LMFDB - Embedded newform 1040.2.da.f.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.2
Root			$-2.79253i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.f.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00284 + 1.73697i) q^{3} -1.00000i q^{5} +(-1.48627 + 0.858099i) q^{7} +(-0.511370 - 0.885719i) q^{9} +O(q^{10})$	\(q+(-1.00284 + 1.73697i) q^{3} -1.00000i q^{5} +(-1.48627 + 0.858099i) q^{7} +(-0.511370 - 0.885719i) q^{9} +(4.59199 + 2.65119i) q^{11} +(2.34769 - 2.73649i) q^{13} +(1.73697 + 1.00284i) q^{15} +(0.811344 + 1.40529i) q^{17} +(-1.96681 + 1.13554i) q^{19} -3.44214i q^{21} +(2.52585 - 4.37490i) q^{23} -1.00000 q^{25} -3.96574 q^{27} +(-2.08770 + 3.61600i) q^{29} +8.79183i q^{31} +(-9.21004 + 5.31742i) q^{33} +(0.858099 + 1.48627i) q^{35} +(-0.942563 - 0.544189i) q^{37} +(2.39884 + 6.82211i) q^{39} +(7.86992 + 4.54370i) q^{41} +(4.18560 + 7.24968i) q^{43} +(-0.885719 + 0.511370i) q^{45} -2.45297i q^{47} +(-2.02733 + 3.51144i) q^{49} -3.25459 q^{51} -5.54358 q^{53} +(2.65119 - 4.59199i) q^{55} -4.55505i q^{57} +(-8.57344 + 4.94988i) q^{59} +(0.373308 + 0.646589i) q^{61} +(1.52007 + 0.877612i) q^{63} +(-2.73649 - 2.34769i) q^{65} +(-13.5181 - 7.80468i) q^{67} +(5.06604 + 8.77464i) q^{69} +(-2.13260 + 1.23126i) q^{71} +12.7513i q^{73} +(1.00284 - 1.73697i) q^{75} -9.09991 q^{77} -0.702839 q^{79} +(5.51111 - 9.54553i) q^{81} -3.57032i q^{83} +(1.40529 - 0.811344i) q^{85} +(-4.18725 - 7.25253i) q^{87} +(9.93763 + 5.73750i) q^{89} +(-1.14112 + 6.08171i) q^{91} +(-15.2711 - 8.81679i) q^{93} +(1.13554 + 1.96681i) q^{95} +(12.1902 - 7.03799i) q^{97} -5.42295i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00284	+	1.73697i	−0.578989	+	1.00284i	0.416607	+	0.909087i	$0.363219\pi$
$3$	−1.00284	+	1.73697i	−0.578989	+	1.00284i	−0.995596	+	0.0937516i	$0.970114\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−1.48627	+	0.858099i	−0.561757	+	0.324331i	−0.753851	−	0.657046i	$-0.771806\pi$
$7$	−1.48627	+	0.858099i	−0.561757	+	0.324331i	0.192093	+	0.981377i	$0.438472\pi$
$8$		0			0
$9$	−0.511370	−	0.885719i	−0.170457	−	0.295240i
$10$		0			0
$11$	4.59199	+	2.65119i	1.38454	+	0.799362i	0.992693	−	0.120670i	$-0.0385041\pi$
$11$	4.59199	+	2.65119i	1.38454	+	0.799362i	0.391844	+	0.920032i	$0.371837\pi$
$12$		0			0
$13$	2.34769	−	2.73649i	0.651132	−	0.758965i
$13$	2.34769	−	2.73649i	0.651132	−	0.758965i
$14$		0			0
$15$	1.73697	+	1.00284i	0.448483	+	0.258932i
$16$		0			0
$17$	0.811344	+	1.40529i	0.196780	+	0.340833i	0.947483	−	0.319808i	$-0.103618\pi$
$17$	0.811344	+	1.40529i	0.196780	+	0.340833i	−0.750703	+	0.660640i	$0.770285\pi$
$18$		0			0
$19$	−1.96681	+	1.13554i	−0.451217	+	0.260510i	−0.708344	−	0.705867i	$-0.750557\pi$
$19$	−1.96681	+	1.13554i	−0.451217	+	0.260510i	0.257127	+	0.966378i	$0.417224\pi$
$20$		0			0
$21$		−	3.44214i		−	0.751136i
$22$		0			0
$23$	2.52585	−	4.37490i	0.526677	−	0.912230i	−0.472840	−	0.881148i	$-0.656771\pi$
