LMFDB - Embedded newform 1148.2.i.d.821.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.6
Root			$-0.856454 - 1.48342i$ of defining polynomial
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.d.165.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.856454 + 1.48342i) q^{3} +(-1.07560 + 1.86299i) q^{5} +(1.55192 - 2.14279i) q^{7} +(0.0329726 - 0.0571103i) q^{9} +O(q^{10})$	\(q+(0.856454 + 1.48342i) q^{3} +(-1.07560 + 1.86299i) q^{5} +(1.55192 - 2.14279i) q^{7} +(0.0329726 - 0.0571103i) q^{9} +(1.51384 + 2.62205i) q^{11} +0.848387 q^{13} -3.68481 q^{15} +(2.38048 + 4.12311i) q^{17} +(1.95046 - 3.37829i) q^{19} +(4.50781 + 0.466951i) q^{21} +(-4.12636 + 7.14706i) q^{23} +(0.186172 + 0.322460i) q^{25} +5.25168 q^{27} +0.0576440 q^{29} +(-2.15025 - 3.72434i) q^{31} +(-2.59308 + 4.49134i) q^{33} +(2.32276 + 5.19600i) q^{35} +(-0.237658 + 0.411635i) q^{37} +(0.726605 + 1.25852i) q^{39} +1.00000 q^{41} +2.82667 q^{43} +(0.0709307 + 0.122856i) q^{45} +(-3.35988 + 5.81948i) q^{47} +(-2.18309 - 6.65087i) q^{49} +(-4.07754 + 7.06251i) q^{51} +(1.71470 + 2.96995i) q^{53} -6.51316 q^{55} +6.68191 q^{57} +(-2.86447 - 4.96141i) q^{59} +(-2.98357 + 5.16770i) q^{61} +(-0.0712044 - 0.159284i) q^{63} +(-0.912525 + 1.58054i) q^{65} +(4.76775 + 8.25798i) q^{67} -14.1362 q^{69} -1.84489 q^{71} +(-1.94939 - 3.37644i) q^{73} +(-0.318896 + 0.552345i) q^{75} +(7.96788 + 0.825370i) q^{77} +(-2.55871 + 4.43181i) q^{79} +(4.39891 + 7.61913i) q^{81} -7.41218 q^{83} -10.2418 q^{85} +(0.0493694 + 0.0855103i) q^{87} +(0.152570 - 0.264258i) q^{89} +(1.31663 - 1.81791i) q^{91} +(3.68317 - 6.37945i) q^{93} +(4.19582 + 7.26737i) q^{95} -11.7545 q^{97} +0.199662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.856454	+	1.48342i	0.494474	+	0.856454i	0.999980	−	0.00636914i	$-0.00202737\pi$
$3$	0.856454	+	1.48342i	0.494474	+	0.856454i	−0.505506	+	0.862823i	$0.668694\pi$
$4$		0			0
$5$	−1.07560	+	1.86299i	−0.481023	+	0.833156i	−0.999763	−	0.0217763i	$-0.993068\pi$
$5$	−1.07560	+	1.86299i	−0.481023	+	0.833156i	0.518740	+	0.854932i	$0.326401\pi$
$6$		0			0
$7$	1.55192	−	2.14279i	0.586571	−	0.809898i
$7$	1.55192	−	2.14279i	0.586571	−	0.809898i
$8$		0			0
$9$	0.0329726	−	0.0571103i	0.0109909	−	0.0190368i
$10$		0			0
$11$	1.51384	+	2.62205i	0.456441	+	0.790579i	0.998770	−	0.0495872i	$-0.0157906\pi$
$11$	1.51384	+	2.62205i	0.456441	+	0.790579i	−0.542329	+	0.840166i	$0.682457\pi$
$12$		0			0
$13$	0.848387			0.235300			0.117650	−	0.993055i	$-0.462464\pi$
$13$	0.848387			0.235300			0.117650	+	0.993055i	$0.462464\pi$
$14$		0			0
$15$	−3.68481			−0.951413
$16$		0			0
$17$	2.38048	+	4.12311i	0.577351	+	1.00000i	0.995782	+	0.0917524i	$0.0292468\pi$
$17$	2.38048	+	4.12311i	0.577351	+	1.00000i	−0.418431	+	0.908249i	$0.637420\pi$
$18$		0			0
$19$	1.95046	−	3.37829i	0.447465	−	0.775033i	−0.550755	−	0.834667i	$-0.685660\pi$
$19$	1.95046	−	3.37829i	0.447465	−	0.775033i	0.998220	+	0.0596341i	$0.0189934\pi$
$20$		0			0
$21$	4.50781	+	0.466951i	0.983685	+	0.101897i
$22$		0			0
$23$	−4.12636	+	7.14706i	−0.860405	+	1.49027i	0.0111326	+	0.999938i	$0.496456\pi$
$23$	−4.12636	+	7.14706i	−0.860405	+	1.49027i	−0.871538	+	0.490328i	$0.836877\pi$
$24$		0			0
$25$	0.186172	+	0.322460i	0.0372345	+	0.0644920i
$26$		0			0
$27$	5.25168			1.01069
$28$		0			0
$29$	0.0576440			0.0107042			0.00535211	−	0.999986i	$-0.498296\pi$
$29$	0.0576440			0.0107042			0.00535211	+	0.999986i	$0.498296\pi$
$30$		0			0
$31$	−2.15025	−	3.72434i	−0.386196	−	0.668910i	0.605739	−	0.795664i	$-0.292878\pi$
$31$	−2.15025	−	3.72434i	−0.386196	−	0.668910i	−0.991934	+	0.126753i	$0.959544\pi$
$32$		0			0
$33$	−2.59308	+	4.49134i	−0.451397	+	0.781842i
$34$		0			0
$35$	2.32276	+	5.19600i	0.392617	+	0.878284i
$36$		0			0
$37$	−0.237658	+	0.411635i	−0.0390707	+	0.0676724i	−0.884899	−	0.465782i	$-0.845773\pi$
$37$	−0.237658	+	0.411635i	−0.0390707	+	0.0676724i	0.845829	+	0.533454i	$0.179106\pi$
$38$		0			0
$39$	0.726605	+	1.25852i	0.116350	+	0.201524i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	2.82667			0.431063			0.215531	−	0.976497i	$-0.430852\pi$
$43$	2.82667			0.431063			0.215531	+	0.976497i	$0.430852\pi$
$44$		0			0
$45$	0.0709307	+	0.122856i	0.0105737	+	0.0183142i
$46$		0			0
$47$	−3.35988	+	5.81948i	−0.490089	+	0.848859i	−0.999935	−	0.0114069i	$-0.996369\pi$
$47$	−3.35988	+	5.81948i	−0.490089	+	0.848859i	0.509846	+	0.860266i	$0.329702\pi$
$48$		0			0
$49$	−2.18309	−	6.65087i	−0.311870	−	0.950125i
$50$		0			0
$51$	−4.07754	+	7.06251i	−0.570970	+	0.988949i
$52$		0			0
$53$	1.71470	+	2.96995i	0.235533	+	0.407954i	0.959427	−	0.281956i	$-0.0909832\pi$
$53$	1.71470	+	2.96995i	0.235533	+	0.407954i	−0.723895	+	0.689910i	$0.757650\pi$
$54$		0			0
$55$	−6.51316			−0.878234
$56$		0			0
$57$	6.68191			0.885040
$58$		0			0
$59$	−2.86447	−	4.96141i	−0.372922	−	0.645920i	0.617091	−	0.786891i	$-0.288311\pi$
$59$	−2.86447	−	4.96141i	−0.372922	−	0.645920i	−0.990014	+	0.140971i	$0.954978\pi$
$60$		0			0
$61$	−2.98357	+	5.16770i	−0.382007	+	0.661656i	−0.991349	−	0.131252i	$-0.958100\pi$
$61$	−2.98357	+	5.16770i	−0.382007	+	0.661656i	0.609342	+	0.792908i	$0.291434\pi$
$62$		0			0
$63$	−0.0712044	−	0.159284i	−0.00897091	−	0.0200679i
$64$		0			0
$65$	−0.912525	+	1.58054i	−0.113185	+	0.196042i
$66$		0			0
$67$	4.76775	+	8.25798i	0.582473	+	1.00887i	0.995185	+	0.0980114i	$0.0312482\pi$
$67$	4.76775	+	8.25798i	0.582473	+	1.00887i	−0.412712	+	0.910861i	$0.635419\pi$
$68$		0			0
$69$	−14.1362			−1.70179
$70$		0			0
$71$	−1.84489			−0.218948			−0.109474	−	0.993990i	$-0.534917\pi$
$71$	−1.84489			−0.218948			−0.109474	+	0.993990i	$0.534917\pi$
$72$		0			0
$73$	−1.94939	−	3.37644i	−0.228158	−	0.395182i	0.729104	−	0.684403i	$-0.239937\pi$
$73$	−1.94939	−	3.37644i	−0.228158	−	0.395182i	−0.957262	+	0.289221i	$0.906604\pi$
$74$		0			0
$75$	−0.318896	+	0.552345i	−0.0368230	+	0.0637793i
$76$		0			0
$77$	7.96788	+	0.825370i	0.908024	+	0.0940597i
$78$		0			0
$79$	−2.55871	+	4.43181i	−0.287877	+	0.498618i	−0.973303	−	0.229525i	$-0.926283\pi$
$79$	−2.55871	+	4.43181i	−0.287877	+	0.498618i	0.685426	+	0.728143i	$0.259616\pi$
$80$		0			0
$81$	4.39891	+	7.61913i	0.488768	+	0.846570i
$82$		0			0
$83$	−7.41218			−0.813592			−0.406796	−	0.913519i	$-0.633354\pi$
$83$	−7.41218			−0.813592			−0.406796	+	0.913519i	$0.633354\pi$
