LMFDB - Embedded newform 572.2.bq.a.49.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.188862 - 1.79690i) q^{3} +(0.283508 + 0.0921172i) q^{5} +(0.331103 - 0.0348003i) q^{7} +(-0.258739 - 0.0549966i) q^{9} +O(q^{10})$	\(q+(0.188862 - 1.79690i) q^{3} +(0.283508 + 0.0921172i) q^{5} +(0.331103 - 0.0348003i) q^{7} +(-0.258739 - 0.0549966i) q^{9} +(3.31611 - 0.0584646i) q^{11} +(-0.126208 - 3.60334i) q^{13} +(0.219069 - 0.492037i) q^{15} +(1.99984 + 2.22105i) q^{17} +(-0.927249 - 2.08263i) q^{19} -0.601532i q^{21} +(-1.64089 - 2.84211i) q^{23} +(-3.97319 - 2.88669i) q^{25} +(1.52730 - 4.70056i) q^{27} +(2.21344 + 0.985488i) q^{29} +(5.38573 - 1.74993i) q^{31} +(0.521231 - 5.96976i) q^{33} +(0.0970760 + 0.0206341i) q^{35} +(-4.22491 + 9.48929i) q^{37} +(-6.49868 - 0.453751i) q^{39} +(-7.23016 - 0.759920i) q^{41} +(0.0691846 - 0.119831i) q^{43} +(-0.0682882 - 0.0394262i) q^{45} +(2.00137 - 2.75465i) q^{47} +(-6.73861 + 1.43234i) q^{49} +(4.36870 - 3.17404i) q^{51} +(-2.78126 - 8.55983i) q^{53} +(0.945528 + 0.288896i) q^{55} +(-3.91741 + 1.27284i) q^{57} +(3.82254 - 0.401766i) q^{59} +(7.91399 + 8.78938i) q^{61} +(-0.0875830 - 0.00920535i) q^{63} +(0.296149 - 1.03320i) q^{65} +(9.08386 - 5.24457i) q^{67} +(-5.41689 + 2.41176i) q^{69} +(-2.96890 + 2.67321i) q^{71} +(2.31121 + 3.18110i) q^{73} +(-5.93749 + 6.59425i) q^{75} +(1.09594 - 0.134760i) q^{77} +(3.54293 + 10.9040i) q^{79} +(-8.88294 - 3.95494i) q^{81} +(10.9092 + 3.54461i) q^{83} +(0.362373 + 0.813904i) q^{85} +(2.18886 - 3.79121i) q^{87} +(11.7015 - 6.75586i) q^{89} +(-0.167185 - 1.18869i) q^{91} +(-2.12729 - 10.0081i) q^{93} +(-0.0710356 - 0.675858i) q^{95} +(-2.13375 + 10.0385i) q^{97} +(-0.861221 - 0.167248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.188862	−	1.79690i	0.109039	−	1.03744i	−0.794010	−	0.607904i	$-0.792010\pi$
$3$	0.188862	−	1.79690i	0.109039	−	1.03744i	0.903050	−	0.429536i	$-0.141323\pi$
$4$		0			0
$5$	0.283508	+	0.0921172i	0.126788	+	0.0411961i	0.371724	−	0.928343i	$-0.378767\pi$
$5$	0.283508	+	0.0921172i	0.126788	+	0.0411961i	−0.244935	+	0.969539i	$0.578767\pi$
$6$		0			0
$7$	0.331103	−	0.0348003i	0.125145	−	0.0131533i	−0.0417488	−	0.999128i	$-0.513293\pi$
$7$	0.331103	−	0.0348003i	0.125145	−	0.0131533i	0.166894	+	0.985975i	$0.446626\pi$
$8$		0			0
$9$	−0.258739	−	0.0549966i	−0.0862462	−	0.0183322i
$10$		0			0
$11$	3.31611	−	0.0584646i	0.999845	−	0.0176277i
$11$	3.31611	−	0.0584646i	0.999845	−	0.0176277i
$12$		0			0
$13$	−0.126208	−	3.60334i	−0.0350038	−	0.999387i
$13$	−0.126208	−	3.60334i	−0.0350038	−	0.999387i
$14$		0			0
$15$	0.219069	−	0.492037i	0.0565634	−	0.127044i
$16$		0			0
$17$	1.99984	+	2.22105i	0.485033	+	0.538683i	0.935134	−	0.354294i	$-0.115279\pi$
$17$	1.99984	+	2.22105i	0.485033	+	0.538683i	−0.450101	+	0.892977i	$0.648612\pi$
$18$		0			0
$19$	−0.927249	−	2.08263i	−0.212725	−	0.477789i	0.775394	−	0.631478i	$-0.217551\pi$
$19$	−0.927249	−	2.08263i	−0.212725	−	0.477789i	−0.988119	+	0.153689i	$0.950885\pi$
$20$		0			0
$21$		−	0.601532i		−	0.131265i
$22$		0			0
$23$	−1.64089	−	2.84211i	−0.342150	−	0.592621i	0.642682	−	0.766133i	$-0.277822\pi$
$23$	−1.64089	−	2.84211i	−0.342150	−	0.592621i	−0.984832	+	0.173512i	$0.944488\pi$
$24$		0			0
$25$	−3.97319	−	2.88669i	−0.794639	−	0.577339i
$26$		0			0
$27$	1.52730	−	4.70056i	0.293930	−	0.904623i
$28$		0			0
$29$	2.21344	+	0.985488i	0.411026	+	0.183001i	0.601824	−	0.798629i	$-0.294441\pi$
$29$	2.21344	+	0.985488i	0.411026	+	0.183001i	−0.190798	+	0.981629i	$0.561108\pi$
$30$		0			0
$31$	5.38573	−	1.74993i	0.967306	−	0.314297i	0.217578	−	0.976043i	$-0.430184\pi$
$31$	5.38573	−	1.74993i	0.967306	−	0.314297i	0.749728	+	0.661746i	$0.230184\pi$
$32$		0			0
$33$	0.521231	−	5.96976i	0.0907347	−	1.03920i
$34$		0			0
$35$	0.0970760	+	0.0206341i	0.0164088	+	0.00348781i
$36$		0			0
$37$	−4.22491	+	9.48929i	−0.694570	+	1.56003i	0.128259	+	0.991741i	$0.459061\pi$
$37$	−4.22491	+	9.48929i	−0.694570	+	1.56003i	−0.822829	+	0.568289i	$0.807605\pi$
$38$		0			0
$39$	−6.49868	−	0.453751i	−1.04062	−	0.0726583i
$40$		0			0
$41$	−7.23016	−	0.759920i	−1.12916	−	0.118680i	−0.478528	−	0.878072i	$-0.658830\pi$
$41$	−7.23016	−	0.759920i	−1.12916	−	0.118680i	−0.650633	+	0.759393i	$0.725496\pi$
$42$		0			0
$43$	0.0691846	−	0.119831i	0.0105506	−	0.0182741i	−0.860702	−	0.509109i	$-0.829975\pi$
$43$	0.0691846	−	0.119831i	0.0105506	−	0.0182741i	0.871252	+	0.490835i	$0.163308\pi$
$44$		0			0
$45$	−0.0682882	−	0.0394262i	−0.0101798	−	0.00587731i
$46$		0			0
$47$	2.00137	−	2.75465i	0.291930	−	0.401807i	−0.637710	−	0.770277i	$-0.720118\pi$
$47$	2.00137	−	2.75465i	0.291930	−	0.401807i	0.929640	+	0.368469i	$0.120118\pi$
$48$		0			0
$49$	−6.73861	+	1.43234i	−0.962659	+	0.204620i
$50$		0			0
$51$	4.36870	−	3.17404i	0.611740	−	0.444455i
$52$		0			0
$53$	−2.78126	−	8.55983i	−0.382035	−	1.17578i	−0.938608	−	0.344985i	$-0.887884\pi$
$53$	−2.78126	−	8.55983i	−0.382035	−	1.17578i	0.556573	−	0.830799i	$-0.312116\pi$
$54$		0			0
$55$	0.945528	+	0.288896i	0.127495	+	0.0389547i
$56$		0			0
$57$	−3.91741	+	1.27284i	−0.518873	+	0.168592i
$58$		0			0
$59$	3.82254	−	0.401766i	0.497653	−	0.0523054i	0.147623	−	0.989044i	$-0.452838\pi$
$59$	3.82254	−	0.401766i	0.497653	−	0.0523054i	0.350030	+	0.936738i	$0.386171\pi$
$60$		0			0
$61$	7.91399	+	8.78938i	1.01328	+	1.12536i	0.992082	+	0.125589i	$0.0400822\pi$
$61$	7.91399	+	8.78938i	1.01328	+	1.12536i	0.0212006	+	0.999775i	$0.493251\pi$
$62$		0			0
$63$	−0.0875830	−	0.00920535i	−0.0110344	−	0.00115976i
$64$		0			0
$65$	0.296149	−	1.03320i	0.0367328	−	0.128153i
$66$		0			0
$67$	9.08386	−	5.24457i	1.10977	−	0.640726i	0.171000	−	0.985271i	$-0.445300\pi$
$67$	9.08386	−	5.24457i	1.10977	−	0.640726i	0.938770	+	0.344545i	$0.111967\pi$
$68$		0			0
$69$	−5.41689	+	2.41176i	−0.652117	+	0.290341i
$70$		0			0
$71$	−2.96890	+	2.67321i	−0.352344	+	0.317252i	−0.826228	−	0.563335i	$-0.809518\pi$
$71$	−2.96890	+	2.67321i	−0.352344	+	0.317252i	0.473885	+	0.880587i	$0.342851\pi$
$72$		0			0
$73$	2.31121	+	3.18110i	0.270506	+	0.372320i	0.922561	−	0.385852i	$-0.126093\pi$
$73$	2.31121	+	3.18110i	0.270506	+	0.372320i	−0.652054	+	0.758172i	$0.726093\pi$
$74$		0			0
$75$	−5.93749	+	6.59425i	−0.685602	+	0.761438i
$76$		0			0
$77$	1.09594	−	0.134760i	0.124894	−	0.0153573i
$78$		0			0
$79$	3.54293	+	10.9040i	0.398610	+	1.22680i	0.926114	+	0.377244i	$0.123128\pi$
$79$	3.54293	+	10.9040i	0.398610	+	1.22680i	−0.527503	+	0.849553i	$0.676872\pi$
$80$		0			0
$81$	−8.88294	−	3.95494i	−0.986993	−	0.439438i
$82$		0			0
$83$	10.9092	+	3.54461i	1.19744	+	0.389072i	0.838818	−	0.544411i	$-0.183247\pi$
$83$	10.9092	+	3.54461i	1.19744	+	0.389072i	0.358621	+	0.933483i	$0.383247\pi$
$84$		0			0
$85$	0.362373	+	0.813904i	0.0393049	+	0.0882803i
$86$		0			0