$23$	2.52585	−	4.37490i	0.526677	−	0.912230i	0.999517	−	0.0310823i	$-0.00989541\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−3.96574			−0.763208
$28$		0			0
$29$	−2.08770	+	3.61600i	−0.387676	+	0.671475i	−0.992137	−	0.125161i	$-0.960055\pi$
$29$	−2.08770	+	3.61600i	−0.387676	+	0.671475i	0.604460	+	0.796635i	$0.293389\pi$
$30$		0			0
$31$			8.79183i			1.57906i	0.613712	+	0.789530i	$0.289676\pi$
$31$			8.79183i			1.57906i	−0.613712	+	0.789530i	$0.710324\pi$
$32$		0			0
$33$	−9.21004	+	5.31742i	−1.60326	+	0.925644i
$34$		0			0
$35$	0.858099	+	1.48627i	0.145045	+	0.251226i
$36$		0			0
$37$	−0.942563	−	0.544189i	−0.154956	−	0.0894641i	0.420517	−	0.907285i	$-0.361849\pi$
$37$	−0.942563	−	0.544189i	−0.154956	−	0.0894641i	−0.575473	+	0.817821i	$0.695182\pi$
$38$		0			0
$39$	2.39884	+	6.82211i	0.384121	+	1.09241i
$40$		0			0
$41$	7.86992	+	4.54370i	1.22908	+	0.709607i	0.966837	−	0.255396i	$-0.0822058\pi$
$41$	7.86992	+	4.54370i	1.22908	+	0.709607i	0.262239	+	0.965003i	$0.415539\pi$
$42$		0			0
$43$	4.18560	+	7.24968i	0.638299	+	1.10557i	0.985806	+	0.167888i	$0.0536948\pi$
$43$	4.18560	+	7.24968i	0.638299	+	1.10557i	−0.347507	+	0.937677i	$0.612972\pi$
$44$		0			0
$45$	−0.885719	+	0.511370i	−0.132035	+	0.0762306i
$46$		0			0
$47$		−	2.45297i		−	0.357802i	−0.983867	−	0.178901i	$-0.942746\pi$
$47$		−	2.45297i		−	0.357802i	0.983867	−	0.178901i	$-0.0572542\pi$
$48$		0			0
$49$	−2.02733	+	3.51144i	−0.289619	+	0.501635i
$50$		0			0
$51$	−3.25459			−0.455734
$52$		0			0
$53$	−5.54358			−0.761470			−0.380735	−	0.924684i	$-0.624329\pi$
$53$	−5.54358			−0.761470			−0.380735	+	0.924684i	$0.624329\pi$
$54$		0			0
$55$	2.65119	−	4.59199i	0.357486	−	0.619183i
$56$		0			0
$57$		−	4.55505i		−	0.603331i
$58$		0			0
$59$	−8.57344	+	4.94988i	−1.11617	+	0.644419i	−0.940420	−	0.340016i	$-0.889567\pi$
$59$	−8.57344	+	4.94988i	−1.11617	+	0.644419i	−0.175747	+	0.984435i	$0.556234\pi$
$60$		0			0
$61$	0.373308	+	0.646589i	0.0477972	+	0.0827872i	0.888934	−	0.458035i	$-0.151447\pi$
$61$	0.373308	+	0.646589i	0.0477972	+	0.0827872i	−0.841137	+	0.540822i	$0.818113\pi$
$62$		0			0
$63$	1.52007	+	0.877612i	0.191511	+	0.110569i
$64$		0			0
$65$	−2.73649	−	2.34769i	−0.339419	−	0.291195i
$66$		0			0
$67$	−13.5181	−	7.80468i	−1.65150	−	0.953494i	−0.976456	−	0.215716i	$-0.930791\pi$
$67$	−13.5181	−	7.80468i	−1.65150	−	0.953494i	−0.675044	−	0.737778i	$-0.735875\pi$
$68$		0			0
$69$	5.06604	+	8.77464i	0.609880	+	1.05634i
$70$		0			0
$71$	−2.13260	+	1.23126i	−0.253093	+	0.146123i	−0.621180	−	0.783668i	$-0.713346\pi$
$71$	−2.13260	+	1.23126i	−0.253093	+	0.146123i	0.368087	+	0.929791i	$0.380013\pi$
$72$		0			0
$73$			12.7513i			1.49243i	0.665705	+	0.746215i	$0.268131\pi$
$73$			12.7513i			1.49243i	−0.665705	+	0.746215i	$0.731869\pi$
$74$		0			0
$75$	1.00284	−	1.73697i	0.115798	−	0.200568i
$76$		0			0
$77$	−9.09991			−1.03703
$78$		0			0
$79$	−0.702839			−0.0790756			−0.0395378	−	0.999218i	$-0.512589\pi$
$79$	−0.702839			−0.0790756			−0.0395378	+	0.999218i	$0.512589\pi$
$80$		0			0
$81$	5.51111	−	9.54553i	0.612346	−	1.06061i