$84$		0			0
$85$	−10.2418			−1.11088
$86$		0			0
$87$	0.0493694	+	0.0855103i	0.00529296	+	0.00916767i
$88$		0			0
$89$	0.152570	−	0.264258i	0.0161723	−	0.0280113i	−0.857826	−	0.513940i	$-0.828185\pi$
$89$	0.152570	−	0.264258i	0.0161723	−	0.0280113i	0.873998	+	0.485929i	$0.161519\pi$
$90$		0			0
$91$	1.31663	−	1.81791i	0.138020	−	0.190569i
$92$		0			0
$93$	3.68317	−	6.37945i	0.381927	−	0.661518i
$94$		0			0
$95$	4.19582	+	7.26737i	0.430482	+	0.745617i
$96$		0			0
$97$	−11.7545			−1.19349			−0.596743	−	0.802433i	$-0.703539\pi$
$97$	−11.7545			−1.19349			−0.596743	+	0.802433i	$0.703539\pi$
$98$		0			0
$99$	0.199662			0.0200668
$100$		0			0
$101$	−1.06150	−	1.83858i	−0.105623	−	0.182945i	0.808369	−	0.588676i	$-0.200350\pi$
$101$	−1.06150	−	1.83858i	−0.105623	−	0.182945i	−0.913993	+	0.405731i	$0.867017\pi$
$102$		0			0
$103$	3.76168	−	6.51542i	0.370650	−	0.641984i	−0.619016	−	0.785378i	$-0.712468\pi$
$103$	3.76168	−	6.51542i	0.370650	−	0.641984i	0.989666	+	0.143394i	$0.0458018\pi$
$104$		0			0
$105$	−5.71852	+	7.89576i	−0.558071	+	0.770547i
$106$		0			0
$107$	6.45144	−	11.1742i	0.623684	−	1.08025i	−0.365110	−	0.930964i	$-0.618969\pi$
$107$	6.45144	−	11.1742i	0.623684	−	1.08025i	0.988794	−	0.149288i	$-0.0476981\pi$
$108$		0			0
$109$	−0.293737	−	0.508767i	−0.0281349	−	0.0487310i	0.851615	−	0.524168i	$-0.175623\pi$
$109$	−0.293737	−	0.508767i	−0.0281349	−	0.0487310i	−0.879750	+	0.475437i	$0.842290\pi$
$110$		0			0
$111$	−0.814172			−0.0772778
$112$		0			0
$113$	−1.87770			−0.176639			−0.0883197	−	0.996092i	$-0.528150\pi$
$113$	−1.87770			−0.176639			−0.0883197	+	0.996092i	$0.528150\pi$
$114$		0			0
$115$	−8.87662	−	15.3748i	−0.827749	−	1.43370i
$116$		0			0
$117$	0.0279736	−	0.0484516i	0.00258616	−	0.00447935i
$118$		0			0
$119$	12.5293	+	1.29787i	1.14856	+	0.118976i
$120$		0			0
$121$	0.916552	−	1.58751i	0.0833229	−	0.144320i
$122$		0			0
$123$	0.856454	+	1.48342i	0.0772239	+	0.133756i
$124$		0			0
$125$	−11.5570			−1.03369
$126$		0			0
$127$	11.9240			1.05808			0.529040	−	0.848597i	$-0.322552\pi$
$127$	11.9240			1.05808			0.529040	+	0.848597i	$0.322552\pi$
$128$		0			0
$129$	2.42091	+	4.19314i	0.213149	+	0.369185i
$130$		0			0
$131$	9.59409	−	16.6174i	0.838239	−	1.45187i	−0.0531263	−	0.998588i	$-0.516919\pi$
$131$	9.59409	−	16.6174i	0.838239	−	1.45187i	0.891366	−	0.453285i	$-0.149748\pi$
$132$		0			0
$133$	−4.21201	−	9.42225i	−0.365228	−	0.817013i
$134$		0			0
$135$	−5.64871	+	9.78385i	−0.486163	+	0.842059i
$136$		0			0
$137$	4.00557	+	6.93785i	0.342219	+	0.592741i	0.984844	−	0.173440i	$-0.0554882\pi$
$137$	4.00557	+	6.93785i	0.342219	+	0.592741i	−0.642626	+	0.766180i	$0.722155\pi$
$138$		0			0
$139$	20.3407			1.72528			0.862639	−	0.505821i	$-0.168810\pi$
$139$	20.3407			1.72528			0.862639	+	0.505821i	$0.168810\pi$
$140$		0			0
$141$	−11.5103			−0.969345
$142$		0			0
$143$	1.28433	+	2.22452i	0.107401	+	0.186024i
$144$		0			0
$145$	−0.0620018	+	0.107390i	−0.00514897	+	0.00891828i
$146$		0			0
$147$	7.99634	−	8.93461i	0.659527	−	0.736914i
$148$		0			0
$149$	5.29107	−	9.16441i	0.433462	−	0.750778i	−0.563707	−	0.825975i	$-0.690625\pi$
$149$	5.29107	−	9.16441i	0.433462	−	0.750778i	0.997169	+	0.0751971i	$0.0239586\pi$
$150$		0			0
$151$	5.76010	+	9.97679i	0.468750	+	0.811899i	0.999362	−	0.0357157i	$-0.0113711\pi$
$151$	5.76010	+	9.97679i	0.468750	+	0.811899i	−0.530612	+	0.847615i	$0.678038\pi$
$152$		0			0
$153$	0.313963			0.0253824
$154$		0			0
$155$	9.25121			0.743075
$156$		0			0
$157$	−2.01303	−	3.48667i	−0.160657	−	0.278267i	0.774447	−	0.632638i	$-0.218028\pi$
$157$	−2.01303	−	3.48667i	−0.160657	−	0.278267i	−0.935105	+	0.354372i	$0.884695\pi$
$158$		0			0
$159$	−2.93713	+	5.08726i	−0.232930	+	0.403446i
$160$		0			0
$161$	8.91087	+	19.9336i	0.702275	+	1.57099i
$162$		0			0
$163$	9.52808	−	16.5031i	0.746296	−	1.29262i	−0.203290	−	0.979119i	$-0.565163\pi$
$163$	9.52808	−	16.5031i	0.746296	−	1.29262i	0.949587	−	0.313505i	$-0.101503\pi$
$164$		0			0
$165$	−5.57822	−	9.66176i	−0.434264	−	0.752167i
$166$		0			0
$167$	11.7372			0.908252			0.454126	−	0.890937i	$-0.349952\pi$
$167$	11.7372			0.908252			0.454126	+	0.890937i	$0.349952\pi$
$168$		0			0
$169$	−12.2802			−0.944634
$170$		0			0
$171$	−0.128623	−	0.222782i	−0.00983608	−	0.0170366i
$172$		0			0
$173$	0.755145	−	1.30795i	0.0574126	−	0.0994416i	−0.835891	−	0.548896i	$-0.815048\pi$
$173$	0.755145	−	1.30795i	0.0574126	−	0.0994416i	0.893303	+	0.449454i	$0.148382\pi$
$174$		0			0
$175$	0.979889	+	0.101504i	0.0740726	+	0.00767298i
$176$		0			0
$177$	4.90657	−	8.49844i	0.368801	−	0.638782i
$178$		0			0
$179$	0.691339	+	1.19743i	0.0516731	+	0.0895004i	0.890705	−	0.454582i	$-0.150211\pi$
$179$	0.691339	+	1.19743i	0.0516731	+	0.0895004i	−0.839032	+	0.544082i	$0.816878\pi$
$180$		0			0
$181$	−3.21399			−0.238894			−0.119447	−	0.992841i	$-0.538112\pi$
$181$	−3.21399			−0.238894			−0.119447	+	0.992841i	$0.538112\pi$
$182$		0			0
$183$	−10.2212			−0.755571
$184$		0			0
$185$	−0.511249	−	0.885509i	−0.0375878	−	0.0651039i
$186$		0			0
$187$	−7.20735	+	12.4835i	−0.527053	+	0.912883i
$188$		0			0
$189$	8.15019	−	11.2532i	0.592839	−	0.818553i
$190$		0			0
$191$	3.15734	−	5.46868i	0.228457	−	0.395700i	−0.728894	−	0.684627i	$-0.759965\pi$
$191$	3.15734	−	5.46868i	0.228457	−	0.395700i	0.957351	+	0.288927i	$0.0932985\pi$
$192$		0			0
$193$	7.59087	+	13.1478i	0.546403	+	0.946397i	0.998517	+	0.0544375i	$0.0173366\pi$
$193$	7.59087	+	13.1478i	0.546403	+	0.946397i	−0.452114	+	0.891960i	$0.649330\pi$
$194$		0			0
$195$	−3.12614			−0.223868
$196$		0			0
$197$	−17.9461			−1.27861			−0.639304	−	0.768954i	$-0.720778\pi$
$197$	−17.9461			−1.27861			−0.639304	+	0.768954i	$0.720778\pi$
$198$		0			0
$199$	−3.91096	−	6.77399i	−0.277241	−	0.480195i	0.693457	−	0.720498i	$-0.256087\pi$
$199$	−3.91096	−	6.77399i	−0.277241	−	0.480195i	−0.970698	+	0.240303i	$0.922753\pi$
$200$		0			0
$201$	−8.16671	+	14.1452i	−0.576036	+	0.997723i
$202$		0			0
$203$	0.0894588	−	0.123519i	0.00627878	−	0.00866932i
$204$		0			0
$205$	−1.07560	+	1.86299i	−0.0751231	+	0.130117i
$206$		0			0
$207$	0.272114	+	0.471315i	0.0189132	+	0.0327587i
$208$		0			0
$209$	11.8108			0.816967
$210$		0			0
$211$	−2.30039			−0.158366			−0.0791828	−	0.996860i	$-0.525231\pi$
$211$	−2.30039			−0.158366			−0.0791828	+	0.996860i	$0.525231\pi$