$87$	2.18886	−	3.79121i	0.234670	−	0.406461i
$88$		0			0
$89$	11.7015	−	6.75586i	1.24036	−	0.716120i	0.271189	−	0.962526i	$-0.412583\pi$
$89$	11.7015	−	6.75586i	1.24036	−	0.716120i	0.969167	+	0.246407i	$0.0792499\pi$
$90$		0			0
$91$	−0.167185	−	1.18869i	−0.0175258	−	0.124608i
$92$		0			0
$93$	−2.12729	−	10.0081i	−0.220590	−	1.03779i
$94$		0			0
$95$	−0.0710356	−	0.675858i	−0.00728810	−	0.0693416i
$96$		0			0
$97$	−2.13375	+	10.0385i	−0.216650	+	1.01926i	0.726571	+	0.687091i	$0.241113\pi$
$97$	−2.13375	+	10.0385i	−0.216650	+	1.01926i	−0.943221	+	0.332166i	$0.892221\pi$
$98$		0			0
$99$	−0.861221	−	0.167248i	−0.0865559	−	0.0168090i
$100$		0			0
$101$	−5.71824	+	6.35075i	−0.568987	+	0.631924i	−0.957124	−	0.289678i	$-0.906452\pi$
$101$	−5.71824	+	6.35075i	−0.568987	+	0.631924i	0.388138	+	0.921601i	$0.373119\pi$
$102$		0			0
$103$	−10.2846	+	7.47220i	−1.01337	+	0.736257i	−0.964914	−	0.262568i	$-0.915431\pi$
$103$	−10.2846	+	7.47220i	−1.01337	+	0.736257i	−0.0484578	+	0.998825i	$0.515431\pi$
$104$		0			0
$105$	0.0554114	−	0.170539i	0.00540760	−	0.0166429i
$106$		0			0
$107$	−0.783399	+	7.45354i	−0.0757340	+	0.720561i	0.889102	+	0.457709i	$0.151330\pi$
$107$	−0.783399	+	7.45354i	−0.0757340	+	0.720561i	−0.964836	+	0.262852i	$0.915337\pi$
$108$		0			0
$109$			12.3002i			1.17814i	0.808080	+	0.589072i	$0.200507\pi$
$109$			12.3002i			1.17814i	−0.808080	+	0.589072i	$0.799493\pi$
$110$		0			0
$111$	16.2534	+	9.38390i	1.54270	+	0.890680i
$112$		0			0
$113$	−0.393297	+	0.175107i	−0.0369983	+	0.0164727i	−0.425152	−	0.905122i	$-0.639779\pi$
$113$	−0.393297	+	0.175107i	−0.0369983	+	0.0164727i	0.388154	+	0.921594i	$0.373113\pi$
$114$		0			0
$115$	−0.203398	−	0.956914i	−0.0189670	−	0.0892327i
$116$		0			0
$117$	−0.165517	+	0.939264i	−0.0153020	+	0.0868350i
$118$		0			0
$119$	0.739447	+	0.665801i	0.0677850	+	0.0610339i
$120$		0			0
$121$	10.9932	−	0.387750i	0.999379	−	0.0352500i
$122$		0			0
$123$	−2.73100	+	12.8484i	−0.246246	+	1.15850i
$124$		0			0
$125$	−1.73660	−	2.39023i	−0.155327	−	0.213789i
$126$		0			0
$127$	−15.1227	+	3.21443i	−1.34192	+	0.285235i	−0.822248	−	0.569129i	$-0.807280\pi$
$127$	−15.1227	+	3.21443i	−1.34192	+	0.285235i	−0.519675	+	0.854364i	$0.673947\pi$
$128$		0			0
$129$	−0.202259	−	0.146949i	−0.0178079	−	0.0129382i
$130$		0			0
$131$	11.0367			0.964285			0.482142	−	0.876093i	$-0.339859\pi$
$131$	11.0367			0.964285			0.482142	+	0.876093i	$0.339859\pi$
$132$		0			0
$133$	−0.379491	−	0.657298i	−0.0329061	−	0.0569950i
$134$		0			0
$135$	0.866005	−	1.19195i	0.0745338	−	0.102587i
$136$		0			0
$137$	9.90073	−	8.91466i	0.845877	−	0.761631i	−0.127258	−	0.991870i	$-0.540617\pi$
$137$	9.90073	−	8.91466i	0.845877	−	0.761631i	0.973134	+	0.230239i	$0.0739508\pi$
$138$		0			0
$139$	0.882080	+	8.39243i	0.0748170	+	0.711837i	0.966061	+	0.258313i	$0.0831666\pi$
$139$	0.882080	+	8.39243i	0.0748170	+	0.711837i	−0.891244	+	0.453524i	$0.850167\pi$
$140$		0			0
$141$	−4.57185	−	4.11651i	−0.385019	−	0.346673i
$142$		0			0
$143$	−0.629187	−	11.9417i	−0.0526153	−	0.998615i
$144$		0			0
$145$	0.536747	+	0.483290i	0.0445744	+	0.0401350i
$146$		0			0
$147$	1.30110	+	12.3791i	0.107313	+	1.02101i
$148$		0			0
$149$	−13.7150	+	12.3490i	−1.12358	+	1.01167i	−0.123763	+	0.992312i	$0.539496\pi$
$149$	−13.7150	+	12.3490i	−1.12358	+	1.01167i	−0.999813	+	0.0193598i	$0.993837\pi$
$150$		0			0
$151$	−0.0391206	+	0.0538448i	−0.00318359	+	0.00438183i	−0.810606	−	0.585592i	$-0.800862\pi$
$151$	−0.0391206	+	0.0538448i	−0.00318359	+	0.00438183i	0.807422	+	0.589974i	$0.200862\pi$
$152$		0			0
$153$	−0.395286	−	0.684655i	−0.0319570	−	0.0553511i
$154$		0			0
$155$	1.68810			0.135591
$156$		0			0
$157$	−7.24222	−	5.26178i	−0.577992	−	0.419936i	0.260007	−	0.965607i	$-0.416275\pi$
$157$	−7.24222	−	5.26178i	−0.577992	−	0.419936i	−0.838000	+	0.545671i	$0.816275\pi$
$158$		0			0
$159$	−15.9064	+	3.38102i	−1.26146	+	0.268132i
$160$		0			0
$161$	−0.642211	−	0.883928i	−0.0506133	−	0.0696633i
$162$		0			0
$163$	2.73262	−	12.8560i	0.214035	−	1.00696i	−0.731602	−	0.681732i	$-0.761227\pi$
$163$	2.73262	−	12.8560i	0.214035	−	1.00696i	0.945637	−	0.325224i	$-0.105440\pi$
$164$		0			0
$165$	0.697691	−	1.64446i	0.0543151	−	0.128021i
$166$		0			0
$167$	2.63944	+	2.37656i	0.204246	+	0.183904i	0.764905	−	0.644143i	$-0.222786\pi$
$167$	2.63944	+	2.37656i	0.204246	+	0.183904i	−0.560660	+	0.828046i	$0.689452\pi$
$168$		0			0
$169$	−12.9681	+	0.909540i	−0.997549	+	0.0699646i
$170$		0			0
$171$	0.125377	+	0.589853i	0.00958783	+	0.0451072i
$172$		0			0
$173$	−20.0917	+	8.94538i	−1.52754	+	0.680105i	−0.986927	−	0.161166i	$-0.948474\pi$
$173$	−20.0917	+	8.94538i	−1.52754	+	0.680105i	−0.540613	+	0.841271i	$0.681808\pi$
$174$		0			0
$175$	−1.41599	−	0.817525i	−0.107039	−	0.0617991i
$176$		0			0
$177$		−	6.94461i		−	0.521989i
$178$		0			0
$179$	0.508312	−	4.83627i	0.0379930	−	0.361479i	−0.958964	−	0.283528i	$-0.908495\pi$
$179$	0.508312	−	4.83627i	0.0379930	−	0.361479i	0.996957	−	0.0779519i	$-0.0248381\pi$
$180$		0			0
$181$	−3.84467	+	11.8327i	−0.285772	+	0.879515i	0.700394	+	0.713756i	$0.253007\pi$
$181$	−3.84467	+	11.8327i	−0.285772	+	0.879515i	−0.986166	+	0.165759i	$0.946993\pi$
$182$		0			0
$183$	17.2883	−	12.5607i	1.27799	−	0.928512i
$184$		0			0
$185$	−2.07192	+	2.30110i	−0.152331	+	0.169180i
$186$		0			0
$187$	6.76155	+	7.24832i	0.494453	+	0.530050i
$188$		0			0
$189$	0.342114	−	1.60952i	0.0248852	−	0.117075i
$190$		0			0
$191$	0.723919	+	6.88763i	0.0523809	+	0.498371i	0.988989	+	0.147992i	$0.0472808\pi$
$191$	0.723919	+	6.88763i	0.0523809	+	0.498371i	−0.936608	+	0.350380i	$0.886052\pi$
$192$		0			0
$193$	0.346095	+	1.62825i	0.0249124	+	0.117204i	0.988847	−	0.148936i	$-0.0475849\pi$
$193$	0.346095	+	1.62825i	0.0249124	+	0.117204i	−0.963934	+	0.266140i	$0.914252\pi$
$194$		0			0
$195$	−1.80063	−	0.727282i	−0.128946	−	0.0520818i
$196$		0			0
$197$	2.93520	−	1.69464i	0.209124	−	0.120738i	−0.391780	−	0.920059i	$-0.628141\pi$
$197$	2.93520	−	1.69464i	0.209124	−	0.120738i	0.600904	+	0.799321i	$0.294807\pi$
$198$		0			0
$199$	−7.89789	+	13.6796i	−0.559867	+	0.969718i	0.437640	+	0.899150i	$0.355814\pi$
$199$	−7.89789	+	13.6796i	−0.559867	+	0.969718i	−0.997507	+	0.0705676i	$0.977519\pi$
$200$		0			0
$201$	−7.70837	−	17.3133i	−0.543707	−	1.22119i
$202$		0			0
$203$	0.767173	+	0.249270i	0.0538450	+	0.0174953i
$204$		0			0
$205$	−1.97980	−	0.881465i	−0.138275	−	0.0615642i
$206$		0			0
$207$	0.268256	+	0.825607i	0.0186451	+	0.0573836i
$208$		0			0
$209$	−3.19662	−	6.85203i	−0.221115	−	0.473965i
$210$		0			0
$211$	−6.72353	+	7.46724i	−0.462867	+	0.514066i	−0.928713	−	0.370800i	$-0.879083\pi$
$211$	−6.72353	+	7.46724i	−0.462867	+	0.514066i	0.465846	+	0.884866i	$0.345750\pi$
$212$		0			0
$213$	4.24278	+	5.83968i	0.290710	+	0.400129i
$214$		0			0