$82$		0			0
$83$		−	3.57032i		−	0.391893i	−0.980615	−	0.195947i	$-0.937222\pi$
$83$		−	3.57032i		−	0.391893i	0.980615	−	0.195947i	$-0.0627780\pi$
$84$		0			0
$85$	1.40529	−	0.811344i	0.152425	−	0.0880026i
$86$		0			0
$87$	−4.18725	−	7.25253i	−0.448920	−	0.777553i
$88$		0			0
$89$	9.93763	+	5.73750i	1.05339	+	0.608173i	0.923596	−	0.383368i	$-0.125236\pi$
$89$	9.93763	+	5.73750i	1.05339	+	0.608173i	0.129791	+	0.991541i	$0.458569\pi$
$90$		0			0
$91$	−1.14112	+	6.08171i	−0.119622	+	0.637536i
$92$		0			0
$93$	−15.2711	−	8.81679i	−1.58354	−	0.914258i
$94$		0			0
$95$	1.13554	+	1.96681i	0.116504	+	0.201790i
$96$		0			0
$97$	12.1902	−	7.03799i	1.23772	−	0.714600i	0.269095	−	0.963114i	$-0.413275\pi$
$97$	12.1902	−	7.03799i	1.23772	−	0.714600i	0.968628	+	0.248514i	$0.0799421\pi$
$98$		0			0
$99$		−	5.42295i		−	0.545027i
$100$		0			0
$101$	−4.91897	+	8.51991i	−0.489456	+	0.847763i	−0.999926	−	0.0121325i	$-0.996138\pi$
$101$	−4.91897	+	8.51991i	−0.489456	+	0.847763i	0.510470	+	0.859895i	$0.329471\pi$
$102$		0			0
$103$	9.24998			0.911427			0.455714	−	0.890126i	$-0.349384\pi$
$103$	9.24998			0.911427			0.455714	+	0.890126i	$0.349384\pi$
$104$		0			0
$105$	−3.44214			−0.335918
$106$		0			0
$107$	−0.260938	+	0.451957i	−0.0252258	+	0.0436923i	−0.878363	−	0.477995i	$-0.841364\pi$
$107$	−0.260938	+	0.451957i	−0.0252258	+	0.0436923i	0.853137	+	0.521687i	$0.174697\pi$
$108$		0			0
$109$		−	5.45250i		−	0.522254i	−0.965304	−	0.261127i	$-0.915906\pi$
$109$		−	5.45250i		−	0.522254i	0.965304	−	0.261127i	$-0.0840942\pi$
$110$		0			0
$111$	1.89048	−	1.09147i	0.179436	−	0.103597i
$112$		0			0
$113$	6.02393	+	10.4338i	0.566684	+	0.981525i	0.996891	+	0.0787949i	$0.0251072\pi$
$113$	6.02393	+	10.4338i	0.566684	+	0.981525i	−0.430207	+	0.902730i	$0.641559\pi$
$114$		0			0
$115$	−4.37490	−	2.52585i	−0.407962	−	0.235537i
$116$		0			0
$117$	−3.62430	−	0.680035i	−0.335066	−	0.0628693i
$118$		0			0
$119$	−2.41175	−	1.39243i	−0.221085	−	0.127644i
$120$		0			0
$121$	8.55756	+	14.8221i	0.777960	+	1.34747i
$122$		0			0
$123$	−15.7845	+	9.11320i	−1.42324	+	0.821710i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	2.46780	−	4.27436i	0.218982	−	0.379288i	−0.735515	−	0.677508i	$-0.763060\pi$
$127$	2.46780	−	4.27436i	0.218982	−	0.379288i	0.954497	+	0.298220i	$0.0963930\pi$
$128$		0			0
$129$	−16.7899			−1.47827
$130$		0			0
$131$	−11.9892			−1.04750			−0.523749	−	0.851872i	$-0.675467\pi$
$131$	−11.9892			−1.04750			−0.523749	+	0.851872i	$0.675467\pi$
$132$		0			0
$133$	1.94881	−	3.37543i	0.168983	−	0.292687i
$134$		0			0
$135$			3.96574i			0.341317i
$136$		0			0
$137$	−6.49042	+	3.74724i	−0.554514	+	0.320149i	−0.750940	−	0.660370i	$-0.770400\pi$
$137$	−6.49042	+	3.74724i	−0.554514	+	0.320149i	0.196427	+	0.980518i	$0.437066\pi$
$138$		0			0
$139$	0.720969	+	1.24876i	0.0611518	+	0.105918i	0.894981	−	0.446105i	$-0.147189\pi$
$139$	0.720969	+	1.24876i	0.0611518	+	0.105918i	−0.833829	+	0.552023i	$0.813856\pi$
$140$		0			0
$141$	4.26072	+	2.45993i	0.358818	+	0.207163i