$212$		0			0
$213$	−1.58006	−	2.73675i	−0.108264	−	0.187519i
$214$		0			0
$215$	−3.04036	+	5.26606i	−0.207351	+	0.359142i
$216$		0			0
$217$	−11.3175	−	1.17235i	−0.768280	−	0.0795840i
$218$		0			0
$219$	3.33912	−	5.78353i	0.225637	−	0.390815i
$220$		0			0
$221$	2.01957	+	3.49799i	0.135851	+	0.235300i
$222$		0			0
$223$	−6.01186			−0.402584			−0.201292	−	0.979531i	$-0.564514\pi$
$223$	−6.01186			−0.402584			−0.201292	+	0.979531i	$0.564514\pi$
$224$		0			0
$225$	0.0245544			0.00163696
$226$		0			0
$227$	−12.4316	−	21.5322i	−0.825117	−	1.42915i	−0.901830	−	0.432092i	$-0.857776\pi$
$227$	−12.4316	−	21.5322i	−0.825117	−	1.42915i	0.0767123	−	0.997053i	$-0.475558\pi$
$228$		0			0
$229$	12.0155	−	20.8115i	0.794007	−	1.37526i	−0.129460	−	0.991585i	$-0.541324\pi$
$229$	12.0155	−	20.8115i	0.794007	−	1.37526i	0.923468	−	0.383677i	$-0.125342\pi$
$230$		0			0
$231$	5.59975	+	12.5266i	0.368436	+	0.824191i
$232$		0			0
$233$	3.88762	−	6.73355i	0.254686	−	0.441130i	−0.710124	−	0.704077i	$-0.751361\pi$
$233$	3.88762	−	6.73355i	0.254686	−	0.441130i	0.964810	+	0.262947i	$0.0846944\pi$
$234$		0			0
$235$	−7.22777	−	12.5189i	−0.471488	−	0.816640i
$236$		0			0
$237$	−8.76567			−0.569391
$238$		0			0
$239$	19.2557			1.24555			0.622774	−	0.782402i	$-0.286006\pi$
$239$	19.2557			1.24555			0.622774	+	0.782402i	$0.286006\pi$
$240$		0			0
$241$	−2.95944	−	5.12589i	−0.190634	−	0.330188i	0.754827	−	0.655924i	$-0.227721\pi$
$241$	−2.95944	−	5.12589i	−0.190634	−	0.330188i	−0.945461	+	0.325737i	$0.894388\pi$
$242$		0			0
$243$	0.342599	−	0.593399i	0.0219777	−	0.0380666i
$244$		0			0
$245$	14.7387	+	3.08659i	0.941618	+	0.197195i
$246$		0			0
$247$	1.65474	−	2.86610i	0.105289	−	0.182365i
$248$		0			0
$249$	−6.34819	−	10.9954i	−0.402300	−	0.696805i
$250$		0			0
$251$	28.1909			1.77939			0.889697	−	0.456551i	$-0.150916\pi$
$251$	28.1909			1.77939			0.889697	+	0.456551i	$0.150916\pi$
$252$		0			0
$253$	−24.9867			−1.57090
$254$		0			0
$255$	−8.77160	−	15.1929i	−0.549299	−	0.951414i
$256$		0			0
$257$	−2.13937	+	3.70550i	−0.133450	+	0.231142i	−0.925004	−	0.379957i	$-0.875939\pi$
$257$	−2.13937	+	3.70550i	−0.133450	+	0.231142i	0.791554	+	0.611099i	$0.209272\pi$
$258$		0			0
$259$	0.513222	+	1.14808i	0.0318901	+	0.0713379i
$260$		0			0
$261$	0.00190067	−	0.00329206i	0.000117649	−	0.000203774i
$262$		0			0
$263$	2.71898	+	4.70940i	0.167659	+	0.290394i	0.937596	−	0.347725i	$-0.113046\pi$
$263$	2.71898	+	4.70940i	0.167659	+	0.290394i	−0.769937	+	0.638120i	$0.779713\pi$
$264$		0			0
$265$	−7.37733			−0.453186
$266$		0			0
$267$	0.522675			0.0319872
$268$		0			0
$269$	−6.93411	−	12.0102i	−0.422780	−	0.732277i	0.573430	−	0.819255i	$-0.305612\pi$
$269$	−6.93411	−	12.0102i	−0.422780	−	0.732277i	−0.996210	+	0.0869776i	$0.972279\pi$
$270$		0			0
$271$	−6.85550	+	11.8741i	−0.416442	+	0.721299i	−0.995579	−	0.0939319i	$-0.970056\pi$
$271$	−6.85550	+	11.8741i	−0.416442	+	0.721299i	0.579137	+	0.815230i	$0.303390\pi$
$272$		0			0
$273$	3.82437	+	0.396156i	0.231461	+	0.0239764i
$274$		0			0
$275$	−0.563672	+	0.976309i	−0.0339907	+	0.0588736i
$276$		0			0
$277$	3.81315	+	6.60456i	0.229110	+	0.396830i	0.957545	−	0.288285i	$-0.0930852\pi$
$277$	3.81315	+	6.60456i	0.229110	+	0.396830i	−0.728435	+	0.685115i	$0.759752\pi$
$278$		0			0
$279$	−0.283597			−0.0169785
$280$		0			0
$281$	−26.0467			−1.55382			−0.776908	−	0.629614i	$-0.783213\pi$
$281$	−26.0467			−1.55382			−0.776908	+	0.629614i	$0.783213\pi$
$282$		0			0
$283$	−1.73066	−	2.99760i	−0.102877	−	0.178189i	0.809992	−	0.586441i	$-0.199472\pi$
$283$	−1.73066	−	2.99760i	−0.102877	−	0.178189i	−0.912869	+	0.408253i	$0.866138\pi$
$284$		0			0
$285$	−7.18705	+	12.4483i	−0.425724	+	0.737376i
$286$		0			0
$287$	1.55192	−	2.14279i	0.0916069	−	0.126485i
$288$		0			0
$289$	−2.83336	+	4.90752i	−0.166668	+	0.288677i
$290$		0			0
$291$	−10.0672	−	17.4368i	−0.590148	−	1.02217i
$292$		0			0
$293$	−11.2067			−0.654705			−0.327352	−	0.944902i	$-0.606156\pi$
$293$	−11.2067			−0.654705			−0.327352	+	0.944902i	$0.606156\pi$
$294$		0			0
$295$	12.3241			0.717536
$296$		0			0
$297$	7.95023	+	13.7702i	0.461319	+	0.799028i
$298$		0			0
$299$	−3.50075	+	6.06348i	−0.202454	+	0.350660i
$300$		0			0
$301$	4.38676	−	6.05695i	0.252849	−	0.349117i
$302$		0			0
$303$	1.81826	−	3.14931i	0.104456	−	0.180923i
$304$		0			0
$305$	−6.41826	−	11.1167i	−0.367508	−	0.636543i
$306$		0			0
$307$	−0.582689			−0.0332558			−0.0166279	−	0.999862i	$-0.505293\pi$
$307$	−0.582689			−0.0332558			−0.0166279	+	0.999862i	$0.505293\pi$
$308$		0			0
$309$	12.8868			0.733106
$310$		0			0
$311$	−3.12290	−	5.40903i	−0.177084	−	0.306718i	0.763797	−	0.645457i	$-0.223333\pi$
$311$	−3.12290	−	5.40903i	−0.177084	−	0.306718i	−0.940880	+	0.338739i	$0.890000\pi$
$312$		0			0
$313$	8.87076	−	15.3646i	0.501405	−	0.868459i	−0.498594	−	0.866836i	$-0.666150\pi$
$313$	8.87076	−	15.3646i	0.501405	−	0.868459i	0.999999	−	0.00162305i	$-0.000516632\pi$
$314$		0			0
$315$	0.373332	+	0.0386725i	0.0210349	+	0.00217895i
$316$		0			0
$317$	−6.46822	+	11.2033i	−0.363291	+	0.629239i	−0.988500	−	0.151218i	$-0.951680\pi$
$317$	−6.46822	+	11.2033i	−0.363291	+	0.629239i	0.625209	+	0.780457i	$0.285014\pi$
$318$		0			0
$319$	0.0872640	+	0.151146i	0.00488584	+	0.00846253i
$320$		0			0
$321$	22.1014			1.23358
$322$		0			0
$323$	18.5721			1.03338
$324$		0			0
$325$	0.157946	+	0.273571i	0.00876129	+	0.0151750i
$326$		0			0
$327$	0.503144	−	0.871471i	0.0278239	−	0.0481924i
$328$		0			0
$329$	7.25566	+	16.2309i	0.400017	+	0.894838i
$330$		0			0
$331$	9.46350	−	16.3913i	0.520161	−	0.900945i	−0.479564	−	0.877507i	$-0.659205\pi$
$331$	9.46350	−	16.3913i	0.520161	−	0.900945i	0.999725	−	0.0234383i	$-0.00746132\pi$
$332$		0			0
$333$	0.0156724	+	0.0271454i	0.000858842	+	0.00148756i
$334$		0			0
$335$	−20.5127			−1.12073
$336$		0			0
$337$	16.2630			0.885903			0.442951	−	0.896546i	$-0.353931\pi$
$337$	16.2630			0.885903			0.442951	+	0.896546i	$0.353931\pi$
$338$		0			0
$339$	−1.60817	−	2.78543i	−0.0873436	−	0.151284i
$340$		0			0
$341$	6.51027	−	11.2761i	0.352551	−	0.610636i
$342$		0			0
$343$	−17.6394	−	5.64372i	−0.952438	−	0.304732i
$344$		0			0
$345$	15.2048	−	26.3355i	0.818601	−	1.41786i
$346$		0			0
$347$	−1.35912	−	2.35407i	−0.0729615	−	0.126373i	0.827236	−	0.561854i	$-0.189912\pi$