$215$	0.0306529	−	0.0276000i	0.00209051	−	0.00188230i
$216$		0			0
$217$	1.72234	−	0.766833i	0.116920	−	0.0520560i
$218$		0			0
$219$	6.15262	−	3.55222i	0.415756	−	0.240037i
$220$		0			0
$221$	7.75080	−	7.48643i	0.521375	−	0.503591i
$222$		0			0
$223$	−14.5098	−	1.52504i	−0.971650	−	0.102125i	−0.394617	−	0.918846i	$-0.629123\pi$
$223$	−14.5098	−	1.52504i	−0.971650	−	0.102125i	−0.577033	+	0.816721i	$0.695789\pi$
$224$		0			0
$225$	0.869260	+	0.965411i	0.0579507	+	0.0643607i
$226$		0			0
$227$	11.7487	−	1.23484i	0.779788	−	0.0819590i	0.293733	−	0.955887i	$-0.405102\pi$
$227$	11.7487	−	1.23484i	0.779788	−	0.0819590i	0.486055	+	0.873928i	$0.338436\pi$
$228$		0			0
$229$	−0.540077	+	0.175482i	−0.0356893	+	0.0115962i	−0.326807	−	0.945091i	$-0.605973\pi$
$229$	−0.540077	+	0.175482i	−0.0356893	+	0.0115962i	0.291118	+	0.956687i	$0.405973\pi$
$230$		0			0
$231$	−0.0351683	−	1.99475i	−0.00231390	−	0.131245i
$232$		0			0
$233$	0.184222	+	0.566976i	0.0120688	+	0.0371439i	0.956910	−	0.290386i	$-0.0937838\pi$
$233$	0.184222	+	0.566976i	0.0120688	+	0.0371439i	−0.944841	+	0.327530i	$0.893784\pi$
$234$		0			0
$235$	0.821155	−	0.596604i	0.0535662	−	0.0389182i
$236$		0			0
$237$	20.2625	−	4.30694i	1.31619	−	0.279766i
$238$		0			0
$239$	12.7860	−	17.5984i	0.827058	−	1.13835i	−0.161406	−	0.986888i	$-0.551603\pi$
$239$	12.7860	−	17.5984i	0.827058	−	1.13835i	0.988463	−	0.151459i	$-0.0483973\pi$
$240$		0			0
$241$	10.4950	+	6.05930i	0.676043	+	0.390314i	0.798363	−	0.602177i	$-0.205700\pi$
$241$	10.4950	+	6.05930i	0.676043	+	0.390314i	−0.122319	+	0.992491i	$0.539033\pi$
$242$		0			0
$243$	−1.37059	+	2.37392i	−0.0879231	+	0.152287i
$244$		0			0
$245$	−2.04239	−	0.214664i	−0.130484	−	0.0137144i
$246$		0			0
$247$	−7.38742	+	3.60404i	−0.470050	+	0.229319i
$248$		0			0
$249$	8.42964	−	18.9333i	0.534207	−	1.19985i
$250$		0			0
$251$	17.9465	+	3.81465i	1.13277	+	0.240778i	0.735897	−	0.677094i	$-0.236761\pi$
$251$	17.9465	+	3.81465i	1.13277	+	0.240778i	0.396876	+	0.917872i	$0.370094\pi$
$252$		0			0
$253$	−5.60754	−	9.32881i	−0.352543	−	0.586498i
$254$		0			0
$255$	1.53094	−	0.497433i	0.0958714	−	0.0311505i
$256$		0			0
$257$	−25.3338	−	11.2793i	−1.58028	−	0.703585i	−0.585991	−	0.810318i	$-0.699294\pi$
$257$	−25.3338	−	11.2793i	−1.58028	−	0.703585i	−0.994288	+	0.106733i	$0.965961\pi$
$258$		0			0
$259$	−1.06865	+	3.28896i	−0.0664026	+	0.204366i
$260$		0			0
$261$	−0.518504	−	0.376715i	−0.0320946	−	0.0233181i
$262$		0			0
$263$	−5.11013	−	8.85100i	−0.315104	−	0.545776i	0.664356	−	0.747417i	$-0.268706\pi$
$263$	−5.11013	−	8.85100i	−0.315104	−	0.545776i	−0.979460	+	0.201641i	$0.935373\pi$
$264$		0			0
$265$		−	2.68298i		−	0.164814i
$266$		0			0
$267$	−9.92964	−	22.3023i	−0.607684	−	1.36488i
$268$		0			0
$269$	9.58987	+	10.6506i	0.584704	+	0.649380i	0.960814	−	0.277195i	$-0.0894049\pi$
$269$	9.58987	+	10.6506i	0.584704	+	0.649380i	−0.376109	+	0.926575i	$0.622738\pi$
$270$		0			0
$271$	2.36742	−	5.31730i	0.143810	−	0.323003i	−0.827251	−	0.561832i	$-0.810097\pi$
$271$	2.36742	−	5.31730i	0.143810	−	0.323003i	0.971062	+	0.238829i	$0.0767634\pi$
$272$		0			0
$273$	−2.16752	+	0.0759180i	−0.131185	+	0.00459477i
$274$		0			0
$275$	−13.3443	−	9.34030i	−0.804693	−	0.563241i
$276$		0			0
$277$	27.2661	+	5.79558i	1.63826	+	0.348223i	0.932763	−	0.360490i	$-0.117391\pi$
$277$	27.2661	+	5.79558i	1.63826	+	0.348223i	0.705497	+	0.708713i	$0.250724\pi$
$278$		0			0
$279$	−1.48974	+	0.156578i	−0.0891882	+	0.00937406i
$280$		0			0
$281$	−10.2992	−	3.34642i	−0.614400	−	0.199631i	−0.0147474	−	0.999891i	$-0.504694\pi$
$281$	−10.2992	−	3.34642i	−0.614400	−	0.199631i	−0.599652	+	0.800261i	$0.704694\pi$
$282$		0			0
$283$	1.01095	−	9.61851i	0.0600945	−	0.571761i	−0.922500	−	0.385997i	$-0.873857\pi$
$283$	1.01095	−	9.61851i	0.0600945	−	0.571761i	0.982594	−	0.185764i	$-0.0594759\pi$
$284$		0			0
$285$	−1.22787			−0.0727325
$286$		0			0
$287$	−2.42037			−0.142870
$288$		0			0
$289$	0.843292	−	8.02338i	0.0496054	−	0.471964i
$290$		0			0
$291$	17.6352	+	5.73003i	1.03380	+	0.335901i
$292$		0			0
$293$	34.0146	−	3.57508i	1.98715	−	0.208858i	0.989022	−	0.147770i	$-0.0472095\pi$
$293$	34.0146	−	3.57508i	1.98715	−	0.208858i	0.998132	−	0.0610884i	$-0.0194571\pi$
$294$		0			0
$295$	1.12073	+	0.238219i	0.0652514	+	0.0138696i
$296$		0			0
$297$	4.78989	−	15.6769i	0.277938	−	0.909664i
$298$		0			0
$299$	−10.0340	+	6.27140i	−0.580281	+	0.362684i
$300$		0			0
$301$	0.0187371	−	0.0420842i	0.00107999	−	0.00242569i
$302$		0			0
$303$	10.3317	+	11.4745i	0.593541	+	0.659194i
$304$		0			0
$305$	1.43402	+	3.22087i	0.0821120	+	0.184427i
$306$		0			0
$307$			3.27988i			0.187193i	0.995610	+	0.0935964i	$0.0298363\pi$
$307$			3.27988i			0.187193i	−0.995610	+	0.0935964i	$0.970164\pi$
$308$		0			0
$309$	11.4844	+	19.8916i	0.653326	+	1.13159i
$310$		0			0
$311$	−6.57080	−	4.77397i	−0.372596	−	0.270707i	0.385691	−	0.922628i	$-0.373963\pi$
$311$	−6.57080	−	4.77397i	−0.372596	−	0.270707i	−0.758287	+	0.651921i	$0.773963\pi$
$312$		0			0
$313$	5.24622	−	16.1462i	0.296534	−	0.912638i	−0.686168	−	0.727443i	$-0.740708\pi$
$313$	5.24622	−	16.1462i	0.296534	−	0.912638i	0.982702	−	0.185194i	$-0.0592915\pi$
$314$		0			0
$315$	−0.0239825	−	0.0106777i	−0.00135126	−	0.000601620i
$316$		0			0
$317$	−12.1535	+	3.94890i	−0.682607	+	0.221792i	−0.629736	−	0.776809i	$-0.716837\pi$
$317$	−12.1535	+	3.94890i	−0.682607	+	0.221792i	−0.0528706	+	0.998601i	$0.516837\pi$
$318$		0			0
$319$	7.39763	+	3.13858i	0.414188	+	0.175727i
$320$		0			0
$321$	13.2453	+	2.81538i	0.739281	+	0.157139i
$322$		0			0
$323$	2.77128	−	6.22440i	0.154198	−	0.346335i
$324$		0			0
$325$	−9.90030	+	14.6811i	−0.549170	+	0.814361i
$326$		0			0
$327$	22.1022	+	2.32304i	1.22225	+	0.128464i
$328$		0			0
$329$	0.566798	−	0.981722i	0.0312486	−	0.0541241i
$330$		0			0
$331$	−17.3488	−	10.0163i	−0.953574	−	0.550546i	−0.0593847	−	0.998235i	$-0.518914\pi$
$331$	−17.3488	−	10.0163i	−0.953574	−	0.550546i	−0.894189	+	0.447689i	$0.852247\pi$
$332$		0			0
$333$	1.61502	−	2.22289i	0.0885028	−	0.121814i
$334$		0			0
$335$	3.05846	−	0.650095i	0.167101	−	0.0355185i
$336$		0			0
$337$	−9.07610	+	6.59418i	−0.494407	+	0.359208i	−0.806877	−	0.590720i	$-0.798844\pi$
$337$	−9.07610	+	6.59418i	−0.494407	+	0.359208i	0.312470	+	0.949928i	$0.398844\pi$
$338$		0			0
$339$	0.240371	+	0.739787i	0.0130552	+	0.0401797i
$340$		0			0
$341$	17.7574	−	6.11784i	0.961616	−	0.331300i
$342$		0			0
$343$	−4.39776	+	1.42892i	−0.237457	+	0.0771543i
$344$		0			0
$345$	−1.75789	+	0.184762i	−0.0946418	+	0.00994726i
$346$		0			0
$347$	−21.7350	−	24.1392i	−1.16680	−	1.29586i	−0.947337	−	0.320239i	$-0.896237\pi$
$347$	−21.7350	−	24.1392i	−1.16680	−	1.29586i	−0.219461	−	0.975621i	$-0.570430\pi$
$348$		0			0
