	+	0.998376i	$0.481855\pi$
$440$		−	447.831i		−	1.01780i
$441$		0			0
$442$	−94.4941			−0.213788
$443$	−408.956	+	236.111i	−0.923151	+	0.532981i	−0.884639	−	0.466277i	$-0.845595\pi$
$443$	−408.956	+	236.111i	−0.923151	+	0.532981i	−0.0385120	+	0.999258i	$0.512262\pi$
$444$		0			0
$445$	−620.490	+	1074.72i	−1.39436	+	2.41510i
$446$	−272.499	+	157.327i	−0.610983	+	0.352751i
$447$		0			0
$448$		0			0
$449$			739.852i			1.64778i	0.566752	+	0.823888i	$0.308200\pi$
$449$			739.852i			1.64778i	−0.566752	+	0.823888i	$0.691800\pi$
$450$		0			0
$451$	−139.992	+	242.473i	−0.310404	+	0.537635i
$452$	54.2954	+	31.3475i	0.120123	+	0.0693528i
$453$		0			0
$454$	144.000			0.317181
$455$		0			0
$456$		0			0
$457$	124.162	+	215.055i	0.271689	+	0.470580i	0.969295	−	0.245903i	$-0.0790843\pi$
$457$	124.162	+	215.055i	0.271689	+	0.470580i	−0.697605	+	0.716482i	$0.745751\pi$
$458$	−199.737	−	115.318i	−0.436108	−	0.251787i
$459$		0			0
$460$	−158.332	−	274.239i	−0.344200	−	0.596172i
$461$		−	355.970i		−	0.772168i	−0.922464	−	0.386084i	$-0.873827\pi$
$461$		−	355.970i		−	0.772168i	0.922464	−	0.386084i	$-0.126173\pi$
$462$		0			0
$463$	−6.33202			−0.0136761			−0.00683804	−	0.999977i	$-0.502177\pi$
$463$	−6.33202			−0.0136761			−0.00683804	+	0.999977i	$0.502177\pi$
$464$	41.2347	−	23.8069i	0.0888679	−	0.0513079i
$465$		0			0
$466$	−256.579	+	444.408i	−0.550599	+	0.953665i
$467$	−760.968	+	439.345i	−1.62948	+	0.940782i	−0.645236	+	0.763984i	$0.723241\pi$
$467$	−760.968	+	439.345i	−1.62948	+	0.940782i	−0.984247	+	0.176799i	$0.943426\pi$
$468$		0			0
$469$		0			0
$470$		−	213.541i		−	0.454342i
$471$		0			0
$472$	2.33202	−	4.03918i	0.00494072	−	0.00855758i
$473$	670.347	+	387.025i	1.41722	+	0.818235i
$474$		0			0
$475$	−1083.32			−2.28067
$476$		0			0
$477$		0			0
$478$	125.247	+	216.934i	0.262023	+	0.453837i
$479$	194.333	+	112.198i	0.405705	+	0.234234i	0.688943	−	0.724816i	$-0.258075\pi$
$479$	194.333	+	112.198i	0.405705	+	0.234234i	−0.283238	+	0.959050i	$0.591409\pi$
$480$		0			0
$481$	−49.0771	−	85.0040i	−0.102031	−	0.176724i
$482$		−	216.025i		−	0.448185i
$483$		0			0
$484$	391.328			0.808529
$485$	342.224	−	197.583i	0.705617	−	0.407388i
$486$		0			0
$487$	358.745	−	621.365i	0.736643	−	1.27590i	−0.217356	−	0.976092i	$-0.569743\pi$
$487$	358.745	−	621.365i	0.736643	−	1.27590i	0.953999	−	0.299810i	$-0.0969234\pi$
$488$	245.762	−	141.891i	0.503611	−	0.290760i
$489$		0			0
$490$		0			0
$491$		−	274.002i		−	0.558050i	−0.960284	−	0.279025i	$-0.909989\pi$
$491$		−	274.002i		−	0.558050i	0.960284	−	0.279025i	$-0.0900112\pi$
$492$		0			0
$493$	−153.959	+	266.666i	−0.312291	+	0.540904i
$494$	63.2704	+	36.5292i	0.128078	+	0.0739458i
$495$		0			0
$496$	−68.6640			−0.138436
$497$		0			0
$498$		0			0
$499$	364.405	+	631.168i	0.730271	+	1.26487i	0.956767	+	0.290854i	$0.0939395\pi$
$499$	364.405	+	631.168i	0.730271	+	1.26487i	−0.226496	+	0.974012i	$0.572727\pi$
$500$	−449.477	−	259.505i	−0.898953	−	0.519011i
$501$		0			0
$502$	−252.000	−	436.477i	−0.501992	−	0.869476i
$503$			594.657i			1.18222i	0.806590	+	0.591111i	$0.201310\pi$
$503$			594.657i			1.18222i	−0.806590	+	0.591111i	$0.798690\pi$
$504$		0			0
$505$	−283.652			−0.561688
$506$	387.833	−	223.915i	0.766468	−	0.442520i
$507$		0			0
$508$	214.332	−	371.234i	0.421913	−	0.730775i
$509$	860.842	−	497.007i	1.69124	−	0.976439i	0.737723	−	0.675103i	$-0.235901\pi$
$509$	860.842	−	497.007i	1.69124	−	0.976439i	0.953518	−	0.301336i	$-0.0974325\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−42.1216	+	72.9567i	−0.0819486	+	0.141939i
$515$	−34.6899	−	20.0282i	−0.0673589	−	0.0388897i
$516$		0			0
$517$	301.992			0.584124
$518$		0			0
$519$		0			0
$520$	32.5020	+	56.2951i	0.0625038	+	0.108260i