$347$	−1.35912	−	2.35407i	−0.0729615	−	0.126373i	−0.900198	+	0.435481i	$0.856578\pi$
$348$		0			0
$349$	−20.9033			−1.11893			−0.559464	−	0.828855i	$-0.688993\pi$
$349$	−20.9033			−1.11893			−0.559464	+	0.828855i	$0.688993\pi$
$350$		0			0
$351$	4.45546			0.237815
$352$		0			0
$353$	−5.01209	−	8.68119i	−0.266766	−	0.462053i	0.701258	−	0.712907i	$-0.252622\pi$
$353$	−5.01209	−	8.68119i	−0.266766	−	0.462053i	−0.968025	+	0.250854i	$0.919289\pi$
$354$		0			0
$355$	1.98436	−	3.43701i	0.105319	−	0.182418i
$356$		0			0
$357$	8.80545	+	19.6978i	0.466034	+	1.04252i
$358$		0			0
$359$	16.9708	−	29.3943i	0.895686	−	1.55137i	0.0627337	−	0.998030i	$-0.480018\pi$
$359$	16.9708	−	29.3943i	0.895686	−	1.55137i	0.832953	−	0.553344i	$-0.186649\pi$
$360$		0			0
$361$	1.89144	+	3.27606i	0.0995493	+	0.172424i
$362$		0			0
$363$	3.13994			0.164804
$364$		0			0
$365$	8.38704			0.438998
$366$		0			0
$367$	−14.1698	−	24.5428i	−0.739656	−	1.28112i	−0.952650	−	0.304069i	$-0.901655\pi$
$367$	−14.1698	−	24.5428i	−0.739656	−	1.28112i	0.212994	−	0.977054i	$-0.431679\pi$
$368$		0			0
$369$	0.0329726	−	0.0571103i	0.00171649	−	0.00297304i
$370$		0			0
$371$	9.02507	+	0.934882i	0.468558	+	0.0485366i
$372$		0			0
$373$	15.6932	−	27.1815i	0.812565	−	1.40740i	−0.0984982	−	0.995137i	$-0.531404\pi$
$373$	15.6932	−	27.1815i	0.812565	−	1.40740i	0.911063	−	0.412267i	$-0.135263\pi$
$374$		0			0
$375$	−9.89802	−	17.1439i	−0.511132	−	0.885306i
$376$		0			0
$377$	0.0489044			0.00251870
$378$		0			0
$379$	−6.85269			−0.351999			−0.176000	−	0.984390i	$-0.556316\pi$
$379$	−6.85269			−0.351999			−0.176000	+	0.984390i	$0.556316\pi$
$380$		0			0
$381$	10.2123	+	17.6883i	0.523193	+	0.906197i
$382$		0			0
$383$	18.9657	−	32.8496i	0.969102	−	1.67853i	0.270939	−	0.962597i	$-0.412666\pi$
$383$	18.9657	−	32.8496i	0.969102	−	1.67853i	0.698164	−	0.715938i	$-0.254001\pi$
$384$		0			0
$385$	−10.1079	+	13.9563i	−0.515146	+	0.711280i
$386$		0			0
$387$	0.0932026	−	0.161432i	0.00473776	−	0.00820604i
$388$		0			0
$389$	−9.36519	−	16.2210i	−0.474834	−	0.822437i	0.524751	−	0.851256i	$-0.324159\pi$
$389$	−9.36519	−	16.2210i	−0.474834	−	0.822437i	−0.999585	+	0.0288194i	$0.990825\pi$
$390$		0			0
$391$	−39.2908			−1.98702
$392$		0			0
$393$	32.8676			1.65795
$394$		0			0
$395$	−5.50429	−	9.53371i	−0.276951	−	0.479693i
$396$		0			0
$397$	−10.3347	+	17.9001i	−0.518681	+	0.898382i	0.481083	+	0.876675i	$0.340244\pi$
$397$	−10.3347	+	17.9001i	−0.518681	+	0.898382i	−0.999764	+	0.0217074i	$0.993090\pi$
$398$		0			0
$399$	10.3698	−	14.3179i	0.519139	−	0.716792i
$400$		0			0
$401$	−18.3456	+	31.7756i	−0.916137	+	1.58680i	−0.110909	+	0.993831i	$0.535376\pi$
$401$	−18.3456	+	31.7756i	−0.916137	+	1.58680i	−0.805228	+	0.592965i	$0.797957\pi$
$402$		0			0
$403$	−1.82424	−	3.15968i	−0.0908719	−	0.157395i
$404$		0			0
$405$	−18.9258			−0.940433
$406$		0			0
$407$	−1.43911			−0.0713339
$408$		0			0
$409$	13.4339	+	23.2682i	0.664264	+	1.15054i	0.979484	+	0.201521i	$0.0645884\pi$
$409$	13.4339	+	23.2682i	0.664264	+	1.15054i	−0.315220	+	0.949019i	$0.602078\pi$
$410$		0			0
$411$	−6.86117	+	11.8839i	−0.338437	+	0.586190i
$412$		0			0
$413$	−15.0767	−	1.56175i	−0.741875	−	0.0768488i
$414$		0			0
$415$	7.97253	−	13.8088i	0.391356	−	0.677849i
$416$		0			0
$417$	17.4209	+	30.1739i	0.853105	+	1.47762i
$418$		0			0
$419$	−32.5057			−1.58801			−0.794004	−	0.607913i	$-0.792007\pi$
$419$	−32.5057			−1.58801			−0.794004	+	0.607913i	$0.792007\pi$
$420$		0			0
$421$	−39.9668			−1.94786			−0.973931	−	0.226844i	$-0.927159\pi$
$421$	−39.9668			−1.94786			−0.973931	+	0.226844i	$0.927159\pi$
$422$		0			0
$423$	0.221568	+	0.383767i	0.0107730	+	0.0186594i
$424$		0			0
$425$	−0.886359	+	1.53522i	−0.0429947	+	0.0744691i
$426$		0			0
$427$	6.44302	+	14.4130i	0.311800	+	0.697495i
$428$		0			0
$429$	−2.19993	+	3.81039i	−0.106214	+	0.183968i
$430$		0			0
$431$	−17.1287	−	29.6678i	−0.825061	−	1.42905i	−0.901872	−	0.432002i	$-0.857807\pi$
$431$	−17.1287	−	29.6678i	−0.825061	−	1.42905i	0.0768112	−	0.997046i	$-0.475526\pi$
$432$		0			0
$433$	−10.9293			−0.525229			−0.262615	−	0.964901i	$-0.584585\pi$
$433$	−10.9293			−0.525229			−0.262615	+	0.964901i	$0.584585\pi$
$434$		0			0
$435$	−0.212407			−0.0101841
$436$		0			0
$437$	16.0966	+	27.8801i	0.770003	+	1.33369i
$438$		0			0
$439$	−18.0085	+	31.1917i	−0.859499	+	1.48870i	0.0129077	+	0.999917i	$0.495891\pi$
$439$	−18.0085	+	31.1917i	−0.859499	+	1.48870i	−0.872407	+	0.488780i	$0.837442\pi$
$440$		0			0
$441$	−0.451815	−	0.0946199i	−0.0215150	−	0.00450571i
$442$		0			0
$443$	7.64667	−	13.2444i	0.363304	−	0.629262i	−0.625198	−	0.780466i	$-0.714982\pi$
$443$	7.64667	−	13.2444i	0.363304	−	0.629262i	0.988503	+	0.151204i	$0.0483151\pi$
$444$		0			0
$445$	0.328207	+	0.568472i	0.0155585	+	0.0269482i
$446$		0			0
$447$	18.1263			0.857342
$448$		0			0
$449$	−22.7342			−1.07289			−0.536447	−	0.843934i	$-0.680234\pi$
$449$	−22.7342			−1.07289			−0.536447	+	0.843934i	$0.680234\pi$
$450$		0			0
$451$	1.51384	+	2.62205i	0.0712841	+	0.123468i
$452$		0			0
$453$	−9.86652	+	17.0893i	−0.463570	+	0.802926i
$454$		0			0
$455$	1.97060	+	4.40822i	0.0923830	+	0.206660i
$456$		0			0
$457$	2.59185	−	4.48922i	0.121242	−	0.209997i	−0.799016	−	0.601310i	$-0.794646\pi$
$457$	2.59185	−	4.48922i	0.121242	−	0.209997i	0.920258	+	0.391313i	$0.127979\pi$
$458$		0			0
$459$	12.5015	+	21.6533i	0.583521	+	1.01069i
$460$		0			0
$461$	−15.9517			−0.742946			−0.371473	−	0.928444i	$-0.621147\pi$
$461$	−15.9517			−0.742946			−0.371473	+	0.928444i	$0.621147\pi$
$462$		0			0
$463$	−23.8765			−1.10964			−0.554818	−	0.831972i	$-0.687212\pi$
$463$	−23.8765			−1.10964			−0.554818	+	0.831972i	$0.687212\pi$
$464$		0			0
$465$	7.92324	+	13.7235i	0.367431	+	0.636410i
$466$		0			0
$467$	−8.65914	+	14.9981i	−0.400697	+	0.694028i	−0.993810	−	0.111091i	$-0.964565\pi$
$467$	−8.65914	+	14.9981i	−0.400697	+	0.694028i	0.593113	+	0.805119i	$0.297899\pi$
$468$		0			0
$469$	25.0943	+	2.59945i	1.15875	+	0.120031i
$470$		0			0
$471$	3.44814	−	5.97235i	0.158882	−	0.275191i
$472$		0			0
$473$	4.27913	+	7.41168i	0.196755	+	0.340789i
$474$		0			0
$475$	1.45249			0.0666446
$476$		0			0
$477$	0.226153			0.0103548
$478$		0			0
$479$	17.6965	+	30.6513i	0.808575	+	1.40049i	0.913851	+	0.406050i	$0.133094\pi$