$349$	−14.7027	−	1.54531i	−0.787017	−	0.0827188i	−0.297510	−	0.954719i	$-0.596156\pi$
$349$	−14.7027	−	1.54531i	−0.787017	−	0.0827188i	−0.489506	+	0.872000i	$0.662823\pi$
$350$		0			0
$351$	−17.1305	−	4.91015i	−0.914358	−	0.262085i
$352$		0			0
$353$	5.68714	−	3.28347i	0.302696	−	0.174762i	−0.340957	−	0.940079i	$-0.610751\pi$
$353$	5.68714	−	3.28347i	0.302696	−	0.174762i	0.643653	+	0.765317i	$0.277418\pi$
$354$		0			0
$355$	−1.08795	+	0.484389i	−0.0577426	+	0.0257087i
$356$		0			0
$357$	1.33603	−	1.20297i	0.0707103	−	0.0636678i
$358$		0			0
$359$	−13.7108	−	18.8713i	−0.723629	−	0.995991i	−0.999395	−	0.0347657i	$-0.988931\pi$
$359$	−13.7108	−	18.8713i	−0.723629	−	0.995991i	0.275766	−	0.961225i	$-0.411069\pi$
$360$		0			0
$361$	9.23591	−	10.2575i	0.486100	−	0.539869i
$362$		0			0
$363$	1.37944	−	19.8268i	0.0724019	−	1.04064i
$364$		0			0
$365$	0.362210	+	1.11477i	0.0189590	+	0.0583497i
$366$		0			0
$367$	−1.96366	−	0.874277i	−0.102502	−	0.0456369i	0.354845	−	0.934925i	$-0.384534\pi$
$367$	−1.96366	−	0.874277i	−0.102502	−	0.0456369i	−0.457347	+	0.889288i	$0.651200\pi$
$368$		0			0
$369$	1.82893	+	0.594254i	0.0952101	+	0.0309356i
$370$		0			0
$371$	−1.21877	−	2.73740i	−0.0632753	−	0.142119i
$372$		0			0
$373$	−6.31276	+	10.9340i	−0.326862	+	0.566142i	−0.981887	−	0.189465i	$-0.939325\pi$
$373$	−6.31276	+	10.9340i	−0.326862	+	0.566142i	0.655025	+	0.755607i	$0.272658\pi$
$374$		0			0
$375$	−4.62298	+	2.66908i	−0.238730	+	0.137831i
$376$		0			0
$377$	3.27170	−	8.10017i	0.168501	−	0.417180i
$378$		0			0
$379$	5.35161	+	25.1773i	0.274894	+	1.29327i	0.871364	+	0.490637i	$0.163236\pi$
$379$	5.35161	+	25.1773i	0.274894	+	1.29327i	−0.596470	+	0.802635i	$0.703431\pi$
$380$		0			0
$381$	2.91991	+	27.7811i	0.149591	+	1.42327i
$382$		0			0
$383$	6.26950	−	29.4957i	0.320357	−	1.50716i	−0.463433	−	0.886132i	$-0.653382\pi$
$383$	6.26950	−	29.4957i	0.320357	−	1.50716i	0.783789	−	0.621027i	$-0.213284\pi$
$384$		0			0
$385$	0.323121	+	0.0627495i	0.0164678	+	0.00319801i
$386$		0			0
$387$	−0.0244910	+	0.0272000i	−0.00124495	+	0.00138266i
$388$		0			0
$389$	−17.4803	+	12.7002i	−0.886288	+	0.643926i	−0.934907	−	0.354892i	$-0.884518\pi$
$389$	−17.4803	+	12.7002i	−0.886288	+	0.643926i	0.0486198	+	0.998817i	$0.484518\pi$
$390$		0			0
$391$	3.03094	−	9.32827i	0.153281	−	0.471751i
$392$		0			0
$393$	2.08442	−	19.8319i	0.105145	−	1.00039i
$394$		0			0
$395$			3.41773i			0.171965i
$396$		0			0
$397$	3.73198	+	2.15466i	0.187302	+	0.108139i	0.590719	−	0.806877i	$-0.298844\pi$
$397$	3.73198	+	2.15466i	0.187302	+	0.108139i	−0.403417	+	0.915016i	$0.632177\pi$
$398$		0			0
$399$	−1.25277	+	0.557769i	−0.0627170	+	0.0279234i
$400$		0			0
$401$	−1.36789	−	6.43540i	−0.0683090	−	0.321368i	0.930705	−	0.365771i	$-0.119195\pi$
$401$	−1.36789	−	6.43540i	−0.0683090	−	0.321368i	−0.999014	+	0.0444029i	$0.985861\pi$
$402$		0			0
$403$	−6.98532	−	19.1858i	−0.347964	−	0.955712i
$404$		0			0
$405$	−2.15406	−	1.93953i	−0.107036	−	0.0963759i
$406$		0			0
$407$	−13.4555	+	31.7145i	−0.666962	+	1.57203i
$408$		0			0
$409$	−6.52421	+	30.6940i	−0.322602	+	1.51772i	0.455873	+	0.890045i	$0.349327\pi$
$409$	−6.52421	+	30.6940i	−0.322602	+	1.51772i	−0.778475	+	0.627676i	$0.784006\pi$
$410$		0			0
$411$	−14.1489	−	19.4743i	−0.697913	−	0.960595i
$412$		0			0
$413$	1.25167	−	0.266052i	0.0615909	−	0.0130915i
$414$		0			0
$415$	2.76632	+	2.00985i	0.135793	+	0.0986596i
$416$		0			0
$417$	15.2469			0.746646
$418$		0			0
$419$	7.80268	+	13.5146i	0.381186	+	0.660233i	0.991232	−	0.132133i	$-0.0421825\pi$
$419$	7.80268	+	13.5146i	0.381186	+	0.660233i	−0.610046	+	0.792366i	$0.708849\pi$
$420$		0			0
$421$	−10.5896	+	14.5754i	−0.516107	+	0.710360i	−0.984934	−	0.172930i	$-0.944677\pi$
$421$	−10.5896	+	14.5754i	−0.516107	+	0.710360i	0.468827	+	0.883290i	$0.344677\pi$
$422$		0			0
$423$	−0.669328	+	0.602666i	−0.0325439	+	0.0293026i
$424$		0			0
$425$	−1.53427	−	14.5976i	−0.0744229	−	0.708087i
$426$		0			0
$427$	2.92622	+	2.63478i	0.141610	+	0.127506i
$428$		0			0
$429$	−21.5769	−	1.12474i	−1.04174	−	0.0543032i
$430$		0			0
$431$	−7.62027	−	6.86133i	−0.367056	−	0.330498i	0.464877	−	0.885375i	$-0.346099\pi$
$431$	−7.62027	−	6.86133i	−0.367056	−	0.330498i	−0.831932	+	0.554877i	$0.812765\pi$
$432$		0			0
$433$	1.70445	+	16.2168i	0.0819106	+	0.779327i	0.955961	+	0.293493i	$0.0948176\pi$
$433$	1.70445	+	16.2168i	0.0819106	+	0.779327i	−0.874051	+	0.485835i	$0.838516\pi$
$434$		0			0
$435$	0.969794	−	0.873207i	0.0464981	−	0.0418670i
$436$		0			0
$437$	−4.39756	+	6.05272i	−0.210364	+	0.289541i
$438$		0			0
$439$	−12.5469	−	21.7319i	−0.598832	−	1.03721i	−0.992994	−	0.118167i	$-0.962298\pi$
$439$	−12.5469	−	21.7319i	−0.598832	−	1.03721i	0.394162	−	0.919041i	$-0.371035\pi$
$440$		0			0
$441$	1.82231			0.0867768
$442$		0			0
$443$	−12.8771	−	9.35575i	−0.611809	−	0.444505i	0.238242	−	0.971206i	$-0.423429\pi$
$443$	−12.8771	−	9.35575i	−0.611809	−	0.444505i	−0.850051	+	0.526701i	$0.823429\pi$
$444$		0			0
$445$	3.93979	−	0.837429i	0.186764	−	0.0396979i
$446$		0			0
$447$	19.5997	+	26.9767i	0.927035	+	1.27595i
$448$		0			0
$449$	−3.04264	+	14.3145i	−0.143591	+	0.675543i	0.846182	+	0.532894i	$0.178895\pi$
$449$	−3.04264	+	14.3145i	−0.143591	+	0.675543i	−0.989773	+	0.142649i	$0.954438\pi$
$450$		0			0
$451$	−24.0204	−	2.09727i	−1.13108	−	0.0987566i
$452$		0			0
$453$	0.0893654	+	0.0804650i	0.00419875	+	0.00378057i
$454$		0			0
$455$	0.0621001	−	0.352402i	0.00291130	−	0.0165209i
$456$		0			0
$457$	−0.398126	−	1.87304i	−0.0186236	−	0.0876169i	0.967854	−	0.251512i	$-0.0809276\pi$
$457$	−0.398126	−	1.87304i	−0.0186236	−	0.0876169i	−0.986478	+	0.163895i	$0.947594\pi$
$458$		0			0
$459$	13.4945	−	6.00816i	0.629871	−	0.280437i
$460$		0			0
$461$	35.0411	+	20.2310i	1.63203	+	0.942251i	0.983467	+	0.181088i	$0.0579619\pi$
$461$	35.0411	+	20.2310i	1.63203	+	0.942251i	0.648560	+	0.761163i	$0.275371\pi$
$462$		0			0
$463$			31.0969i			1.44519i	0.691270	+	0.722597i	$0.257052\pi$
$463$			31.0969i			1.44519i	−0.691270	+	0.722597i	$0.742948\pi$
$464$		0			0
$465$	0.318817	−	3.03334i	0.0147848	−	0.140668i
$466$		0			0
$467$	−8.76563	+	26.9778i	−0.405625	+	1.24838i	0.514748	+	0.857342i	$0.327886\pi$
$467$	−8.76563	+	26.9778i	−0.405625	+	1.24838i	−0.920372	+	0.391043i	$0.872114\pi$
$468$		0			0
$469$	2.82518	−	2.05261i	0.130455	−	0.0947809i
$470$		0			0
$471$	−10.8227	+	12.0198i	−0.498683	+	0.553843i
$472$		0			0
$473$	0.222418	−	0.401418i	0.0102268	−	0.0184572i
$474$		0			0
$475$	−2.32779	+	10.9514i	−0.106806	+	0.502484i
$476$		0			0
$477$	0.248857	+	2.36772i	0.0113944	+	0.108410i
$478$		0			0
$479$	−4.81660	−	22.6603i	−0.220076	−	1.03538i	−0.939961	−	0.341283i	$-0.889139\pi$
$479$	−4.81660	−	22.6603i	−0.220076	−	1.03538i	0.719885	−	0.694094i	$-0.244195\pi$
$480$		0			0
$481$	34.7264	+	14.0262i	1.58339	+	0.639538i