$521$	−35.3735	−	20.4229i	−0.0678955	−	0.0391995i	0.465668	−	0.884960i	$-0.345814\pi$
$521$	−35.3735	−	20.4229i	−0.0678955	−	0.0391995i	−0.533563	+	0.845760i	$0.679147\pi$
$522$		0			0
$523$	116.000	+	200.918i	0.221797	+	0.384164i	0.955354	−	0.295464i	$-0.0954743\pi$
$523$	116.000	+	200.918i	0.221797	+	0.384164i	−0.733556	+	0.679629i	$0.762141\pi$
$524$		−	182.898i		−	0.349041i
$525$		0			0
$526$	−10.4941			−0.0199507
$527$	384.560	−	222.026i	0.729716	−	0.421302i
$528$		0			0
$529$	−106.168	+	183.888i	−0.200696	+	0.347615i
$530$	−932.333	+	538.283i	−1.75912	+	1.01563i
$531$		0			0
$532$		0			0
$533$		−	40.6405i		−	0.0762487i
$534$		0			0
$535$	765.984	−	1326.72i	1.43175	−	2.47986i
$536$	−89.8082	−	51.8508i	−0.167553	−	0.0967365i
$537$		0			0
$538$	−608.405			−1.13086
$539$		0			0
$540$		0			0
$541$	−125.166	−	216.794i	−0.231360	−	0.400728i	0.726848	−	0.686798i	$-0.240984\pi$
$541$	−125.166	−	216.794i	−0.231360	−	0.400728i	−0.958209	+	0.286070i	$0.907651\pi$
$542$	−50.4179	−	29.1088i	−0.0930219	−	0.0537062i
$543$		0			0
$544$	73.1660	+	126.727i	0.134496	+	0.232954i
$545$		−	1582.25i		−	2.90321i
$546$		0			0
$547$	888.324			1.62399			0.811996	−	0.583662i	$-0.198381\pi$
$547$	888.324			1.62399			0.811996	+	0.583662i	$0.198381\pi$
$548$	185.140	−	106.891i	0.337846	−	0.195056i
$549$		0			0
$550$	681.571	−	1180.52i	1.23922	−	2.14639i
$551$	206.173	−	119.034i	0.374180	−	0.216033i
$552$		0			0
$553$		0			0
$554$		−	45.2548i		−	0.0816874i
$555$		0			0
$556$	−121.328	+	210.146i	−0.218216	+	0.377961i
$557$	−273.931	−	158.154i	−0.491798	−	0.283940i	0.233522	−	0.972351i	$-0.424975\pi$
$557$	−273.931	−	158.154i	−0.491798	−	0.283940i	−0.725320	+	0.688412i	$0.758308\pi$
$558$		0			0
$559$	−112.356			−0.200994
$560$		0			0
$561$		0			0
$562$	−12.0850	−	20.9318i	−0.0215035	−	0.0372452i
$563$	−50.6356	−	29.2345i	−0.0899390	−	0.0519263i	0.454356	−	0.890820i	$-0.349869\pi$
$563$	−50.6356	−	29.2345i	−0.0899390	−	0.0519263i	−0.544295	+	0.838894i	$0.683203\pi$
$564$		0			0
$565$	139.458	+	241.547i	0.246827	+	0.427518i
$566$		−	621.773i		−	1.09854i
$567$		0			0
$568$	−50.3320			−0.0886127
$569$	191.968	−	110.833i	0.337378	−	0.194785i	−0.321734	−	0.946830i	$-0.604266\pi$
$569$	191.968	−	110.833i	0.337378	−	0.194785i	0.659112	+	0.752045i	$0.270932\pi$
$570$		0			0
$571$	243.822	−	422.312i	0.427009	−	0.739601i	−0.569597	−	0.821924i	$-0.692901\pi$
$571$	243.822	−	422.312i	0.427009	−	0.739601i	0.996606	+	0.0823230i	$0.0262339\pi$
$572$	−79.6132	+	45.9647i	−0.139184	+	0.0803579i
$573$		0			0
$574$		0			0
$575$		−	963.887i		−	1.67633i
$576$		0			0
$577$	243.664	−	422.039i	0.422295	−	0.731436i	−0.573869	−	0.818947i	$-0.694558\pi$
$577$	243.664	−	422.039i	0.422295	−	0.731436i	0.996164	+	0.0875114i	$0.0278914\pi$
$578$	−465.597	−	268.812i	−0.805531	−	0.465073i
$579$		0			0
$580$	211.822			0.365211
$581$		0			0
$582$		0			0
$583$	−761.247	−	1318.52i	−1.30574	−	2.26161i
$584$	−70.8271	−	40.8920i	−0.121279	−	0.0700206i
$585$		0			0
$586$	278.867	+	483.011i	0.475882	+	0.824251i
$587$		−	445.701i		−	0.759286i	−0.925133	−	0.379643i	$-0.876047\pi$
$587$		−	445.701i		−	0.759286i	0.925133	−	0.379643i	$-0.123953\pi$
$588$		0			0
$589$	−343.320			−0.582887
$590$	17.9694	−	10.3746i	0.0304565	−	0.0175841i
$591$		0			0
$592$	−76.0000	+	131.636i	−0.128378	+	0.222358i
$593$	−239.584	+	138.324i	−0.404020	+	0.233261i	−0.688217	−	0.725505i	$-0.741606\pi$
$593$	−239.584	+	138.324i	−0.404020	+	0.233261i	0.284197	+	0.958766i	$0.408273\pi$
$594$		0			0
$595$		0			0
$596$			35.3498i			0.0593117i
$597$		0			0
$598$	−32.5020	+	56.2951i	−0.0543511	+	0.0941389i
$599$	71.3426	+	41.1897i	0.119103	+	0.0687641i	0.558368	−	0.829593i	$-0.311428\pi$