$479$	17.6965	+	30.6513i	0.808575	+	1.40049i	−0.105275	+	0.994443i	$0.533572\pi$
$480$		0			0
$481$	−0.201626	+	0.349226i	−0.00919335	+	0.0159233i
$482$		0			0
$483$	−21.9382	+	30.2908i	−0.998221	+	1.37828i
$484$		0			0
$485$	12.6431	−	21.8985i	0.574093	−	0.994359i
$486$		0			0
$487$	17.6182	+	30.5156i	0.798357	+	1.38279i	0.920686	+	0.390305i	$0.127630\pi$
$487$	17.6182	+	30.5156i	0.798357	+	1.38279i	−0.122329	+	0.992490i	$0.539036\pi$
$488$		0			0
$489$	32.6414			1.47610
$490$		0			0
$491$	8.56552			0.386556			0.193278	−	0.981144i	$-0.438088\pi$
$491$	8.56552			0.386556			0.193278	+	0.981144i	$0.438088\pi$
$492$		0			0
$493$	0.137220	+	0.237672i	0.00618009	+	0.0107042i
$494$		0			0
$495$	−0.214756	+	0.371968i	−0.00965256	+	0.0167187i
$496$		0			0
$497$	−2.86312	+	3.95321i	−0.128428	+	0.177325i
$498$		0			0
$499$	−6.83597	+	11.8402i	−0.306020	+	0.530042i	−0.977488	−	0.210991i	$-0.932331\pi$
$499$	−6.83597	+	11.8402i	−0.306020	+	0.530042i	0.671468	+	0.741034i	$0.265664\pi$
$500$		0			0
$501$	10.0524	+	17.4112i	0.449107	+	0.777876i
$502$		0			0
$503$	−21.0857			−0.940167			−0.470084	−	0.882622i	$-0.655776\pi$
$503$	−21.0857			−0.940167			−0.470084	+	0.882622i	$0.655776\pi$
$504$		0			0
$505$	4.56701			0.203229
$506$		0			0
$507$	−10.5175	−	18.2168i	−0.467097	−	0.809036i
$508$		0			0
$509$	13.3446	−	23.1135i	0.591489	−	1.02449i	−0.402544	−	0.915401i	$-0.631874\pi$
$509$	13.3446	−	23.1135i	0.591489	−	1.02449i	0.994032	−	0.109087i	$-0.0347929\pi$
$510$		0			0
$511$	−10.2603	−	1.06283i	−0.453888	−	0.0470170i
$512$		0			0
$513$	10.2432	−	17.7417i	0.452247	−	0.783316i
$514$		0			0
$515$	8.09213	+	14.0160i	0.356582	+	0.617618i
$516$		0			0
$517$	−20.3453			−0.894787
$518$		0			0
$519$	2.58699			0.113556
$520$		0			0
$521$	8.71978	+	15.1031i	0.382020	+	0.661679i	0.991351	−	0.131238i	$-0.0418951\pi$
$521$	8.71978	+	15.1031i	0.382020	+	0.661679i	−0.609330	+	0.792916i	$0.708562\pi$
$522$		0			0
$523$	−19.1826	+	33.2252i	−0.838795	+	1.45284i	0.0521079	+	0.998641i	$0.483406\pi$
$523$	−19.1826	+	33.2252i	−0.838795	+	1.45284i	−0.890903	+	0.454194i	$0.849927\pi$
$524$		0			0
$525$	0.688657	+	1.54052i	0.0300554	+	0.0672339i
$526$		0			0
$527$	10.2372	−	17.7314i	0.445941	−	0.772392i
$528$		0			0
$529$	−22.5537	−	39.0641i	−0.980595	−	1.69844i
$530$		0			0
$531$	−0.377796			−0.0163950
$532$		0			0
$533$	0.848387			0.0367477
$534$		0			0
$535$	13.8783	+	24.0380i	0.600012	+	1.03925i
$536$		0			0
$537$	−1.18420	+	2.05109i	−0.0511020	+	0.0885113i
$538$		0			0
$539$	14.1341	−	15.7926i	0.608799	−	0.680234i
$540$		0			0
$541$	0.930955	−	1.61246i	0.0400249	−	0.0693251i	−0.845319	−	0.534262i	$-0.820590\pi$
$541$	0.930955	−	1.61246i	0.0400249	−	0.0693251i	0.885344	+	0.464937i	$0.153923\pi$
$542$		0			0
$543$	−2.75263	−	4.76770i	−0.118127	−	0.204602i
$544$		0			0
$545$	1.26377			0.0541340
$546$		0			0
$547$	32.7545			1.40048			0.700240	−	0.713908i	$-0.253076\pi$
$547$	32.7545			1.40048			0.700240	+	0.713908i	$0.253076\pi$
$548$		0			0
$549$	0.196752	+	0.340785i	0.00839719	+	0.0145444i
$550$		0			0
$551$	0.112432	−	0.194738i	0.00478977	−	0.00829612i
$552$		0			0
$553$	5.52553	+	12.3606i	0.234970	+	0.525626i
$554$		0			0
$555$	0.875723	−	1.51680i	0.0371724	−	0.0643844i
$556$		0			0
$557$	16.9886	+	29.4250i	0.719828	+	1.24678i	0.961068	+	0.276314i	$0.0891128\pi$
$557$	16.9886	+	29.4250i	0.719828	+	1.24678i	−0.241239	+	0.970466i	$0.577554\pi$
$558$		0			0
$559$	2.39811			0.101429
$560$		0			0
$561$	−24.6910			−1.04246
$562$		0			0
$563$	16.8593	+	29.2012i	0.710536	+	1.23068i	0.964656	+	0.263512i	$0.0848809\pi$
$563$	16.8593	+	29.2012i	0.710536	+	1.23068i	−0.254120	+	0.967173i	$0.581786\pi$
$564$		0			0
$565$	2.01966	−	3.49815i	0.0849676	−	0.147168i
$566$		0			0
$567$	23.1529	+	2.39835i	0.972332	+	0.100721i
$568$		0			0
$569$	−7.92141	+	13.7203i	−0.332083	+	0.575184i	−0.982920	−	0.184033i	$-0.941085\pi$
$569$	−7.92141	+	13.7203i	−0.332083	+	0.575184i	0.650837	+	0.759217i	$0.274418\pi$
$570$		0			0
$571$	21.2687	+	36.8384i	0.890065	+	1.54164i	0.839796	+	0.542903i	$0.182675\pi$
$571$	21.2687	+	36.8384i	0.890065	+	1.54164i	0.0502697	+	0.998736i	$0.483992\pi$
$572$		0			0
$573$	10.8165			0.451865
$574$		0			0
$575$	−3.07286			−0.128147
$576$		0			0
$577$	2.39918	+	4.15550i	0.0998791	+	0.172996i	0.911634	−	0.411002i	$-0.134821\pi$
$577$	2.39918	+	4.15550i	0.0998791	+	0.172996i	−0.811755	+	0.583998i	$0.801488\pi$
$578$		0			0
$579$	−13.0025	+	22.5209i	−0.540364	+	0.935938i
$580$		0			0
$581$	−11.5031	+	15.8827i	−0.477229	+	0.658927i
$582$		0			0
$583$	−5.19159	+	8.99209i	−0.215014	+	0.372414i
$584$		0			0
$585$	0.0601767	+	0.104229i	0.00248800	+	0.00430934i
$586$		0			0
$587$	0.292839			0.0120868			0.00604339	−	0.999982i	$-0.498076\pi$
$587$	0.292839			0.0120868			0.00604339	+	0.999982i	$0.498076\pi$
$588$		0			0
$589$	−16.7758			−0.691237
$590$		0			0
$591$	−15.3700	−	26.6217i	−0.632239	−	1.09507i
$592$		0			0
$593$	−1.33939	+	2.31989i	−0.0550022	+	0.0952666i	−0.892216	−	0.451610i	$-0.850850\pi$
$593$	−1.33939	+	2.31989i	−0.0550022	+	0.0952666i	0.837213	+	0.546876i	$0.184183\pi$
$594$		0			0
$595$	−15.8944	+	21.9459i	−0.651607	+	0.899696i
$596$		0			0
$597$	6.69912	−	11.6032i	0.274177	−	0.474888i
$598$		0			0
$599$	7.98117	+	13.8238i	0.326102	+	0.564825i	0.981735	−	0.190255i	$-0.0609314\pi$
$599$	7.98117	+	13.8238i	0.326102	+	0.564825i	−0.655633	+	0.755080i	$0.727598\pi$
$600$		0			0
$601$	7.88205			0.321516			0.160758	−	0.986994i	$-0.448606\pi$
$601$	7.88205			0.321516			0.160758	+	0.986994i	$0.448606\pi$
$602$		0			0
$603$	0.628821			0.0256076
$604$		0			0
$605$	1.97169	+	3.41506i	0.0801604	+	0.138842i
$606$		0			0
$607$	16.7550	−	29.0205i	0.680064	−	1.17790i	−0.294897	−	0.955529i	$-0.595285\pi$
$607$	16.7550	−	29.0205i	0.680064	−	1.17790i	0.974961	−	0.222376i	$-0.0713812\pi$
$608$		0			0
$609$	0.259848	+	0.0269169i	0.0105296	+	0.00109073i
$610$		0			0
$611$	−2.85048	+	4.93717i	−0.115318	+	0.199737i
$612$		0			0
$613$	−16.7545	−	29.0197i	−0.676708	−	1.17209i	−0.975966	−	0.217921i	$-0.930072\pi$
$613$	−16.7545	−	29.0197i	−0.676708	−	1.17209i	0.299258	−	0.954172i	$-0.403261\pi$
$614$		0			0
$615$	−3.68481			−0.148586
$616$		0			0
$617$	45.8922			1.84755			0.923775	−	0.382935i	$-0.125087\pi$
$617$	45.8922			1.84755			0.923775	+	0.382935i	$0.125087\pi$