$482$		0			0
$483$	−1.70962	+	0.987049i	−0.0777904	+	0.0449123i
$484$		0			0
$485$	−1.52966	+	2.64944i	−0.0694581	+	0.120305i
$486$		0			0
$487$	−4.77147	−	10.7169i	−0.216216	−	0.485629i	0.772577	−	0.634921i	$-0.218967\pi$
$487$	−4.77147	−	10.7169i	−0.216216	−	0.485629i	−0.988793	+	0.149292i	$0.952301\pi$
$488$		0			0
$489$	−22.5848	−	7.33824i	−1.02132	−	0.331847i
$490$		0			0
$491$	2.79209	+	1.24312i	0.126005	+	0.0561012i	0.468771	−	0.883320i	$-0.344697\pi$
$491$	2.79209	+	1.24312i	0.126005	+	0.0561012i	−0.342766	+	0.939421i	$0.611364\pi$
$492$		0			0
$493$	2.23772	+	6.88698i	0.100782	+	0.310174i
$494$		0			0
$495$	−0.228756	−	0.126749i	−0.0102818	−	0.00569695i
$496$		0			0
$497$	−0.889984	+	0.988427i	−0.0399212	+	0.0443370i
$498$		0			0
$499$	−14.1183	−	19.4322i	−0.632024	−	0.869906i	0.366135	−	0.930562i	$-0.380681\pi$
$499$	−14.1183	−	19.4322i	−0.632024	−	0.869906i	−0.998159	+	0.0606555i	$0.980681\pi$
$500$		0			0
$501$	4.76893	−	4.29397i	0.213060	−	0.191840i
$502$		0			0
$503$	3.48399	−	1.55117i	0.155343	−	0.0691633i	−0.327592	−	0.944819i	$-0.606237\pi$
$503$	3.48399	−	1.55117i	0.155343	−	0.0691633i	0.482936	+	0.875656i	$0.339571\pi$
$504$		0			0
$505$	−2.20618	+	1.27374i	−0.0981737	+	0.0566806i
$506$		0			0
$507$	−0.814834	+	23.4742i	−0.0361881	+	1.04253i
$508$		0			0
$509$	6.98394	+	0.734041i	0.309558	+	0.0325358i	0.258034	−	0.966136i	$-0.416925\pi$
$509$	6.98394	+	0.734041i	0.309558	+	0.0325358i	0.0515240	+	0.998672i	$0.483592\pi$
$510$		0			0
$511$	0.875951	+	0.972842i	0.0387498	+	0.0430360i
$512$		0			0
$513$	−11.2057	+	1.17777i	−0.494745	+	0.0519998i
$514$		0			0
$515$	−3.60408	+	1.17104i	−0.158815	+	0.0516020i
$516$		0			0
$517$	6.47572	−	9.25174i	0.284802	−	0.406891i
$518$		0			0
$519$	12.2794	+	37.7921i	0.539006	+	1.65889i
$520$		0			0
$521$	12.0687	−	8.76840i	0.528738	−	0.384151i	−0.291148	−	0.956678i	$-0.594037\pi$
$521$	12.0687	−	8.76840i	0.528738	−	0.384151i	0.819885	+	0.572528i	$0.194037\pi$
$522$		0			0
$523$	−31.9473	+	6.79060i	−1.39696	+	0.296932i	−0.844029	−	0.536298i	$-0.819823\pi$
$523$	−31.9473	+	6.79060i	−1.39696	+	0.296932i	−0.552927	+	0.833230i	$0.686489\pi$
$524$		0			0
$525$	−1.73644	+	2.39000i	−0.0757844	+	0.104308i
$526$		0			0
$527$	14.6573	+	8.46239i	0.638482	+	0.368628i
$528$		0			0
$529$	6.11494	−	10.5914i	0.265867	−	0.460495i
$530$		0			0
$531$	−1.01114	−	0.106275i	−0.0438795	−	0.00461192i
$532$		0			0
$533$	−1.82575	+	26.1486i	−0.0790820	+	1.13262i
$534$		0			0
$535$	−0.908699	+	2.04097i	−0.0392865	+	0.0882389i
$536$		0			0
$537$	−8.59429	−	1.82677i	−0.370871	−	0.0788310i
$538$		0			0
$539$	−22.2622	+	5.14376i	−0.958903	+	0.221557i
$540$		0			0
$541$	7.88427	−	2.56176i	0.338971	−	0.110138i	−0.134585	−	0.990902i	$-0.542970\pi$
$541$	7.88427	−	2.56176i	0.338971	−	0.110138i	0.473556	+	0.880764i	$0.342970\pi$
$542$		0			0
$543$	20.5360	+	9.14322i	0.881285	+	0.392373i
$544$		0			0
$545$	−1.13306	+	3.48720i	−0.0485349	+	0.149375i
$546$		0			0
$547$	5.87657	+	4.26958i	0.251264	+	0.182554i	0.706287	−	0.707926i	$-0.250369\pi$
$547$	5.87657	+	4.26958i	0.251264	+	0.182554i	−0.455023	+	0.890480i	$0.650369\pi$
$548$		0			0
$549$	−1.56427	−	2.70939i	−0.0667614	−	0.115634i
$550$		0			0
$551$		−	5.52358i		−	0.235313i
$552$		0			0
$553$	1.55254	+	3.48706i	0.0660206	+	0.148285i
$554$		0			0
$555$	3.74354	+	4.15762i	0.158904	+	0.176481i
$556$		0			0
$557$	14.9173	−	33.5048i	0.632066	−	1.41964i	−0.259049	−	0.965864i	$-0.583409\pi$
$557$	14.9173	−	33.5048i	0.632066	−	1.41964i	0.891115	−	0.453778i	$-0.149924\pi$
$558$		0			0
$559$	−0.440525	−	0.234172i	−0.0186322	−	0.00990443i
$560$		0			0
$561$	14.3015	−	10.7809i	0.603810	−	0.455170i
$562$		0			0
$563$	45.5625	+	9.68461i	1.92023	+	0.408158i	0.999853	+	0.0171256i	$0.00545150\pi$
$563$	45.5625	+	9.68461i	1.92023	+	0.408158i	0.920377	+	0.391032i	$0.127882\pi$
$564$		0			0
$565$	−0.127633	+	0.0134148i	−0.00536957	+	0.000564364i
$566$		0			0
$567$	−3.07880	−	1.00036i	−0.129298	−	0.0420113i
$568$		0			0
$569$	−4.41866	+	42.0407i	−0.185240	+	1.76244i	0.368385	+	0.929673i	$0.379911\pi$
$569$	−4.41866	+	42.0407i	−0.185240	+	1.76244i	−0.553625	+	0.832766i	$0.686756\pi$
$570$		0			0
$571$	−12.7572			−0.533874			−0.266937	−	0.963714i	$-0.586011\pi$
$571$	−12.7572			−0.533874			−0.266937	+	0.963714i	$0.586011\pi$
$572$		0			0
$573$	12.5131			0.522742
$574$		0			0
$575$	−1.68472	+	16.0290i	−0.0702576	+	0.668456i
$576$		0			0
$577$	10.6029	+	3.44511i	0.441406	+	0.143422i	0.521284	−	0.853383i	$-0.325453\pi$
$577$	10.6029	+	3.44511i	0.441406	+	0.143422i	−0.0798780	+	0.996805i	$0.525453\pi$
$578$		0			0
$579$	2.99116	−	0.314384i	0.124308	−	0.0130653i
$580$		0			0
$581$	3.73542	+	0.793988i	0.154971	+	0.0329402i
$582$		0			0
$583$	−9.72340	−	28.2227i	−0.402702	−	1.16887i
$584$		0			0
$585$	−0.133448	+	0.251042i	−0.00551738	+	0.0103793i
$586$		0			0
$587$	0.304566	−	0.684066i	0.0125708	−	0.0282344i	−0.907151	−	0.420805i	$-0.861748\pi$
$587$	0.304566	−	0.684066i	0.0125708	−	0.0282344i	0.919722	+	0.392571i	$0.128414\pi$
$588$		0			0
$589$	−8.63838	−	9.59389i	−0.355938	−	0.395310i
$590$		0			0
$591$	−2.49075	−	5.59431i	−0.102456	−	0.230119i
$592$		0			0
$593$		−	18.1586i		−	0.745683i	−0.927895	−	0.372842i	$-0.878383\pi$
$593$		−	18.1586i		−	0.745683i	0.927895	−	0.372842i	$-0.121617\pi$
$594$		0			0
$595$	0.148307	+	0.256875i	0.00608000	+	0.0105309i
$596$		0			0
$597$	23.0892	+	16.7753i	0.944977	+	0.686566i
$598$		0			0
$599$	−7.45221	+	22.9355i	−0.304489	+	0.937121i	0.675378	+	0.737471i	$0.263980\pi$
$599$	−7.45221	+	22.9355i	−0.304489	+	0.937121i	−0.979867	+	0.199649i	$0.936020\pi$
$600$		0			0
$601$	5.85011	+	2.60464i	0.238631	+	0.106245i	0.522568	−	0.852598i	$-0.324974\pi$
$601$	5.85011	+	2.60464i	0.238631	+	0.106245i	−0.283937	+	0.958843i	$0.591641\pi$
$602$		0			0
$603$	−2.63878	+	0.857391i	−0.107459	+	0.0349156i
$604$		0			0
$605$	3.15236	+	0.902730i	0.128162	+	0.0367012i
$606$		0			0
$607$	−20.6176	−	4.38240i	−0.836841	−	0.177876i	−0.230491	−	0.973074i	$-0.574033\pi$
$607$	−20.6176	−	4.38240i	−0.836841	−	0.177876i	−0.606349	+	0.795198i	$0.707367\pi$
$608$		0			0
$609$	0.592802	−	1.33146i	0.0240216	−	0.0539533i
$610$		0			0
$611$	−10.1785	−	6.86397i	−0.411780	−	0.277686i
$612$		0			0
$613$	11.7439	+	1.23434i	0.474333	+	0.0498544i	0.338679	−	0.940902i	$-0.390020\pi$
$613$	11.7439	+	1.23434i	0.474333	+	0.0498544i	0.135654	+	0.990756i	$0.456687\pi$
$614$		0			0
$615$	−1.95781	+	3.39103i	−0.0789467	+	0.136740i
$616$		0			0
$617$	−7.81844	−	4.51398i	−0.314758	−	0.181726i	0.334295	−	0.942468i	$-0.391502\pi$
$617$	−7.81844	−	4.51398i	−0.314758	−	0.181726i	−0.649054	+	0.760742i	$0.724835\pi$
$618$		0			0
$619$	−19.3388	+	26.6176i	−0.777292	+	1.06985i	0.218284	+	0.975885i	$0.429954\pi$