$599$	71.3426	+	41.1897i	0.119103	+	0.0687641i	−0.439265	+	0.898358i	$0.644761\pi$
$600$		0			0
$601$	−418.000			−0.695507			−0.347754	−	0.937586i	$-0.613055\pi$
$601$	−418.000			−0.695507			−0.347754	+	0.937586i	$0.613055\pi$
$602$		0			0
$603$		0			0
$604$	−50.8340	−	88.0471i	−0.0841622	−	0.145773i
$605$	1507.69	+	870.463i	2.49204	+	1.43878i
$606$		0			0
$607$	−38.4209	−	66.5470i	−0.0632964	−	0.109633i	0.832641	−	0.553814i	$-0.186828\pi$
$607$	−38.4209	−	66.5470i	−0.0632964	−	0.109633i	−0.895937	+	0.444181i	$0.853495\pi$
$608$		−	113.137i		−	0.186081i
$609$		0			0
$610$	1262.48			2.06964
$611$	−37.9623	+	21.9175i	−0.0621314	+	0.0358716i
$612$		0			0
$613$	−29.6640	+	51.3796i	−0.0483916	+	0.0838167i	−0.889207	−	0.457506i	$-0.848743\pi$
$613$	−29.6640	+	51.3796i	−0.0483916	+	0.0838167i	0.840815	+	0.541323i	$0.182076\pi$
$614$	28.5806	−	16.5010i	0.0465482	−	0.0268746i
$615$		0			0
$616$		0			0
$617$			29.1143i			0.0471869i	0.999722	+	0.0235935i	$0.00751073\pi$
$617$			29.1143i			0.0471869i	−0.999722	+	0.0235935i	$0.992489\pi$
$618$		0			0
$619$	−227.822	+	394.600i	−0.368049	+	0.637479i	−0.989260	−	0.146164i	$-0.953307\pi$
$619$	−227.822	+	394.600i	−0.368049	+	0.637479i	0.621212	+	0.783643i	$0.286641\pi$
$620$	−264.545	−	152.735i	−0.426685	−	0.246347i
$621$		0			0
$622$	−745.652			−1.19880
$623$		0			0
$624$		0			0
$625$	−477.403	−	826.887i	−0.763845	−	1.32302i
$626$	−361.702	−	208.828i	−0.577798	−	0.333592i
$627$		0			0
$628$	68.9961	+	119.505i	0.109866	+	0.190294i
$629$		−	982.987i		−	1.56278i
$630$		0			0
$631$	−45.0039			−0.0713216			−0.0356608	−	0.999364i	$-0.511354\pi$
$631$	−45.0039			−0.0713216			−0.0356608	+	0.999364i	$0.511354\pi$
$632$	289.853	−	167.347i	0.458628	−	0.264789i
$633$		0			0
$634$	−75.9961	+	131.629i	−0.119868	+	0.207617i
$635$	1651.53	−	953.513i	2.60084	−	1.50159i
$636$		0			0
$637$		0			0
$638$			299.562i			0.469533i
$639$		0			0
$640$	50.3320	−	87.1776i	0.0786438	−	0.136215i
$641$	555.315	+	320.611i	0.866327	+	0.500174i	0.866126	−	0.499826i	$-0.166603\pi$
$641$	555.315	+	320.611i	0.866327	+	0.500174i	0.000200774		1.00000i	$0.499936\pi$
$642$		0			0
$643$	−604.000			−0.939347			−0.469673	−	0.882840i	$-0.655628\pi$
$643$	−604.000			−0.939347			−0.469673	+	0.882840i	$0.655628\pi$
$644$		0			0
$645$		0			0
$646$	365.830	+	633.636i	0.566300	+	0.980861i
$647$	155.538	+	89.7998i	0.240398	+	0.138794i	0.615360	−	0.788246i	$-0.289011\pi$
$647$	155.538	+	89.7998i	0.240398	+	0.138794i	−0.374961	+	0.927040i	$0.622344\pi$
$648$		0			0
$649$	14.6719	+	25.4125i	0.0226070	+	0.0391564i
$650$			197.864i			0.304406i
$651$		0			0
$652$	333.992			0.512258
$653$	339.562	−	196.046i	0.520003	−	0.300224i	−0.216933	−	0.976186i	$-0.569605\pi$
$653$	339.562	−	196.046i	0.520003	−	0.300224i	0.736936	+	0.675963i	$0.236272\pi$
$654$		0			0
$655$	406.834	−	704.657i	0.621121	−	1.07581i
$656$	−54.5036	+	31.4676i	−0.0830847	+	0.0479690i
$657$		0			0
$658$		0			0
$659$			1266.54i			1.92191i	0.276701	+	0.960956i	$0.410759\pi$
$659$			1266.54i			1.92191i	−0.276701	+	0.960956i	$0.589241\pi$
$660$		0			0
$661$	−458.822	+	794.703i	−0.694133	+	1.20227i	0.276339	+	0.961060i	$0.410879\pi$
$661$	−458.822	+	794.703i	−0.694133	+	1.20227i	−0.970472	+	0.241214i	$0.922454\pi$
$662$	−334.956	−	193.387i	−0.505975	−	0.292125i
$663$		0			0
$664$	340.664			0.513048
$665$		0			0
$666$		0			0
$667$	105.911	+	183.443i	0.158787	+	0.275028i
$668$	208.613	+	120.443i	0.312295	+	0.180304i
$669$		0			0
$670$	−230.672	−	399.535i	−0.344286	−	0.596322i
$671$			1785.41i			2.66083i
$672$		0			0
$673$	−152.008			−0.225866			−0.112933	−	0.993603i	$-0.536025\pi$
$673$	−152.008			−0.225866			−0.112933	+	0.993603i	$0.536025\pi$