$618$		0			0
$619$	−14.9381	−	25.8735i	−0.600412	−	1.03994i	−0.992759	−	0.120127i	$-0.961670\pi$
$619$	−14.9381	−	25.8735i	−0.600412	−	1.03994i	0.392346	−	0.919818i	$-0.371663\pi$
$620$		0			0
$621$	−21.6703	+	37.5341i	−0.869600	+	1.50619i
$622$		0			0
$623$	−0.329474	−	0.737032i	−0.0132001	−	0.0295286i
$624$		0			0
$625$	11.4998	−	19.9183i	0.459993	−	0.796731i
$626$		0			0
$627$	10.1154	+	17.5203i	0.403969	+	0.699694i
$628$		0			0
$629$	−2.26296			−0.0902300
$630$		0			0
$631$	5.54997			0.220941			0.110470	−	0.993879i	$-0.464764\pi$
$631$	5.54997			0.220941			0.110470	+	0.993879i	$0.464764\pi$
$632$		0			0
$633$	−1.97018	−	3.41245i	−0.0783077	−	0.135633i
$634$		0			0
$635$	−12.8254	+	22.2142i	−0.508960	+	0.881545i
$636$		0			0
$637$	−1.85211	−	5.64252i	−0.0733831	−	0.223565i
$638$		0			0
$639$	−0.0608308	+	0.105362i	−0.00240643	+	0.00416806i
$640$		0			0
$641$	−13.0005	−	22.5175i	−0.513489	−	0.889389i	−0.999878	−	0.0156464i	$-0.995019\pi$
$641$	−13.0005	−	22.5175i	−0.513489	−	0.889389i	0.486389	−	0.873743i	$-0.338314\pi$
$642$		0			0
$643$	25.0891			0.989419			0.494709	−	0.869058i	$-0.335275\pi$
$643$	25.0891			0.989419			0.494709	+	0.869058i	$0.335275\pi$
$644$		0			0
$645$	−10.4157			−0.410119
$646$		0			0
$647$	8.64521	+	14.9739i	0.339878	+	0.588686i	0.984410	−	0.175891i	$-0.0562808\pi$
$647$	8.64521	+	14.9739i	0.339878	+	0.588686i	−0.644531	+	0.764578i	$0.722947\pi$
$648$		0			0
$649$	8.67272	−	15.0216i	0.340434	−	0.589649i
$650$		0			0
$651$	−7.95381	−	17.7927i	−0.311735	−	0.697349i
$652$		0			0
$653$	−4.64842	+	8.05130i	−0.181907	+	0.315072i	−0.942530	−	0.334122i	$-0.891560\pi$
$653$	−4.64842	+	8.05130i	−0.181907	+	0.315072i	0.760623	+	0.649194i	$0.224894\pi$
$654$		0			0
$655$	20.6388	+	35.7474i	0.806424	+	1.39677i
$656$		0			0
$657$	−0.257106			−0.0100306
$658$		0			0
$659$	5.40667			0.210614			0.105307	−	0.994440i	$-0.466417\pi$
$659$	5.40667			0.210614			0.105307	+	0.994440i	$0.466417\pi$
$660$		0			0
$661$	−12.3611	−	21.4101i	−0.480792	−	0.832757i	0.518965	−	0.854796i	$-0.326318\pi$
$661$	−12.3611	−	21.4101i	−0.480792	−	0.832757i	−0.999757	+	0.0220390i	$0.992984\pi$
$662$		0			0
$663$	−3.45933	+	5.99174i	−0.134349	+	0.232700i
$664$		0			0
$665$	22.0840	+	2.28762i	0.856382	+	0.0887102i
$666$		0			0
$667$	−0.237860	+	0.411985i	−0.00920996	+	0.0159521i
$668$		0			0
$669$	−5.14888	−	8.91812i	−0.199067	−	0.344795i
$670$		0			0
$671$	−18.0667			−0.697456
$672$		0			0
$673$	−19.7190			−0.760110			−0.380055	−	0.924964i	$-0.624095\pi$
$673$	−19.7190			−0.760110			−0.380055	+	0.924964i	$0.624095\pi$
$674$		0			0
$675$	0.977719	+	1.69346i	0.0376324	+	0.0651813i
$676$		0			0
$677$	8.82481	−	15.2850i	0.339165	−	0.587451i	−0.645111	−	0.764089i	$-0.723189\pi$
$677$	8.82481	−	15.2850i	0.339165	−	0.587451i	0.984276	+	0.176638i	$0.0565222\pi$
$678$		0			0
$679$	−18.2420	+	25.1873i	−0.700063	+	0.966602i
$680$		0			0
$681$	21.2943	−	36.8828i	0.815998	−	1.41335i
$682$		0			0
$683$	22.9542	+	39.7578i	0.878317	+	1.52129i	0.853187	+	0.521605i	$0.174666\pi$
$683$	22.9542	+	39.7578i	0.878317	+	1.52129i	0.0251292	+	0.999684i	$0.492000\pi$
$684$		0			0
$685$	−17.2336			−0.658460
$686$		0			0
$687$	41.1629			1.57046
$688$		0			0
$689$	1.45473	+	2.51967i	0.0554209	+	0.0959918i
$690$		0			0
$691$	19.4638	−	33.7123i	0.740439	−	1.28248i	−0.211857	−	0.977301i	$-0.567951\pi$
$691$	19.4638	−	33.7123i	0.740439	−	1.28248i	0.952296	−	0.305177i	$-0.0987156\pi$
$692$		0			0
$693$	0.309859	−	0.427833i	0.0117706	−	0.0162520i
$694$		0			0
$695$	−21.8785	+	37.8946i	−0.829897	+	1.43742i
$696$		0			0
$697$	2.38048	+	4.12311i	0.0901671	+	0.156174i
$698$		0			0
$699$	13.3183			0.503743
$700$		0			0
$701$	19.2696			0.727803			0.363902	−	0.931437i	$-0.381444\pi$
$701$	19.2696			0.727803			0.363902	+	0.931437i	$0.381444\pi$
$702$		0			0
$703$	0.927083	+	1.60575i	0.0349656	+	0.0605622i
$704$		0			0
$705$	12.3805	−	21.4437i	0.466277	−	0.807615i
$706$		0			0
$707$	−5.58705	−	0.578747i	−0.210123	−	0.0217660i
$708$		0			0
$709$	12.1248	−	21.0007i	0.455355	−	0.788697i	−0.543354	−	0.839504i	$-0.682846\pi$
$709$	12.1248	−	21.0007i	0.455355	−	0.788697i	0.998709	+	0.0508064i	$0.0161792\pi$
$710$		0			0
$711$	0.168735	+	0.292257i	0.00632805	+	0.0109605i
$712$		0			0
$713$	35.4908			1.32914
$714$		0			0
$715$	−5.52568			−0.206649
$716$		0			0
$717$	16.4916	+	28.5643i	0.615891	+	1.06675i
$718$		0			0
$719$	8.21677	−	14.2319i	0.306434	−	0.530759i	−0.671146	−	0.741325i	$-0.734198\pi$
$719$	8.21677	−	14.2319i	0.306434	−	0.530759i	0.977580	+	0.210567i	$0.0675309\pi$
$720$		0			0
$721$	−8.12335	−	18.1719i	−0.302529	−	0.676757i
$722$		0			0
$723$	5.06924	−	8.78018i	0.188527	−	0.326539i
$724$		0			0
$725$	0.0107317	+	0.0185879i	0.000398566	+	0.000690337i
$726$		0			0
$727$	−47.2145			−1.75109			−0.875545	−	0.483136i	$-0.839497\pi$
$727$	−47.2145			−1.75109			−0.875545	+	0.483136i	$0.839497\pi$
$728$		0			0
$729$	27.5671			1.02100
$730$		0			0
$731$	6.72882	+	11.6547i	0.248874	+	0.431063i
$732$		0			0
$733$	0.430006	−	0.744792i	0.0158826	−	0.0275095i	−0.857975	−	0.513692i	$-0.828278\pi$
$733$	0.430006	−	0.744792i	0.0158826	−	0.0275095i	0.873857	+	0.486182i	$0.161611\pi$
$734$		0			0
$735$	8.04426	+	24.5072i	0.296717	+	0.903961i
$736$		0			0
$737$	−14.4353	+	25.0026i	−0.531729	+	0.920982i
$738$		0			0
$739$	−8.90421	−	15.4225i	−0.327547	−	0.567328i	0.654478	−	0.756081i	$-0.272889\pi$
$739$	−8.90421	−	15.4225i	−0.327547	−	0.567328i	−0.982024	+	0.188754i	$0.939555\pi$
$740$		0			0
$741$	5.66884			0.208250
$742$		0			0
$743$	−2.23502			−0.0819950			−0.0409975	−	0.999159i	$-0.513054\pi$
$743$	−2.23502			−0.0819950			−0.0409975	+	0.999159i	$0.513054\pi$
$744$		0			0
$745$	11.3822	+	19.7145i	0.417010	+	0.722282i
$746$		0			0
$747$	−0.244399	+	0.423312i	−0.00894209	+	0.0154882i
$748$		0			0
$749$	−13.9319	−	31.1656i	−0.509060	−	1.13876i
$750$		0			0
$751$	−26.0368	+	45.0971i	−0.950097	+	1.64562i	−0.204888	+	0.978785i	$0.565683\pi$
$751$	−26.0368	+	45.0971i	−0.950097	+	1.64562i	−0.745209	+	0.666831i	$0.767650\pi$
$752$		0			0
$753$	24.1442	+	41.8190i	0.879864	+	1.52397i
$754$		0			0
$755$	−24.7822			−0.901918
$756$		0			0
$757$	3.36576			0.122331			0.0611653	−	0.998128i	$-0.480518\pi$
$757$	3.36576			0.122331			0.0611653	+	0.998128i	$0.480518\pi$