$619$	−19.3388	+	26.6176i	−0.777292	+	1.06985i	−0.995575	+	0.0939652i	$0.970046\pi$
$620$		0			0
$621$	−15.8657	+	3.37235i	−0.636667	+	0.135328i
$622$		0			0
$623$	3.63929	−	2.64410i	0.145805	−	0.105934i
$624$		0			0
$625$	7.31597	+	22.5162i	0.292639	+	0.900649i
$626$		0			0
$627$	−12.9161	+	4.44992i	−0.515821	+	0.177713i
$628$		0			0
$629$	−29.5253	+	9.59336i	−1.17725	+	0.382512i
$630$		0			0
$631$	12.5482	−	1.31887i	0.499537	−	0.0525035i	0.148590	−	0.988899i	$-0.452526\pi$
$631$	12.5482	−	1.31887i	0.499537	−	0.0525035i	0.350947	+	0.936395i	$0.385860\pi$
$632$		0			0
$633$	12.1481	+	13.4918i	0.482842	+	0.536250i
$634$		0			0
$635$	−4.58351	−	0.481746i	−0.181891	−	0.0191175i
$636$		0			0
$637$	6.01167	+	24.1008i	0.238191	+	0.954907i
$638$		0			0
$639$	0.915186	−	0.528383i	0.0362042	−	0.0209025i
$640$		0			0
$641$	15.4474	−	6.87763i	0.610136	−	0.271650i	−0.0783201	−	0.996928i	$-0.524956\pi$
$641$	15.4474	−	6.87763i	0.610136	−	0.271650i	0.688456	+	0.725278i	$0.258289\pi$
$642$		0			0
$643$	30.7967	−	27.7295i	1.21450	−	1.09354i	0.221536	−	0.975152i	$-0.428893\pi$
$643$	30.7967	−	27.7295i	1.21450	−	1.09354i	0.992967	−	0.118391i	$-0.0377736\pi$
$644$		0			0
$645$	−0.0438053	−	0.0602928i	−0.00172483	−	0.00237403i
$646$		0			0
$647$	18.3586	−	20.3893i	0.721751	−	0.801586i	−0.264927	−	0.964268i	$-0.585348\pi$
$647$	18.3586	−	20.3893i	0.721751	−	0.801586i	0.986678	+	0.162683i	$0.0520147\pi$
$648$		0			0
$649$	12.6525	−	1.55578i	0.496654	−	0.0610698i
$650$		0			0
$651$	−1.05264	−	3.23969i	−0.0412562	−	0.126973i
$652$		0			0
$653$	−9.07020	−	4.03831i	−0.354944	−	0.158031i	0.221516	−	0.975157i	$-0.428900\pi$
$653$	−9.07020	−	4.03831i	−0.354944	−	0.158031i	−0.576460	+	0.817125i	$0.695566\pi$
$654$		0			0
$655$	3.12900	+	1.01667i	0.122260	+	0.0397247i
$656$		0			0
$657$	−0.423048	−	0.950182i	−0.0165047	−	0.0370701i
$658$		0			0
$659$	−16.6343	+	28.8115i	−0.647980	+	1.12233i	0.335624	+	0.941996i	$0.391053\pi$
$659$	−16.6343	+	28.8115i	−0.647980	+	1.12233i	−0.983605	+	0.180339i	$0.942281\pi$
$660$		0			0
$661$	−3.40437	+	1.96551i	−0.132415	+	0.0764496i	−0.564744	−	0.825266i	$-0.691025\pi$
$661$	−3.40437	+	1.96551i	−0.132415	+	0.0764496i	0.432329	+	0.901716i	$0.357692\pi$
$662$		0			0
$663$	−11.9885	−	15.3413i	−0.465596	−	0.595807i
$664$		0			0
$665$	−0.0470402	−	0.221307i	−0.00182414	−	0.00858191i
$666$		0			0
$667$	−0.831157	−	7.90793i	−0.0321825	−	0.306196i
$668$		0			0
$669$	−5.48070	+	25.7847i	−0.211896	+	0.996894i
$670$		0			0
$671$	26.7575	+	28.6839i	1.03296	+	1.10733i
$672$		0			0
$673$	28.4974	−	31.6496i	1.09850	−	1.22000i	0.124792	−	0.992183i	$-0.460174\pi$
$673$	28.4974	−	31.6496i	1.09850	−	1.22000i	0.973703	−	0.227819i	$-0.0731596\pi$
$674$		0			0
$675$	−19.6374	+	14.2674i	−0.755842	+	0.549152i
$676$		0			0
$677$	−6.07285	+	18.6903i	−0.233399	+	0.718327i	0.763931	+	0.645298i	$0.223267\pi$
$677$	−6.07285	+	18.6903i	−0.233399	+	0.718327i	−0.997330	+	0.0730295i	$0.976733\pi$
$678$		0			0
$679$	−0.357148	+	3.39804i	−0.0137061	+	0.130405i
$680$		0			0
$681$		−	21.3444i		−	0.817921i
$682$		0			0
$683$	−29.2215	−	16.8711i	−1.11813	−	0.645553i	−0.177208	−	0.984174i	$-0.556706\pi$
$683$	−29.2215	−	16.8711i	−1.11813	−	0.645553i	−0.940923	+	0.338621i	$0.890040\pi$
$684$		0			0
$685$	3.62813	−	1.61535i	0.138624	−	0.0617192i
$686$		0			0
$687$	0.213323	+	1.00361i	0.00813879	+	0.0382900i
$688$		0			0
$689$	−30.4930	+	11.1021i	−1.16169	+	0.422958i
$690$		0			0
$691$	−2.38024	−	2.14318i	−0.0905485	−	0.0815302i	0.622613	−	0.782530i	$-0.286071\pi$
$691$	−2.38024	−	2.14318i	−0.0905485	−	0.0815302i	−0.713162	+	0.700999i	$0.752738\pi$
$692$		0			0
$693$	−0.290973	−	0.0254054i	−0.0110532	−	0.000965073i
$694$		0			0
$695$	−0.523011	+	2.46057i	−0.0198389	+	0.0933348i
$696$		0			0
$697$	−12.7713	−	17.5783i	−0.483749	−	0.665824i
$698$		0			0
$699$	1.05359	−	0.223948i	0.0398505	−	0.00847049i
$700$		0			0
$701$	−22.9337	−	16.6623i	−0.866193	−	0.629326i	0.0633700	−	0.997990i	$-0.479815\pi$
$701$	−22.9337	−	16.6623i	−0.866193	−	0.629326i	−0.929563	+	0.368664i	$0.879815\pi$
$702$		0			0
$703$	23.6803			0.893118
$704$		0			0
$705$	−0.916953	−	1.58821i	−0.0345344	−	0.0598154i
$706$		0			0
$707$	−1.67232	+	2.30175i	−0.0628941	+	0.0865663i
$708$		0			0
$709$	12.8938	−	11.6096i	0.484237	−	0.436009i	−0.390503	−	0.920602i	$-0.627699\pi$
$709$	12.8938	−	11.6096i	0.484237	−	0.436009i	0.874740	+	0.484593i	$0.161032\pi$
$710$		0			0
$711$	−0.317009	−	3.01614i	−0.0118888	−	0.113114i
$712$		0			0
$713$	−13.8109	−	12.4354i	−0.517223	−	0.465709i
$714$		0			0
$715$	0.921657	−	3.44352i	0.0344680	−	0.128780i
$716$		0			0
$717$	−29.2078	−	26.2988i	−1.09079	−	0.982148i
$718$		0			0
$719$	−0.174745	−	1.66259i	−0.00651689	−	0.0620041i	0.990780	−	0.135480i	$-0.0432576\pi$
$719$	−0.174745	−	1.66259i	−0.00651689	−	0.0620041i	−0.997297	+	0.0734756i	$0.976591\pi$
$720$		0			0
$721$	−3.14523	+	2.83197i	−0.117134	+	0.105468i
$722$		0			0
$723$	12.8701	−	17.7141i	0.478643	−	0.658795i
$724$		0			0
$725$	−5.94963	−	10.3051i	−0.220964	−	0.382721i
$726$		0			0
$727$	−21.8822			−0.811565			−0.405782	−	0.913970i	$-0.633001\pi$
$727$	−21.8822			−0.811565			−0.405782	+	0.913970i	$0.633001\pi$
$728$		0			0
$729$	−19.5928	−	14.2350i	−0.725659	−	0.527222i
$730$		0			0
$731$	0.404509	−	0.0859811i	0.0149613	−	0.00318013i
$732$		0			0
$733$	6.09922	+	8.39485i	0.225280	+	0.310071i	0.906663	−	0.421856i	$-0.138621\pi$
$733$	6.09922	+	8.39485i	0.225280	+	0.310071i	−0.681383	+	0.731927i	$0.738621\pi$
$734$		0			0
$735$	−0.771460	+	3.62943i	−0.0284557	+	0.133874i
$736$		0			0
$737$	29.8164	−	17.9226i	1.09830	−	0.660189i
$738$		0			0
$739$	−10.4306	−	9.39177i	−0.383696	−	0.345482i	0.454601	−	0.890695i	$-0.349782\pi$
$739$	−10.4306	−	9.39177i	−0.383696	−	0.345482i	−0.838297	+	0.545214i	$0.816449\pi$
$740$		0			0
$741$	5.08090	+	13.9551i	0.186651	+	0.512654i
$742$		0			0
$743$	5.55605	+	26.1392i	0.203832	+	0.958953i	0.954486	+	0.298257i	$0.0964053\pi$
$743$	5.55605	+	26.1392i	0.203832	+	0.958953i	−0.750654	+	0.660696i	$0.770261\pi$
$744$		0			0
$745$	−5.02586	+	2.23766i	−0.184133	+	0.0819814i
$746$		0			0
$747$	−2.62769	−	1.51710i	−0.0961420	−	0.0555076i
$748$		0			0
$749$			2.49515i			0.0911709i
$750$		0			0
$751$	2.66495	−	25.3553i	0.0972454	−	0.925228i	−0.831753	−	0.555145i	$-0.812663\pi$
$751$	2.66495	−	25.3553i	0.0972454	−	0.925228i	0.928999	−	0.370083i	$-0.120671\pi$
$752$		0			0
$753$	10.2439	−	31.5276i	0.373310	−	1.14893i
$754$		0			0
$755$	−0.0160510	+	0.0116617i	−0.000584156	+	0.000424414i
$756$		0			0
$757$	24.7794	−	27.5203i	0.900622	−	1.00024i	−0.0993649	−	0.995051i	$-0.531681\pi$
$757$	24.7794	−	27.5203i	0.900622	−	1.00024i	0.999987	−	0.00519059i	$-0.00165222\pi$
$758$		0			0
$759$	−17.8220	+	8.31434i	−0.646898	+	0.301791i