$674$	417.841	−	241.241i	0.619943	−	0.357924i
$675$		0			0
$676$	−162.328	+	281.160i	−0.240130	+	0.415918i
$677$	141.316	−	81.5891i	0.208739	−	0.120516i	−0.391986	−	0.919971i	$-0.628212\pi$
$677$	141.316	−	81.5891i	0.208739	−	0.120516i	0.600725	+	0.799456i	$0.294879\pi$
$678$		0			0
$679$		0			0
$680$			650.997i			0.957348i
$681$		0			0
$682$	216.000	−	374.123i	0.316716	−	0.548567i
$683$	281.384	+	162.457i	0.411982	+	0.237858i	0.691641	−	0.722241i	$-0.256888\pi$
$683$	281.384	+	162.457i	0.411982	+	0.237858i	−0.279659	+	0.960099i	$0.590221\pi$
$684$		0			0
$685$	951.061			1.38841
$686$		0			0
$687$		0			0
$688$	86.9961	+	150.682i	0.126448	+	0.219014i
$689$	191.387	+	110.497i	0.277775	+	0.160373i
$690$		0			0
$691$	−609.490	−	1055.67i	−0.882041	−	1.52774i	−0.849068	−	0.528283i	$-0.822836\pi$
$691$	−609.490	−	1055.67i	−0.882041	−	1.52774i	−0.0329725	−	0.999456i	$-0.510497\pi$
$692$			183.722i			0.265494i
$693$		0			0
$694$	164.502			0.237035
$695$	−934.892	+	539.760i	−1.34517	+	0.776633i
$696$		0			0
$697$	203.502	−	352.476i	0.291968	−	0.505704i
$698$	193.907	−	111.952i	0.277803	−	0.160390i
$699$		0			0
$700$		0			0
$701$		−	427.202i		−	0.609417i	−0.952446	−	0.304709i	$-0.901441\pi$
$701$		−	427.202i		−	0.609417i	0.952446	−	0.304709i	$-0.0985591\pi$
$702$		0			0
$703$	−380.000	+	658.179i	−0.540541	+	0.936244i
$704$	123.288	+	71.1802i	0.175125	+	0.101108i
$705$		0			0
$706$	−325.749			−0.461401
$707$		0			0
$708$		0			0
$709$	−35.7490	−	61.9191i	−0.0504217	−	0.0873330i	0.839713	−	0.543031i	$-0.182723\pi$
$709$	−35.7490	−	61.9191i	−0.0504217	−	0.0873330i	−0.890135	+	0.455697i	$0.849390\pi$
$710$	−193.916	−	111.958i	−0.273122	−	0.157687i
$711$		0			0
$712$	−197.247	−	341.642i	−0.277032	−	0.479834i
$713$		−	305.470i		−	0.428429i
$714$		0			0
$715$	−408.972			−0.571989
$716$	−230.867	+	133.291i	−0.322440	+	0.186161i
$717$		0			0
$718$	−121.409	+	210.287i	−0.169093	+	0.292879i
$719$	−96.1545	+	55.5148i	−0.133734	+	0.0772112i	−0.565374	−	0.824835i	$-0.691268\pi$
$719$	−96.1545	+	55.5148i	−0.133734	+	0.0772112i	0.431641	+	0.902046i	$0.357935\pi$
$720$		0			0
$721$		0			0
$722$		−	55.1543i		−	0.0763910i
$723$		0			0
$724$	83.0850	−	143.907i	0.114758	−	0.198767i
$725$	558.380	+	322.381i	0.770179	+	0.444663i
$726$		0			0
$727$	−1338.82			−1.84157			−0.920783	−	0.390076i	$-0.872449\pi$
$727$	−1338.82			−1.84157			−0.920783	+	0.390076i	$0.872449\pi$
$728$		0			0
$729$		0			0
$730$	−181.919	−	315.093i	−0.249204	−	0.431634i
$731$	−974.461	−	562.606i	−1.33305	−	0.769638i
$732$		0			0
$733$	−24.5385	−	42.5020i	−0.0334769	−	0.0579836i	0.848802	−	0.528712i	$-0.177325\pi$
$733$	−24.5385	−	42.5020i	−0.0334769	−	0.0579836i	−0.882278	+	0.470728i	$0.843991\pi$
$734$		−	731.842i		−	0.997059i
$735$		0			0
$736$	100.664			0.136772
$737$	565.028	−	326.219i	0.766660	−	0.442631i
$738$		0			0
$739$	−715.158	+	1238.69i	−0.967738	+	1.67617i	−0.265665	+	0.964065i	$0.585592\pi$
$739$	−715.158	+	1238.69i	−0.967738	+	1.67617i	−0.702073	+	0.712105i	$0.747742\pi$
$740$	−585.617	+	338.106i	−0.791374	+	0.456900i
$741$		0			0
$742$		0			0
$743$			875.736i			1.17865i	0.807896	+	0.589325i	$0.200606\pi$
$743$			875.736i			1.17865i	−0.807896	+	0.589325i	$0.799394\pi$
$744$		0			0
$745$	−78.6314	+	136.194i	−0.105546	+	0.182810i
$746$	−285.777	−	164.993i	−0.383079	−	0.221171i
$747$		0			0
$748$	−920.648			−1.23081
$749$		0			0
$750$		0			0
$751$	−160.413	−	277.844i	−0.213599	−	0.369965i	0.739239	−	0.673443i	$-0.235185\pi$
$751$	−160.413	−	277.844i	−0.213599	−	0.369965i	−0.952838	+	0.303478i	$0.901852\pi$
$752$	58.7878	+	33.9411i	0.0781752	+	0.0451345i
$753$		0			0
$754$	−21.7411	−	37.6568i	−0.0288344	−	0.0499427i
$755$		−	452.297i		−	0.599069i
$756$		0			0