$758$		0			0
$759$	−21.3999	−	37.0658i	−0.776768	−	1.34540i
$760$		0			0
$761$	−3.59454	+	6.22593i	−0.130302	+	0.225690i	−0.923793	−	0.382892i	$-0.874928\pi$
$761$	−3.59454	+	6.22593i	−0.130302	+	0.225690i	0.793491	+	0.608582i	$0.208261\pi$
$762$		0			0
$763$	−1.54604	−	0.160150i	−0.0559702	−	0.00579780i
$764$		0			0
$765$	−0.337698	+	0.584910i	−0.0122095	+	0.0211475i
$766$		0			0
$767$	−2.43018	−	4.20919i	−0.0877487	−	0.151985i
$768$		0			0
$769$	3.07410			0.110855			0.0554275	−	0.998463i	$-0.482348\pi$
$769$	3.07410			0.110855			0.0554275	+	0.998463i	$0.482348\pi$
$770$		0			0
$771$	−7.32908			−0.263951
$772$		0			0
$773$	9.36690	+	16.2239i	0.336904	+	0.583535i	0.983849	−	0.179002i	$-0.0572869\pi$
$773$	9.36690	+	16.2239i	0.336904	+	0.583535i	−0.646945	+	0.762537i	$0.723954\pi$
$774$		0			0
$775$	0.800633	−	1.38674i	0.0287596	−	0.0498131i
$776$		0			0
$777$	−1.26353	+	1.74460i	−0.0453289	+	0.0625871i
$778$		0			0
$779$	1.95046	−	3.37829i	0.0698824	−	0.121040i
$780$		0			0
$781$	−2.79287	−	4.83740i	−0.0999368	−	0.173096i
$782$		0			0
$783$	0.302728			0.0108186
$784$		0			0
$785$	8.66086			0.309119
$786$		0			0
$787$	−18.7784	−	32.5251i	−0.669377	−	1.15939i	−0.978079	−	0.208236i	$-0.933228\pi$
$787$	−18.7784	−	32.5251i	−0.669377	−	1.15939i	0.308702	−	0.951159i	$-0.400105\pi$
$788$		0			0
$789$	−4.65736	+	8.06678i	−0.165806	+	0.287185i
$790$		0			0
$791$	−2.91404	+	4.02352i	−0.103611	+	0.143060i
$792$		0			0
$793$	−2.53122	+	4.38421i	−0.0898864	+	0.155688i
$794$		0			0
$795$	−6.31835	−	10.9437i	−0.224089	−	0.388133i
$796$		0			0
$797$	−13.5950			−0.481559			−0.240779	−	0.970580i	$-0.577403\pi$
$797$	−13.5950			−0.481559			−0.240779	+	0.970580i	$0.577403\pi$
$798$		0			0
$799$	−31.9925			−1.13181
$800$		0			0
$801$	−0.0100612	−	0.0174266i	−0.000355496	−	0.000615738i
$802$		0			0
$803$	5.90214	−	10.2228i	0.208282	−	0.360755i
$804$		0			0
$805$	−46.7207	−	4.83966i	−1.64669	−	0.170576i
$806$		0			0
$807$	11.8775	−	20.5724i	0.418108	−	0.724184i
$808$		0			0
$809$	−11.3095	−	19.5886i	−0.397621	−	0.688700i	0.595811	−	0.803125i	$-0.296831\pi$
$809$	−11.3095	−	19.5886i	−0.397621	−	0.688700i	−0.993432	+	0.114425i	$0.963497\pi$
$810$		0			0
$811$	−36.5762			−1.28437			−0.642183	−	0.766552i	$-0.721971\pi$
$811$	−36.5762			−1.28437			−0.642183	+	0.766552i	$0.721971\pi$
$812$		0			0
$813$	−23.4857			−0.823679
$814$		0			0
$815$	20.4968	+	35.5015i	0.717971	+	1.24356i
$816$		0			0
$817$	5.51329	−	9.54930i	0.192886	−	0.334088i
$818$		0			0
$819$	−0.0604089	−	0.135134i	−0.00211086	−	0.00472198i
$820$		0			0
$821$	−21.9220	+	37.9701i	−0.765084	+	1.32517i	0.175118	+	0.984548i	$0.443969\pi$
$821$	−21.9220	+	37.9701i	−0.765084	+	1.32517i	−0.940202	+	0.340618i	$0.889364\pi$
$822$		0			0
$823$	−12.4342	−	21.5367i	−0.433429	−	0.750722i	0.563737	−	0.825955i	$-0.309363\pi$
$823$	−12.4342	−	21.5367i	−0.433429	−	0.750722i	−0.997166	+	0.0752329i	$0.976030\pi$
$824$		0			0
$825$	−1.93104			−0.0672301
$826$		0			0
$827$	−19.4951			−0.677911			−0.338956	−	0.940802i	$-0.610074\pi$
$827$	−19.4951			−0.677911			−0.338956	+	0.940802i	$0.610074\pi$
$828$		0			0
$829$	3.73417	+	6.46778i	0.129693	+	0.224635i	0.923558	−	0.383460i	$-0.125267\pi$
$829$	3.73417	+	6.46778i	0.129693	+	0.224635i	−0.793865	+	0.608095i	$0.791934\pi$
$830$		0			0
$831$	−6.53157	+	11.3130i	−0.226578	+	0.392444i
$832$		0			0
$833$	22.2255	−	24.8334i	0.770067	−	0.860426i
$834$		0			0
$835$	−12.6245	+	21.8663i	−0.436890	+	0.756715i
$836$		0			0
$837$	−11.2924	−	19.5590i	−0.390323	−	0.676059i
$838$		0			0
$839$	−0.549539			−0.0189722			−0.00948610	−	0.999955i	$-0.503020\pi$
$839$	−0.549539			−0.0189722			−0.00948610	+	0.999955i	$0.503020\pi$
$840$		0			0
$841$	−28.9967			−0.999885
$842$		0			0
$843$	−22.3078	−	38.6383i	−0.768322	−	1.33077i
$844$		0			0
$845$	13.2086	−	22.8780i	0.454390	−	0.787027i
$846$		0			0
$847$	−1.97929	−	4.42767i	−0.0680094	−	0.152137i
$848$		0			0
$849$	2.96447	−	5.13461i	0.101740	−	0.176219i
$850$		0			0
$851$	−1.96132	−	3.39711i	−0.0672333	−	0.116451i
$852$		0			0
$853$	13.6543			0.467516			0.233758	−	0.972295i	$-0.424898\pi$
$853$	13.6543			0.467516			0.233758	+	0.972295i	$0.424898\pi$
$854$		0			0
$855$	0.553389			0.0189255
$856$		0			0
$857$	−16.9533	−	29.3640i	−0.579115	−	1.00306i	−0.995581	−	0.0939048i	$-0.970065\pi$
$857$	−16.9533	−	29.3640i	−0.579115	−	1.00306i	0.416467	−	0.909151i	$-0.363268\pi$
$858$		0			0
$859$	17.9104	−	31.0217i	0.611095	−	1.05845i	−0.379961	−	0.925002i	$-0.624063\pi$
$859$	17.9104	−	31.0217i	0.611095	−	1.05845i	0.991056	−	0.133445i	$-0.0426039\pi$
$860$		0			0
$861$	4.50781	+	0.466951i	0.153626	+	0.0159137i
$862$		0			0
$863$	−17.2319	+	29.8466i	−0.586582	+	1.01599i	0.408094	+	0.912940i	$0.366194\pi$
$863$	−17.2319	+	29.8466i	−0.586582	+	1.01599i	−0.994676	+	0.103050i	$0.967140\pi$
$864$		0			0
$865$	1.62447	+	2.81366i	0.0552335	+	0.0956673i
$866$		0			0
$867$	−9.70656			−0.329652
$868$		0			0
$869$	−15.4939			−0.525596
$870$		0			0
$871$	4.04489	+	7.00596i	0.137056	+	0.237388i
$872$		0			0
$873$	−0.387576	+	0.671301i	−0.0131175	+	0.0227201i
$874$		0			0
$875$	−17.9355	+	24.7642i	−0.606331	+	0.837182i
$876$		0			0
$877$	24.6580	−	42.7088i	0.832640	−	1.44217i	−0.0632977	−	0.997995i	$-0.520162\pi$
$877$	24.6580	−	42.7088i	0.832640	−	1.44217i	0.895938	−	0.444180i	$-0.146505\pi$
$878$		0			0
$879$	−9.59806	−	16.6243i	−0.323734	−	0.560725i
$880$		0			0
$881$	−52.6993			−1.77548			−0.887742	−	0.460342i	$-0.847727\pi$
$881$	−52.6993			−1.77548			−0.887742	+	0.460342i	$0.847727\pi$
$882$		0			0
$883$	47.2828			1.59119			0.795597	−	0.605827i	$-0.207157\pi$
$883$	47.2828			1.59119			0.795597	+	0.605827i	$0.207157\pi$
$884$		0			0
$885$	10.5550	+	18.2818i	0.354803	+	0.614537i
$886$		0			0
$887$	−5.50213	+	9.52997i	−0.184744	+	0.319985i	−0.943490	−	0.331401i	$-0.892479\pi$
$887$	−5.50213	+	9.52997i	−0.184744	+	0.319985i	0.758747	+	0.651386i	$0.225812\pi$
$888$		0			0
$889$	18.5050	−	25.5505i	0.620638	−	0.856937i
$890$		0			0
$891$	−13.3185	+	23.0684i	−0.446187	+	0.772819i
$892$		0			0
$893$	13.1066	+	22.7013i	0.438596	+	0.759670i
$894$		0			0
$895$	−2.97441			−0.0994237
$896$		0			0
$897$	−11.9929			−0.400432
$898$		0			0
$899$	−0.123949	−	0.214685i	−0.00413392	−	0.00716016i
$900$		0			0
$901$	−8.16363	+	14.1398i	−0.271970	+	0.471066i