$760$		0			0
$761$	2.09687	−	9.86498i	0.0760113	−	0.357605i	−0.923661	−	0.383211i	$-0.874818\pi$
$761$	2.09687	−	9.86498i	0.0760113	−	0.357605i	0.999672	+	0.0256059i	$0.00815150\pi$
$762$		0			0
$763$	0.428051	+	4.07263i	0.0154965	+	0.147439i
$764$		0			0
$765$	−0.0489980	−	0.230518i	−0.00177153	−	0.00833438i
$766$		0			0
$767$	−1.93013	−	13.7232i	−0.0696931	−	0.495517i
$768$		0			0
$769$	−16.3161	+	9.42008i	−0.588372	+	0.339697i	−0.764454	−	0.644679i	$-0.776991\pi$
$769$	−16.3161	+	9.42008i	−0.588372	+	0.339697i	0.176082	+	0.984376i	$0.443658\pi$
$770$		0			0
$771$	−25.0524	+	43.3921i	−0.902241	+	1.56273i
$772$		0			0
$773$	−2.47010	−	5.54793i	−0.0888432	−	0.199545i	0.863659	−	0.504076i	$-0.168167\pi$
$773$	−2.47010	−	5.54793i	−0.0888432	−	0.199545i	−0.952502	+	0.304531i	$0.901500\pi$
$774$		0			0
$775$	−26.4501	−	8.59415i	−0.950115	−	0.308711i
$776$		0			0
$777$	5.70811	+	2.54141i	0.204777	+	0.0911727i
$778$		0			0
$779$	5.12152	+	15.7624i	0.183497	+	0.564747i
$780$		0			0
$781$	−9.68891	+	9.03823i	−0.346696	+	0.323413i
$782$		0			0
$783$	8.01295	−	8.89928i	0.286359	−	0.318034i
$784$		0			0
$785$	−1.56852	−	2.15889i	−0.0559830	−	0.0770541i
$786$		0			0
$787$	4.65343	−	4.18996i	0.165877	−	0.149356i	−0.582012	−	0.813180i	$-0.697734\pi$
$787$	4.65343	−	4.18996i	0.165877	−	0.149356i	0.747889	+	0.663824i	$0.231068\pi$
$788$		0			0
$789$	−16.8695	+	7.51077i	−0.600569	+	0.267391i
$790$		0			0
$791$	−0.124128	+	0.0716654i	−0.00441349	+	0.00254813i
$792$		0			0
$793$	30.6723	−	29.6261i	1.08921	−	1.05205i
$794$		0			0
$795$	−4.82105	−	0.506712i	−0.170985	−	0.0179712i
$796$		0			0
$797$	−15.4023	−	17.1060i	−0.545578	−	0.605926i	0.405796	−	0.913964i	$-0.366994\pi$
$797$	−15.4023	−	17.1060i	−0.545578	−	0.605926i	−0.951374	+	0.308038i	$0.900328\pi$
$798$		0			0
$799$	10.1206	−	1.06372i	0.358043	−	0.0376318i
$800$		0			0
$801$	−3.39918	+	1.10446i	−0.120104	+	0.0390241i
$802$		0			0
$803$	7.85019	+	10.4138i	0.277027	+	0.367494i
$804$		0			0
$805$	−0.100647	−	0.309759i	−0.00354733	−	0.0109176i
$806$		0			0
$807$	20.9493	−	15.2205i	0.737449	−	0.535788i
$808$		0			0
$809$	30.7515	−	6.53643i	1.08116	−	0.229808i	0.367307	−	0.930100i	$-0.380280\pi$
$809$	30.7515	−	6.53643i	1.08116	−	0.229808i	0.713857	+	0.700291i	$0.246947\pi$
$810$		0			0
$811$	10.5597	−	14.5342i	0.370803	−	0.510367i	−0.582316	−	0.812963i	$-0.697853\pi$
$811$	10.5597	−	14.5342i	0.370803	−	0.510367i	0.953119	+	0.302596i	$0.0978533\pi$
$812$		0			0
$813$	−9.10755	−	5.25825i	−0.319416	−	0.184415i
$814$		0			0
$815$	1.95897	−	3.39304i	0.0686198	−	0.118853i
$816$		0			0
$817$	−0.313716	−	0.0329729i	−0.0109755	−	0.00115358i
$818$		0			0
$819$	−0.0221163	+	0.316753i	−0.000772808	+	0.0110683i
$820$		0			0
$821$	−10.0293	+	22.5262i	−0.350026	+	0.786171i	0.649638	+	0.760244i	$0.274920\pi$
$821$	−10.0293	+	22.5262i	−0.350026	+	0.786171i	−0.999664	+	0.0259271i	$0.991746\pi$
$822$		0			0
$823$	22.2294	+	4.72500i	0.774867	+	0.164703i	0.578340	−	0.815796i	$-0.303701\pi$
$823$	22.2294	+	4.72500i	0.774867	+	0.164703i	0.196526	+	0.980499i	$0.437034\pi$
$824$		0			0
$825$	−19.3038	+	22.2144i	−0.672073	+	0.773405i
$826$		0			0
$827$	23.3239	−	7.57839i	0.811051	−	0.263527i	0.126008	−	0.992029i	$-0.459783\pi$
$827$	23.3239	−	7.57839i	0.811051	−	0.263527i	0.685043	+	0.728503i	$0.259783\pi$
$828$		0			0
$829$	10.3185	+	4.59407i	0.358375	+	0.159559i	0.578023	−	0.816020i	$-0.303824\pi$
$829$	10.3185	+	4.59407i	0.358375	+	0.159559i	−0.219648	+	0.975579i	$0.570491\pi$
$830$		0			0
$831$	15.5636	−	47.8999i	0.539896	−	1.66163i
$832$		0			0
$833$	−16.6574	−	12.1023i	−0.577146	−	0.419321i
$834$		0			0
$835$	0.529379	+	0.916911i	0.0183199	+	0.0317310i
$836$		0			0
$837$		−	27.9886i		−	0.967429i
$838$		0			0
$839$	11.6299	+	26.1213i	0.401510	+	0.901807i	0.995268	+	0.0971632i	$0.0309769\pi$
$839$	11.6299	+	26.1213i	0.401510	+	0.901807i	−0.593758	+	0.804643i	$0.702356\pi$
$840$		0			0
$841$	−15.4766	−	17.1886i	−0.533677	−	0.592709i
$842$		0			0
$843$	−7.95831	+	17.8747i	−0.274099	+	0.615636i
$844$		0			0
$845$	−3.76035	−	0.936728i	−0.129360	−	0.0322244i
$846$		0			0
$847$	3.62638	−	0.510951i	0.124604	−	0.0175565i
$848$		0			0
$849$	−17.0926	−	3.63314i	−0.586616	−	0.124689i
$850$		0			0
$851$	33.9022	−	3.56327i	1.16215	−	0.122147i
$852$		0			0
$853$	32.3176	+	10.5006i	1.10653	+	0.359534i	0.804613	−	0.593799i	$-0.202373\pi$
$853$	32.3176	+	10.5006i	1.10653	+	0.359534i	0.301919	+	0.953334i	$0.402373\pi$
$854$		0			0
$855$	−0.0187902	+	0.178777i	−0.000642613	+	0.00611405i
$856$		0			0
$857$	−34.9882			−1.19518			−0.597588	−	0.801804i	$-0.703874\pi$
$857$	−34.9882			−1.19518			−0.597588	+	0.801804i	$0.703874\pi$
$858$		0			0
$859$	−8.88249			−0.303066			−0.151533	−	0.988452i	$-0.548421\pi$
$859$	−8.88249			−0.303066			−0.151533	+	0.988452i	$0.548421\pi$
$860$		0			0
$861$	−0.457116	+	4.34917i	−0.0155785	+	0.148219i
$862$		0			0
$863$	44.9620	+	14.6091i	1.53053	+	0.497298i	0.948744	−	0.316047i	$-0.102356\pi$
$863$	44.9620	+	14.6091i	1.53053	+	0.497298i	0.581782	+	0.813345i	$0.302356\pi$
$864$		0			0
$865$	−6.52016	+	0.685297i	−0.221692	+	0.0233008i
$866$		0			0
$867$	−14.2580	−	3.03062i	−0.484225	−	0.102925i
$868$		0			0
$869$	12.3862	+	35.9518i	0.420174	+	1.21958i
$870$		0			0
$871$	−20.0444	−	32.0703i	−0.679179	−	1.08666i
$872$		0			0
$873$	1.10417	−	2.48000i	0.0373704	−	0.0839354i
$874$		0			0
$875$	−0.658176	−	0.730978i	−0.0222504	−	0.0247116i
$876$		0			0
$877$	−20.8837	−	46.9055i	−0.705192	−	1.58389i	−0.807998	−	0.589185i	$-0.799449\pi$
$877$	−20.8837	−	46.9055i	−0.705192	−	1.58389i	0.102807	−	0.994701i	$-0.467218\pi$
$878$		0			0
$879$		−	61.7960i		−	2.08433i
$880$		0			0
$881$	−3.91314	−	6.77776i	−0.131837	−	0.228349i	0.792548	−	0.609810i	$-0.208754\pi$
$881$	−3.91314	−	6.77776i	−0.131837	−	0.228349i	−0.924385	+	0.381461i	$0.875421\pi$
$882$		0			0
$883$	40.3172	+	29.2921i	1.35678	+	0.985759i	0.998642	+	0.0520902i	$0.0165883\pi$
$883$	40.3172	+	29.2921i	1.35678	+	0.985759i	0.358138	+	0.933669i	$0.383412\pi$
$884$		0			0
$885$	0.639718	−	1.96885i	0.0215039	−	0.0661822i
$886$		0			0
$887$	−17.1228	−	7.62356i	−0.574927	−	0.255974i	0.0986116	−	0.995126i	$-0.468560\pi$
$887$	−17.1228	−	7.62356i	−0.574927	−	0.255974i	−0.673539	+	0.739152i	$0.735227\pi$
$888$		0			0
$889$	−4.89531	+	1.59058i	−0.164184	+	0.0533465i
$890$		0			0
$891$	−29.6880	−	12.5957i	−0.994586	−	0.421971i
$892$		0			0
$893$	−7.59270	−	1.61388i	−0.254080	−	0.0540064i
$894$		0			0
$895$	0.589614	−	1.32429i	0.0197086	−	0.0442663i
$896$		0			0
$897$	9.37403	+	19.2145i	0.312990	+	0.641554i
$898$		0			0
$899$	13.6455	+	1.43421i	0.455105	+	0.0478334i
$900$		0			0
$901$	13.4497	−	23.2956i	0.448076	−	0.776090i
$902$		0			0
$903$	−0.0720823	−	0.0416167i	−0.00239875	−	0.00138492i