$757$	289.830			0.382867			0.191433	−	0.981506i	$-0.438686\pi$
$757$	289.830			0.382867			0.191433	+	0.981506i	$0.438686\pi$
$758$	−540.316	+	311.951i	−0.712818	+	0.411545i
$759$		0			0
$760$	251.660	−	435.888i	0.331132	−	0.573537i
$761$	−610.251	+	352.329i	−0.801907	+	0.462981i	−0.844137	−	0.536127i	$-0.819887\pi$
$761$	−610.251	+	352.329i	−0.801907	+	0.462981i	0.0422307	+	0.999108i	$0.486554\pi$
$762$		0			0
$763$		0			0
$764$		−	82.7231i		−	0.108276i
$765$		0			0
$766$	150.656	−	260.944i	0.196679	−	0.340658i
$767$	−3.68870	−	2.12967i	−0.00480926	−	0.00277663i
$768$		0			0
$769$	−117.320			−0.152562			−0.0762810	−	0.997086i	$-0.524305\pi$
$769$	−117.320			−0.152562			−0.0762810	+	0.997086i	$0.524305\pi$
$770$		0			0
$771$		0			0
$772$	134.000	+	232.095i	0.173575	+	0.300641i
$773$	−569.849	−	329.002i	−0.737191	−	0.425618i	0.0838559	−	0.996478i	$-0.473276\pi$
$773$	−569.849	−	329.002i	−0.737191	−	0.425618i	−0.821047	+	0.570860i	$0.806610\pi$
$774$		0			0
$775$	−464.907	−	805.243i	−0.599880	−	1.03902i
$776$			125.619i			0.161880i
$777$		0			0
$778$	−799.166			−1.02721
$779$	−272.518	+	157.338i	−0.349830	+	0.201975i
$780$		0			0
$781$	158.332	−	274.239i	0.202730	−	0.351138i
$782$	−563.780	+	325.498i	−0.720946	+	0.416238i
$783$		0			0
$784$		0			0
$785$			613.894i			0.782031i
$786$		0			0
$787$	600.324	−	1039.79i	0.762801	−	1.32121i	−0.178601	−	0.983922i	$-0.557157\pi$
$787$	600.324	−	1039.79i	0.762801	−	1.32121i	0.941402	−	0.337288i	$-0.109510\pi$
$788$	−119.212	−	68.8269i	−0.151284	−	0.0873438i
$789$		0			0
$790$	1488.97			1.88478
$791$		0			0
$792$		0			0
$793$	−129.579	−	224.438i	−0.163404	−	0.283023i
$794$	610.320	+	352.368i	0.768665	+	0.443789i
$795$		0			0
$796$	−278.494	−	482.366i	−0.349867	−	0.605987i
$797$			797.411i			1.00052i	0.865876	+	0.500258i	$0.166761\pi$
$797$			797.411i			1.00052i	−0.865876	+	0.500258i	$0.833239\pi$
$798$		0			0
$799$	−438.996			−0.549432
$800$	265.358	−	153.205i	0.331698	−	0.191506i
$801$		0			0
$802$	136.749	−	236.856i	0.170510	−	0.295332i
$803$	445.609	−	257.272i	0.554930	−	0.320389i
$804$		0			0
$805$		0			0
$806$			62.7061i			0.0777991i
$807$		0			0
$808$	45.0850	−	78.0895i	0.0557982	−	0.0966454i
$809$	135.114	+	78.0082i	0.167014	+	0.0964254i	0.581177	−	0.813777i	$-0.302592\pi$
$809$	135.114	+	78.0082i	0.167014	+	0.0964254i	−0.414163	+	0.910203i	$0.635926\pi$
$810$		0			0
$811$	−598.316			−0.737751			−0.368876	−	0.929479i	$-0.620257\pi$
$811$	−598.316			−0.737751			−0.368876	+	0.929479i	$0.620257\pi$
$812$		0			0
$813$		0			0
$814$	−478.154	−	828.187i	−0.587413	−	1.01743i
$815$	1286.79	+	742.926i	1.57888	+	0.911566i
$816$		0			0
$817$	434.980	+	753.408i	0.532412	+	0.922164i
$818$			642.397i			0.785326i
$819$		0			0
$820$	−279.984			−0.341444
$821$	−849.552	+	490.489i	−1.03478	+	0.597429i	−0.918349	−	0.395770i	$-0.870478\pi$
$821$	−849.552	+	490.489i	−1.03478	+	0.597429i	−0.116427	+	0.993199i	$0.537144\pi$
$822$		0			0
$823$	215.668	−	373.548i	0.262051	−	0.453886i	−0.704736	−	0.709470i	$-0.748934\pi$
$823$	215.668	−	373.548i	0.262051	−	0.453886i	0.966787	+	0.255584i	$0.0822678\pi$
$824$	11.0275	−	6.36674i	0.0133829	−	0.00772663i
$825$		0			0
$826$		0			0
$827$		−	1219.41i		−	1.47449i	−0.675623	−	0.737247i	$-0.736125\pi$
$827$		−	1219.41i		−	1.47449i	0.675623	−	0.737247i	$-0.263875\pi$
$828$		0			0
$829$	385.041	−	666.910i	0.464464	−	0.804475i	−0.534713	−	0.845034i	$-0.679580\pi$
$829$	385.041	−	666.910i	0.464464	−	0.804475i	0.999177	+	0.0405586i	$0.0129137\pi$
$830$	1312.49	+	757.767i	1.58131	+	0.912972i
$831$		0			0
$832$	−20.6640			−0.0248366
$833$		0			0
$834$		0			0
$835$	535.822	+	928.071i	0.641703	+	1.11146i
$836$	616.439	+	355.901i	0.737367	+	0.425719i