$902$		0			0
$903$	12.7421	+	1.31992i	0.424030	+	0.0439241i
$904$		0			0
$905$	3.45696	−	5.98764i	0.114913	−	0.199036i
$906$		0			0
$907$	25.1805	+	43.6140i	0.836106	+	1.44818i	0.893127	+	0.449805i	$0.148506\pi$
$907$	25.1805	+	43.6140i	0.836106	+	1.44818i	−0.0570210	+	0.998373i	$0.518160\pi$
$908$		0			0
$909$	−0.140002			−0.00464358
$910$		0			0
$911$	9.11340			0.301940			0.150970	−	0.988538i	$-0.451760\pi$
$911$	9.11340			0.301940			0.150970	+	0.988538i	$0.451760\pi$
$912$		0			0
$913$	−11.2209	−	19.4351i	−0.371357	−	0.643209i
$914$		0			0
$915$	10.9939	−	19.0420i	0.363447	−	0.629508i
$916$		0			0
$917$	−20.7184	−	46.3470i	−0.684183	−	1.53051i
$918$		0			0
$919$	−11.8791	+	20.5753i	−0.391857	+	0.678716i	−0.992694	−	0.120655i	$-0.961501\pi$
$919$	−11.8791	+	20.5753i	−0.391857	+	0.678716i	0.600838	+	0.799371i	$0.294834\pi$
$920$		0			0
$921$	−0.499047	−	0.864374i	−0.0164441	−	0.0284821i
$922$		0			0
$923$	−1.56518			−0.0515185
$924$		0			0
$925$	−0.176981			−0.00581911
$926$		0			0
$927$	−0.248065	−	0.429661i	−0.00814753	−	0.0141119i
$928$		0			0
$929$	−0.0898216	+	0.155576i	−0.00294695	+	0.00510427i	−0.867495	−	0.497446i	$-0.834271\pi$
$929$	−0.0898216	+	0.155576i	−0.00294695	+	0.00510427i	0.864548	+	0.502550i	$0.167605\pi$
$930$		0			0
$931$	−26.7266	−	5.59713i	−0.875929	−	0.183439i
$932$		0			0
$933$	5.34925	−	9.26517i	0.175126	−	0.303328i
$934$		0			0
$935$	−15.5044	−	26.8545i	−0.507049	−	0.878235i
$936$		0			0
$937$	25.1739			0.822396			0.411198	−	0.911546i	$-0.365110\pi$
$937$	25.1739			0.822396			0.411198	+	0.911546i	$0.365110\pi$
$938$		0			0
$939$	30.3896			0.991727
$940$		0			0
$941$	5.50547	+	9.53576i	0.179473	+	0.310857i	0.941700	−	0.336453i	$-0.109227\pi$
$941$	5.50547	+	9.53576i	0.179473	+	0.310857i	−0.762227	+	0.647310i	$0.775894\pi$
$942$		0			0
$943$	−4.12636	+	7.14706i	−0.134373	+	0.232740i
$944$		0			0
$945$	12.1984	+	27.2877i	0.396813	+	0.887670i
$946$		0			0
$947$	4.63959	−	8.03601i	0.150767	−	0.261135i	−0.780743	−	0.624852i	$-0.785159\pi$
$947$	4.63959	−	8.03601i	0.150767	−	0.261135i	0.931509	+	0.363717i	$0.118492\pi$
$948$		0			0
$949$	−1.65383	−	2.86453i	−0.0536857	−	0.0929864i
$950$		0			0
$951$	−22.1589			−0.718553
$952$		0			0
$953$	24.8414			0.804691			0.402345	−	0.915488i	$-0.368195\pi$
$953$	24.8414			0.804691			0.402345	+	0.915488i	$0.368195\pi$
$954$		0			0
$955$	6.79208	+	11.7642i	0.219786	+	0.380681i
$956$		0			0
$957$	−0.149475	+	0.258899i	−0.00483185	+	0.00836900i
$958$		0			0
$959$	21.0827	+	2.18390i	0.680795	+	0.0705217i
$960$		0			0
$961$	6.25288	−	10.8303i	0.201706	−	0.349365i
$962$		0			0
$963$	−0.425442	−	0.736887i	−0.0137097	−	0.0237458i
$964$		0			0
$965$	−32.6589			−1.05133
$966$		0			0
$967$	−24.4773			−0.787138			−0.393569	−	0.919295i	$-0.628760\pi$
$967$	−24.4773			−0.787138			−0.393569	+	0.919295i	$0.628760\pi$
$968$		0			0
$969$	15.9061	+	27.5502i	0.510979	+	0.885041i
$970$		0			0
$971$	8.68728	−	15.0468i	0.278788	−	0.482875i	−0.692296	−	0.721614i	$-0.743401\pi$
$971$	8.68728	−	15.0468i	0.278788	−	0.482875i	0.971084	+	0.238739i	$0.0767340\pi$
$972$		0			0
$973$	31.5672	−	43.5859i	1.01200	−	1.39730i
$974$		0			0
$975$	−0.270548	+	0.468602i	−0.00866446	+	0.0150073i
$976$		0			0
$977$	−20.5523	−	35.5976i	−0.657525	−	1.13887i	−0.981254	−	0.192718i	$-0.938270\pi$
$977$	−20.5523	−	35.5976i	−0.657525	−	1.13887i	0.323729	−	0.946150i	$-0.395063\pi$
$978$		0			0
$979$	0.923866			0.0295269
$980$		0			0
$981$	−0.0387411			−0.00123691
$982$		0			0
$983$	15.0847	+	26.1275i	0.481127	+	0.833337i	0.999765	−	0.0216568i	$-0.00689411\pi$
$983$	15.0847	+	26.1275i	0.481127	+	0.833337i	−0.518638	+	0.854994i	$0.673561\pi$
$984$		0			0
$985$	19.3028	−	33.4335i	0.615040	−	1.06528i
$986$		0			0
$987$	−17.8631	+	24.6642i	−0.568589	+	0.785071i
$988$		0			0
$989$	−11.6638	+	20.2024i	−0.370889	+	0.642398i
$990$		0			0
$991$	−4.47869	−	7.75732i	−0.142270	−	0.246419i	0.786081	−	0.618124i	$-0.212107\pi$
$991$	−4.47869	−	7.75732i	−0.142270	−	0.246419i	−0.928351	+	0.371704i	$0.878774\pi$
$992$		0			0
$993$	32.4202			1.02882
$994$		0			0
$995$	16.8265			0.533436
$996$		0			0
$997$	−20.4129	−	35.3561i	−0.646482	−	1.11974i	−0.983957	−	0.178405i	$-0.942906\pi$
$997$	−20.4129	−	35.3561i	−0.646482	−	1.11974i	0.337476	−	0.941334i	$-0.390427\pi$
$998$		0			0
$999$	−1.24810	+	2.16178i	−0.0394882	+	0.0683956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.821.6	yes	16
7.2	even	3		8036.2.a.m.1.3		8
7.4	even	3	inner	1148.2.i.d.165.6	✓	16
7.5	odd	6		8036.2.a.n.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.6	✓	16	7.4	even	3	inner
1148.2.i.d.821.6	yes	16	1.1	even	1	trivial
8036.2.a.m.1.3		8	7.2	even	3
8036.2.a.n.1.6		8	7.5	odd	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.856454 + 1.48342i) q^{3} +(-1.07560 + 1.86299i) q^{5} +(1.55192 - 2.14279i) q^{7} +(0.0329726 - 0.0571103i) q^{9} +O(q^{10})\)	\(q+(0.856454 + 1.48342i) q^{3} +(-1.07560 + 1.86299i) q^{5} +(1.55192 - 2.14279i) q^{7} +(0.0329726 - 0.0571103i) q^{9} +(1.51384 + 2.62205i) q^{11} +0.848387 q^{13} -3.68481 q^{15} +(2.38048 + 4.12311i) q^{17} +(1.95046 - 3.37829i) q^{19} +(4.50781 + 0.466951i) q^{21} +(-4.12636 + 7.14706i) q^{23} +(0.186172 + 0.322460i) q^{25} +5.25168 q^{27} +0.0576440 q^{29} +(-2.15025 - 3.72434i) q^{31} +(-2.59308 + 4.49134i) q^{33} +(2.32276 + 5.19600i) q^{35} +(-0.237658 + 0.411635i) q^{37} +(0.726605 + 1.25852i) q^{39} +1.00000 q^{41} +2.82667 q^{43} +(0.0709307 + 0.122856i) q^{45} +(-3.35988 + 5.81948i) q^{47} +(-2.18309 - 6.65087i) q^{49} +(-4.07754 + 7.06251i) q^{51} +(1.71470 + 2.96995i) q^{53} -6.51316 q^{55} +6.68191 q^{57} +(-2.86447 - 4.96141i) q^{59} +(-2.98357 + 5.16770i) q^{61} +(-0.0712044 - 0.159284i) q^{63} +(-0.912525 + 1.58054i) q^{65} +(4.76775 + 8.25798i) q^{67} -14.1362 q^{69} -1.84489 q^{71} +(-1.94939 - 3.37644i) q^{73} +(-0.318896 + 0.552345i) q^{75} +(7.96788 + 0.825370i) q^{77} +(-2.55871 + 4.43181i) q^{79} +(4.39891 + 7.61913i) q^{81} -7.41218 q^{83} -10.2418 q^{85} +(0.0493694 + 0.0855103i) q^{87} +(0.152570 - 0.264258i) q^{89} +(1.31663 - 1.81791i) q^{91} +(3.68317 - 6.37945i) q^{93} +(4.19582 + 7.26737i) q^{95} -11.7545 q^{97} +0.199662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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