$904$		0			0
$905$	−2.17998	+	3.00049i	−0.0724651	+	0.0997397i
$906$		0			0
$907$	−33.4702	+	7.11430i	−1.11136	+	0.236226i	−0.726783	−	0.686867i	$-0.758985\pi$
$907$	−33.4702	+	7.11430i	−1.11136	+	0.236226i	−0.384575	+	0.923094i	$0.625652\pi$
$908$		0			0
$909$	1.82880	−	1.32870i	0.0606575	−	0.0440702i
$910$		0			0
$911$	−11.3304	−	34.8714i	−0.375394	−	1.15534i	−0.943213	−	0.332189i	$-0.892213\pi$
$911$	−11.3304	−	34.8714i	−0.375394	−	1.15534i	0.567819	−	0.823153i	$-0.307787\pi$
$912$		0			0
$913$	36.3833	+	11.1165i	1.20411	+	0.367903i
$914$		0			0
$915$	6.05842	−	1.96850i	0.200285	−	0.0650766i
$916$		0			0
$917$	3.65430	−	0.384082i	0.120676	−	0.0126835i
$918$		0			0
$919$	−13.5983	−	15.1024i	−0.448567	−	0.498184i	0.475872	−	0.879515i	$-0.342133\pi$
$919$	−13.5983	−	15.1024i	−0.448567	−	0.498184i	−0.924439	+	0.381331i	$0.875466\pi$
$920$		0			0
$921$	5.89362	+	0.619445i	0.194201	+	0.0204114i
$922$		0			0
$923$	10.0072	+	10.3606i	0.329391	+	0.341023i
$924$		0			0
$925$	44.1791	−	25.5068i	1.45260	−	0.838658i
$926$		0			0
$927$	3.07197	−	1.36773i	0.100897	−	0.0449221i
$928$		0			0
$929$	17.6970	−	15.9345i	0.580621	−	0.522793i	−0.325650	−	0.945490i	$-0.605583\pi$
$929$	17.6970	−	15.9345i	0.580621	−	0.522793i	0.906271	+	0.422697i	$0.138917\pi$
$930$		0			0
$931$	9.23140	+	12.7059i	0.302547	+	0.416420i
$932$		0			0
$933$	−9.81932	+	10.9055i	−0.321470	+	0.357029i
$934$		0			0
$935$	1.24925	+	2.67781i	0.0408550	+	0.0875737i
$936$		0			0
$937$	−4.15730	−	12.7949i	−0.135813	−	0.417990i	0.859903	−	0.510458i	$-0.170524\pi$
$937$	−4.15730	−	12.7949i	−0.135813	−	0.417990i	−0.995716	+	0.0924686i	$0.970524\pi$
$938$		0			0
$939$	−28.0223	−	12.4763i	−0.914474	−	0.407150i
$940$		0			0
$941$	22.5665	+	7.33229i	0.735646	+	0.239026i	0.652794	−	0.757536i	$-0.273597\pi$
$941$	22.5665	+	7.33229i	0.735646	+	0.239026i	0.0828527	+	0.996562i	$0.473597\pi$
$942$		0			0
$943$	9.70414	+	21.7959i	0.316010	+	0.709771i
$944$		0			0
$945$	0.245257	−	0.424797i	0.00797820	−	0.0138186i
$946$		0			0
$947$	−7.90036	+	4.56127i	−0.256727	+	0.148222i	−0.622841	−	0.782349i	$-0.714022\pi$
$947$	−7.90036	+	4.56127i	−0.256727	+	0.148222i	0.366113	+	0.930570i	$0.380688\pi$
$948$		0			0
$949$	11.1709	−	8.72955i	0.362623	−	0.283373i
$950$		0			0
$951$	4.80046	+	22.5844i	0.155665	+	0.732348i
$952$		0			0
$953$	−4.04777	−	38.5120i	−0.131120	−	1.24752i	−0.840153	−	0.542349i	$-0.817535\pi$
$953$	−4.04777	−	38.5120i	−0.131120	−	1.24752i	0.709033	−	0.705175i	$-0.249132\pi$
$954$		0			0
$955$	−0.429233	+	2.01938i	−0.0138896	+	0.0653456i
$956$		0			0
$957$	7.03684	−	12.7001i	0.227469	−	0.410534i
$958$		0			0
$959$	2.96793	−	3.29622i	0.0958395	−	0.106440i
$960$		0			0
$961$	0.864350	−	0.627987i	0.0278822	−	0.0202576i
$962$		0			0
$963$	0.612615	−	1.88543i	0.0197412	−	0.0607573i
$964$		0			0
$965$	−0.0518691	+	0.493502i	−0.00166973	+	0.0158864i
$966$		0			0
$967$			18.4318i			0.592728i	0.955075	+	0.296364i	$0.0957741\pi$
$967$			18.4318i			0.592728i	−0.955075	+	0.296364i	$0.904226\pi$
$968$		0			0
$969$	−10.6612	−	6.15527i	−0.342488	−	0.197736i
$970$		0			0
$971$	56.0787	−	24.9678i	1.79965	−	0.801256i	0.829597	−	0.558363i	$-0.188570\pi$
$971$	56.0787	−	24.9678i	1.79965	−	0.801256i	0.970053	−	0.242893i	$-0.0780965\pi$
$972$		0			0
$973$	0.584119	+	2.74806i	0.0187260	+	0.0880989i
$974$		0			0
$975$	24.5107	+	20.5625i	0.784970	+	0.658529i
$976$		0			0
$977$	−27.1888	−	24.4809i	−0.869847	−	0.783214i	0.107644	−	0.994189i	$-0.465669\pi$
$977$	−27.1888	−	24.4809i	−0.869847	−	0.783214i	−0.977491	+	0.210976i	$0.932336\pi$
$978$		0			0
$979$	38.4084	−	23.0873i	1.22754	−	0.737873i
$980$		0			0
$981$	0.676468	−	3.18253i	0.0215980	−	0.101610i
$982$		0			0
$983$	22.1739	+	30.5197i	0.707237	+	0.973428i	0.999852	+	0.0171981i	$0.00547459\pi$
$983$	22.1739	+	30.5197i	0.707237	+	0.973428i	−0.292615	+	0.956230i	$0.594525\pi$
$984$		0			0
$985$	0.988255	−	0.210060i	0.0314884	−	0.00669307i
$986$		0			0
$987$	−1.65701	−	1.20389i	−0.0527432	−	0.0383202i
$988$		0			0
$989$	−0.454098			−0.0144395
$990$		0			0
$991$	−8.32198	−	14.4141i	−0.264356	−	0.457879i	0.703038	−	0.711152i	$-0.251826\pi$
$991$	−8.32198	−	14.4141i	−0.264356	−	0.457879i	−0.967395	+	0.253273i	$0.918493\pi$
$992$		0			0
$993$	−21.2748	+	29.2823i	−0.675136	+	0.929245i
$994$		0			0
$995$	−3.49924	+	3.15073i	−0.110933	+	0.0998847i
$996$		0			0
$997$	2.62372	+	24.9631i	0.0830942	+	0.790588i	0.954135	+	0.299377i	$0.0967790\pi$
$997$	2.62372	+	24.9631i	0.0830942	+	0.790588i	−0.871041	+	0.491211i	$0.836554\pi$
$998$		0			0
$999$	38.1523	+	34.3525i	1.20708	+	1.08686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.11	✓	112
11.9	even	5	inner	572.2.bq.a.361.4	yes	112
13.4	even	6	inner	572.2.bq.a.225.4	yes	112
143.108	even	30	inner	572.2.bq.a.537.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.11	✓	112	1.1	even	1	trivial
572.2.bq.a.225.4	yes	112	13.4	even	6	inner
572.2.bq.a.361.4	yes	112	11.9	even	5	inner
572.2.bq.a.537.11	yes	112	143.108	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.188862 - 1.79690i) q^{3} +(0.283508 + 0.0921172i) q^{5} +(0.331103 - 0.0348003i) q^{7} +(-0.258739 - 0.0549966i) q^{9} +O(q^{10})\)	\(q+(0.188862 - 1.79690i) q^{3} +(0.283508 + 0.0921172i) q^{5} +(0.331103 - 0.0348003i) q^{7} +(-0.258739 - 0.0549966i) q^{9} +(3.31611 - 0.0584646i) q^{11} +(-0.126208 - 3.60334i) q^{13} +(0.219069 - 0.492037i) q^{15} +(1.99984 + 2.22105i) q^{17} +(-0.927249 - 2.08263i) q^{19} -0.601532i q^{21} +(-1.64089 - 2.84211i) q^{23} +(-3.97319 - 2.88669i) q^{25} +(1.52730 - 4.70056i) q^{27} +(2.21344 + 0.985488i) q^{29} +(5.38573 - 1.74993i) q^{31} +(0.521231 - 5.96976i) q^{33} +(0.0970760 + 0.0206341i) q^{35} +(-4.22491 + 9.48929i) q^{37} +(-6.49868 - 0.453751i) q^{39} +(-7.23016 - 0.759920i) q^{41} +(0.0691846 - 0.119831i) q^{43} +(-0.0682882 - 0.0394262i) q^{45} +(2.00137 - 2.75465i) q^{47} +(-6.73861 + 1.43234i) q^{49} +(4.36870 - 3.17404i) q^{51} +(-2.78126 - 8.55983i) q^{53} +(0.945528 + 0.288896i) q^{55} +(-3.91741 + 1.27284i) q^{57} +(3.82254 - 0.401766i) q^{59} +(7.91399 + 8.78938i) q^{61} +(-0.0875830 - 0.00920535i) q^{63} +(0.296149 - 1.03320i) q^{65} +(9.08386 - 5.24457i) q^{67} +(-5.41689 + 2.41176i) q^{69} +(-2.96890 + 2.67321i) q^{71} +(2.31121 + 3.18110i) q^{73} +(-5.93749 + 6.59425i) q^{75} +(1.09594 - 0.134760i) q^{77} +(3.54293 + 10.9040i) q^{79} +(-8.88294 - 3.95494i) q^{81} +(10.9092 + 3.54461i) q^{83} +(0.362373 + 0.813904i) q^{85} +(2.18886 - 3.79121i) q^{87} +(11.7015 - 6.75586i) q^{89} +(-0.167185 - 1.18869i) q^{91} +(-2.12729 - 10.0081i) q^{93} +(-0.0710356 - 0.675858i) q^{95} +(-2.13375 + 10.0385i) q^{97} +(-0.861221 - 0.167248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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