$837$		0			0
$838$	−240.000	−	415.692i	−0.286396	−	0.496053i
$839$			1310.03i			1.56142i	0.624894	+	0.780710i	$0.285142\pi$
$839$			1310.03i			1.56142i	−0.624894	+	0.780710i	$0.714858\pi$
$840$		0			0
$841$	699.308			0.831520
$842$	−302.904	+	174.882i	−0.359744	+	0.207698i
$843$		0			0
$844$	−211.498	+	366.325i	−0.250590	+	0.434035i
$845$	−1250.82	+	722.159i	−1.48026	+	0.854626i
$846$		0			0
$847$		0			0
$848$		−	342.229i		−	0.403571i
$849$		0			0
$850$	−990.778	+	1716.08i	−1.16562	+	2.01891i
$851$	−585.617	−	338.106i	−0.688151	−	0.397304i
$852$		0			0
$853$	898.988			1.05391			0.526957	−	0.849892i	$-0.323333\pi$
$853$	898.988			1.05391			0.526957	+	0.849892i	$0.323333\pi$
$854$		0			0
$855$		0			0
$856$	243.498	+	421.751i	0.284460	+	0.492700i
$857$	646.190	+	373.078i	0.754014	+	0.435330i	0.827142	−	0.561993i	$-0.189965\pi$
$857$	646.190	+	373.078i	0.754014	+	0.435330i	−0.0731286	+	0.997323i	$0.523298\pi$
$858$		0			0
$859$	495.992	+	859.084i	0.577406	+	1.00010i	0.995776	+	0.0918202i	$0.0292685\pi$
$859$	495.992	+	859.084i	0.577406	+	1.00010i	−0.418369	+	0.908277i	$0.637398\pi$
$860$			774.050i			0.900058i
$861$		0			0
$862$	−645.474			−0.748810
$863$	−181.361	+	104.709i	−0.210152	+	0.121332i	−0.601382	−	0.798961i	$-0.705383\pi$
$863$	−181.361	+	104.709i	−0.210152	+	0.121332i	0.391230	+	0.920293i	$0.372050\pi$
$864$		0			0
$865$	−408.668	+	707.834i	−0.472449	+	0.818305i
$866$	781.368	−	451.123i	0.902272	−	0.520927i
$867$		0			0
$868$		0			0
$869$			2105.73i			2.42316i
$870$		0			0
$871$	−47.3517	+	82.0156i	−0.0543648	+	0.0941625i
$872$	435.593	+	251.490i	0.499533	+	0.288406i
$873$		0			0
$874$	503.320			0.575881
$875$		0			0
$876$		0			0
$877$	432.652	+	749.376i	0.493332	+	0.854476i	0.999970	−	0.00768242i	$-0.00244541\pi$
$877$	432.652	+	749.376i	0.493332	+	0.854476i	−0.506638	+	0.862159i	$0.669112\pi$
$878$	−960.379	−	554.475i	−1.09383	−	0.631521i
$879$		0			0
$880$	316.664	+	548.478i	0.359846	+	0.623271i
$881$		−	995.046i		−	1.12945i	−0.825279	−	0.564725i	$-0.808982\pi$
$881$		−	995.046i		−	1.12945i	0.825279	−	0.564725i	$-0.191018\pi$
$882$		0			0
$883$	101.474			0.114920			0.0574600	−	0.998348i	$-0.481700\pi$
$883$	101.474			0.114920			0.0574600	+	0.998348i	$0.481700\pi$
$884$	115.731	−	66.8174i	0.130918	−	0.0755853i
$885$		0			0
$886$	333.911	−	578.351i	0.376875	−	0.652766i
$887$	−930.191	+	537.046i	−1.04869	+	0.605464i	−0.922283	−	0.386514i	$-0.873679\pi$
$887$	−930.191	+	537.046i	−1.04869	+	0.605464i	−0.126410	+	0.991978i	$0.540346\pi$
$888$		0			0
$889$		0			0
$890$		−	1755.01i		−	1.97192i
$891$		0			0
$892$	222.494	−	385.371i	0.249433	−	0.432030i
$893$	293.939	+	169.706i	0.329159	+	0.190040i
$894$		0			0
$895$	−1185.96			−1.32510
$896$		0			0
$897$		0			0
$898$	−523.154	−	906.130i	−0.582577	−	1.00905i
$899$	176.959	+	102.167i	0.196840	+	0.113645i
$900$		0			0
$901$	1106.60	+	1916.69i	1.22819	+	2.12729i
$902$		−	395.958i		−	0.438977i
$903$		0			0
$904$	−88.6640			−0.0980797
$905$	640.210	−	369.625i	0.707414	−	0.408426i
$906$		0			0
$907$	216.081	−	374.263i	0.238237	−	0.412639i	−0.721971	−	0.691923i	$-0.756764\pi$
$907$	216.081	−	374.263i	0.238237	−	0.412639i	0.960209	+	0.279284i	$0.0900971\pi$
$908$	−176.363	+	101.823i	−0.194233	+	0.112140i
$909$		0			0
$910$		0			0
$911$			104.984i			0.115241i	0.998339	+	0.0576205i	$0.0183513\pi$
$911$			104.984i			0.115241i	−0.998339	+	0.0576205i	$0.981649\pi$
$912$		0			0
$913$	−1071.64	+	1856.14i	−1.17376	+	2.03301i
$914$	−304.134	−	175.592i	−0.332750	−	0.192113i
$915$		0			0
$916$	326.170			0.356081
$917$		0			0
$918$		0			0
$919$	45.9190	+	79.5340i	0.0499662	+	0.0865440i	0.889927	−	0.456103i	$-0.150755\pi$
$919$	45.9190	+	79.5340i	0.0499662	+	0.0865440i	−0.839961	+	0.542647i	$0.817422\pi$
$920$	387.833	+	223.915i	0.421557	+	0.243386i
$921$		0			0
$922$	251.708	+	435.972i	0.273003	+	0.472855i
$923$			45.9647i			0.0497993i
$924$		0			0
$925$	−2058.31			−2.22520
$926$	7.75511	−	4.47741i	0.00837485	−	0.00483522i
$927$		0			0
$928$	−33.6680	+	58.3147i	−0.0362801	+	0.0628391i
$929$	1133.63	−	654.501i	1.22027	−	0.704522i	0.255293	−	0.966864i	$-0.417828\pi$
$929$	1133.63	−	654.501i	1.22027	−	0.704522i	0.964975	+	0.262342i	$0.0844949\pi$
$930$		0			0
$931$		0			0
$932$		−	725.715i		−	0.778664i
$933$		0			0
$934$	621.328	−	1076.17i	0.665233	−	1.15222i
$935$	−3547.02	−	2047.87i	−3.79361	−	2.19024i
$936$		0			0
$937$	1262.00			1.34685			0.673426	−	0.739255i	$-0.264822\pi$
$937$	1262.00			1.34685			0.673426	+	0.739255i	$0.264822\pi$
$938$		0			0
$939$		0			0
$940$	150.996	+	261.533i	0.160634	+	0.278226i
$941$	−1139.67	−	657.987i	−1.21112	−	0.699243i	−0.248120	−	0.968729i	$-0.579813\pi$
$941$	−1139.67	−	657.987i	−1.21112	−	0.699243i	−0.963004	+	0.269487i	$0.913146\pi$
$942$		0			0
$943$	−139.992	−	242.473i	−0.148454	−	0.257130i
$944$			6.59595i			0.00698724i
$945$		0			0
$946$	−1094.67			−1.15716
$947$	−421.392	+	243.291i	−0.444976	+	0.256907i	−0.705706	−	0.708505i	$-0.749370\pi$
$947$	−421.392	+	243.291i	−0.444976	+	0.256907i	0.260730	+	0.965412i	$0.416037\pi$
$948$		0			0
$949$	−37.3438	+	64.6814i	−0.0393507	+	0.0681574i
$950$	1326.79	−	766.023i	1.39662	−	0.806340i
$951$		0			0
$952$		0			0
$953$		−	43.3711i		−	0.0455100i	−0.999741	−	0.0227550i	$-0.992756\pi$
$953$		−	43.3711i		−	0.0455100i	0.999741	−	0.0227550i	$-0.00724377\pi$
$954$		0			0
$955$	184.008	−	318.711i	0.192678	−	0.333729i
$956$	−306.791	−	177.126i	−0.320911	−	0.185278i
$957$		0			0
$958$	−317.344			−0.331257
$959$		0			0
$960$		0			0
$961$	333.164	+	577.057i	0.346685	+	0.600476i
$962$	120.214	+	69.4055i	0.124962	+	0.0721471i
$963$		0			0
$964$	152.753	+	264.576i	0.158457	+	0.274456i
$965$			1192.27i			1.23551i
$966$		0			0
$967$	1648.99			1.70526			0.852631	−	0.522514i	$-0.175006\pi$
$967$	1648.99			1.70526			0.852631	+	0.522514i	$0.175006\pi$
$968$	−479.277	+	276.711i	−0.495121	+	0.285858i
$969$		0			0
$970$	−279.425	+	483.978i	−0.288067	+	0.498946i
$971$	−448.881	+	259.162i	−0.462287	+	0.266902i	−0.713006	−	0.701158i	$-0.752667\pi$
$971$	−448.881	+	259.162i	−0.462287	+	0.266902i	0.250718	+	0.968060i	$0.419333\pi$
$972$		0			0
$973$		0			0
$974$			1014.68i			1.04177i
$975$		0			0
$976$	−200.664	+	347.560i	−0.205598	+	0.356107i
$977$	95.2179	+	54.9741i	0.0974595	+	0.0562682i	0.547938	−	0.836519i	$-0.315413\pi$
$977$	95.2179	+	54.9741i	0.0974595	+	0.0562682i	−0.450478	+	0.892787i	$0.648746\pi$
$978$		0			0
$979$	2481.96			2.53520
$980$		0			0
$981$		0			0
$982$	193.749	+	335.583i	0.197300	+	0.341734i
$983$	−510.704	−	294.855i	−0.519536	−	0.299954i	0.217209	−	0.976125i	$-0.430305\pi$
$983$	−510.704	−	294.855i	−0.519536	−	0.299954i	−0.736745	+	0.676171i	$0.763638\pi$
$984$		0			0
$985$	−306.195	−	530.345i	−0.310858	−	0.538421i
$986$		−	435.463i		−	0.441646i
$987$		0			0
$988$	−103.320			−0.104575
$989$	−670.347	+	387.025i	−0.677803	+	0.391330i
$990$		0			0
$991$	−356.737	+	617.887i	−0.359977	+	0.623498i	−0.987957	−	0.154731i	$-0.950549\pi$
$991$	−356.737	+	617.887i	−0.359977	+	0.623498i	0.627980	+	0.778230i	$0.283882\pi$
$992$	84.0959	−	48.5528i	0.0847741	−	0.0489444i
$993$		0			0
$994$		0			0
$995$		−	2477.91i		−	2.49036i
$996$		0			0
$997$	−611.494	+	1059.14i	−0.613334	+	1.06233i	0.377340	+	0.926075i	$0.376839\pi$
$997$	−611.494	+	1059.14i	−0.613334	+	1.06233i	−0.990674	+	0.136251i	$0.956495\pi$
$998$	−892.607	−	515.347i	−0.894396	−	0.516380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.s.e.557.2		8
3.2	odd	2	inner	882.3.s.e.557.3		8
7.2	even	3	inner	882.3.s.e.863.3		8
7.3	odd	6		882.3.b.f.197.1		4
7.4	even	3		126.3.b.a.71.2	✓	4
7.5	odd	6		882.3.s.i.863.4		8
7.6	odd	2		882.3.s.i.557.1		8
21.2	odd	6	inner	882.3.s.e.863.2		8
21.5	even	6		882.3.s.i.863.1		8
21.11	odd	6		126.3.b.a.71.3	yes	4
21.17	even	6		882.3.b.f.197.4		4
21.20	even	2		882.3.s.i.557.4		8
28.11	odd	6		1008.3.d.a.449.4		4
35.4	even	6		3150.3.e.e.701.3		4
35.18	odd	12		3150.3.c.b.449.2		8
35.32	odd	12		3150.3.c.b.449.8		8
56.11	odd	6		4032.3.d.j.449.1		4
56.53	even	6		4032.3.d.i.449.1		4
63.4	even	3		1134.3.q.c.1079.4		8
63.11	odd	6		1134.3.q.c.701.4		8
63.25	even	3		1134.3.q.c.701.1		8
63.32	odd	6		1134.3.q.c.1079.1		8
84.11	even	6		1008.3.d.a.449.1		4
105.32	even	12		3150.3.c.b.449.3		8
105.53	even	12		3150.3.c.b.449.5		8
105.74	odd	6		3150.3.e.e.701.1		4
168.11	even	6		4032.3.d.j.449.4		4
168.53	odd	6		4032.3.d.i.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.b.a.71.2	✓	4	7.4	even	3
126.3.b.a.71.3	yes	4	21.11	odd	6
882.3.b.f.197.1		4	7.3	odd	6
882.3.b.f.197.4		4	21.17	even	6
882.3.s.e.557.2		8	1.1	even	1	trivial
882.3.s.e.557.3		8	3.2	odd	2	inner
882.3.s.e.863.2		8	21.2	odd	6	inner
882.3.s.e.863.3		8	7.2	even	3	inner
882.3.s.i.557.1		8	7.6	odd	2
882.3.s.i.557.4		8	21.20	even	2
882.3.s.i.863.1		8	21.5	even	6
882.3.s.i.863.4		8	7.5	odd	6
1008.3.d.a.449.1		4	84.11	even	6
1008.3.d.a.449.4		4	28.11	odd	6
1134.3.q.c.701.1		8	63.25	even	3
1134.3.q.c.701.4		8	63.11	odd	6
1134.3.q.c.1079.1		8	63.32	odd	6
1134.3.q.c.1079.4		8	63.4	even	3
3150.3.c.b.449.2		8	35.18	odd	12
3150.3.c.b.449.3		8	105.32	even	12
3150.3.c.b.449.5		8	105.53	even	12
3150.3.c.b.449.8		8	35.32	odd	12
3150.3.e.e.701.1		4	105.74	odd	6
3150.3.e.e.701.3		4	35.4	even	6
4032.3.d.i.449.1		4	56.53	even	6
4032.3.d.i.449.4		4	168.53	odd	6
4032.3.d.j.449.1		4	56.11	odd	6
4032.3.d.j.449.4		4	168.11	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +(-6.29150 + 10.8972i) q^{10} +(-15.4110 - 8.89753i) q^{11} +2.58301 q^{13} +(-2.00000 - 3.46410i) q^{16} +(22.4024 + 12.9340i) q^{17} +(-10.0000 - 17.3205i) q^{19} -17.7951i q^{20} +25.1660 q^{22} +(15.4110 - 8.89753i) q^{23} +(27.0830 - 46.9091i) q^{25} +(-3.16352 + 1.82646i) q^{26} +11.9034i q^{29} +(8.58301 - 14.8662i) q^{31} +(4.89898 + 2.82843i) q^{32} -36.5830 q^{34} +(-19.0000 - 32.9090i) q^{37} +(24.4949 + 14.1421i) q^{38} +(12.5830 + 21.7944i) q^{40} -15.7338i q^{41} -43.4980 q^{43} +(-30.8219 + 17.7951i) q^{44} +(-12.5830 + 21.7944i) q^{46} +(-14.6969 + 8.48528i) q^{47} +76.6023i q^{50} +(2.58301 - 4.47390i) q^{52} +(74.0947 + 42.7786i) q^{53} -158.332 q^{55} +(-8.41699 - 14.5787i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-50.1660 - 86.8901i) q^{61} +24.2764i q^{62} -8.00000 q^{64} +(19.9033 - 11.4912i) q^{65} +(-18.3320 + 31.7520i) q^{67} +(44.8048 - 25.8681i) q^{68} +17.7951i q^{71} +(-14.4575 + 25.0411i) q^{73} +(46.5403 + 26.8701i) q^{74} -40.0000 q^{76} +(-59.1660 - 102.479i) q^{79} +(-30.8219 - 17.7951i) q^{80} +(11.1255 + 19.2699i) q^{82} -120.443i q^{83} +230.162 q^{85} +(53.2740 - 30.7578i) q^{86} +(25.1660 - 43.5888i) q^{88} +(-120.789 + 69.7374i) q^{89} -35.5901i q^{92} +(12.0000 - 20.7846i) q^{94} +(-154.110 - 88.9753i) q^{95} +44.4131 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^10 - 64 * q^13 - 16 * q^16 - 80 * q^19 + 32 * q^22 + 132 * q^25 - 16 * q^31 - 208 * q^34 - 152 * q^37 + 16 * q^40 + 160 * q^43 - 16 * q^46 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 + 96 * q^73 - 320 * q^76 - 304 * q^79 + 216 * q^82 + 656 * q^85 + 32 * q^88 + 96 * q^94 - 576 * q^97

Introduction

L-functions

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