$142$		0			0
$143$	18.0355	−	6.34175i	1.50820	−	0.530324i
$144$		0			0
$145$	3.61600	+	2.08770i	0.300293	+	0.173374i
$146$		0			0
$147$	−4.06618	−	7.04282i	−0.335373	−	0.580882i
$148$		0			0
$149$	2.05708	−	1.18765i	0.168522	−	0.0972964i	−0.413367	−	0.910565i	$-0.635647\pi$
$149$	2.05708	−	1.18765i	0.168522	−	0.0972964i	0.581889	+	0.813268i	$0.302314\pi$
$150$		0			0
$151$		−	22.4022i		−	1.82307i	−0.411226	−	0.911533i	$-0.634899\pi$
$151$		−	22.4022i		−	1.82307i	0.411226	−	0.911533i	$-0.365101\pi$
$152$		0			0
$153$	0.829794	−	1.43725i	0.0670849	−	0.116194i
$154$		0			0
$155$	8.79183			0.706177
$156$		0			0
$157$	4.85797			0.387708			0.193854	−	0.981030i	$-0.437901\pi$
$157$	4.85797			0.387708			0.193854	+	0.981030i	$0.437901\pi$
$158$		0			0
$159$	5.55932	−	9.62902i	0.440883	−	0.763631i
$160$		0			0
$161$			8.66972i			0.683270i
$162$		0			0
$163$	18.7808	−	10.8431i	1.47103	−	0.849299i	0.471558	−	0.881835i	$-0.343692\pi$
$163$	18.7808	−	10.8431i	1.47103	−	0.849299i	0.999471	+	0.0325366i	$0.0103585\pi$
$164$		0			0
$165$	5.31742	+	9.21004i	0.413961	+	0.717001i
$166$		0			0
$167$	6.73636	+	3.88924i	0.521275	+	0.300958i	0.737456	−	0.675395i	$-0.236027\pi$
$167$	6.73636	+	3.88924i	0.521275	+	0.300958i	−0.216181	+	0.976353i	$0.569360\pi$
$168$		0			0
$169$	−1.97672	−	12.8488i	−0.152055	−	0.988372i
$170$		0			0
$171$	2.01154	+	1.16136i	0.153826	+	0.0888115i
$172$		0			0
$173$	4.56690	+	7.91010i	0.347215	+	0.601394i	0.985754	−	0.168196i	$-0.0537942\pi$
$173$	4.56690	+	7.91010i	0.347215	+	0.601394i	−0.638539	+	0.769590i	$0.720461\pi$
$174$		0			0
$175$	1.48627	−	0.858099i	0.112351	−	0.0648662i
$176$		0			0
$177$		−	19.8557i		−	1.49245i
$178$		0			0
$179$	6.19014	−	10.7216i	0.462673	−	0.801373i	−0.536420	−	0.843951i	$-0.680224\pi$
$179$	6.19014	−	10.7216i	0.462673	−	0.801373i	0.999093	+	0.0425782i	$0.0135572\pi$
$180$		0			0
$181$	25.9739			1.93062			0.965311	−	0.261101i	$-0.0840857\pi$
$181$	25.9739			1.93062			0.965311	+	0.261101i	$0.0840857\pi$
$182$		0			0
$183$	−1.49747			−0.110696
$184$		0			0
$185$	−0.544189	+	0.942563i	−0.0400096	+	0.0692986i
$186$		0			0
$187$			8.60409i			0.629194i
$188$		0			0
$189$	5.89417	−	3.40300i	0.428738	−	0.247532i
$190$		0			0
$191$	4.32834	+	7.49691i	0.313188	+	0.542457i	0.979051	−	0.203617i	$-0.0652697\pi$
$191$	4.32834	+	7.49691i	0.313188	+	0.542457i	−0.665863	+	0.746074i	$0.731936\pi$
$192$		0			0
$193$	−10.7967	−	6.23348i	−0.777164	−	0.448696i	0.0582602	−	0.998301i	$-0.481445\pi$
$193$	−10.7967	−	6.23348i	−0.777164	−	0.448696i	−0.835424	+	0.549606i	$0.814778\pi$
$194$		0			0
$195$	6.82211	−	2.39884i	0.488542	−	0.171784i
$196$		0			0
$197$	−18.7568	−	10.8292i	−1.33637	−	0.771551i	−0.350099	−	0.936713i	$-0.613852\pi$
$197$	−18.7568	−	10.8292i	−1.33637	−	0.771551i	−0.986267	+	0.165162i	$0.947185\pi$
$198$		0			0
$199$	10.1999	+	17.6668i	0.723052	+	1.25236i	0.959771	+	0.280785i	$0.0905947\pi$
$199$	10.1999	+	17.6668i	0.723052	+	1.25236i	−0.236719	+	0.971578i	$0.576072\pi$
$200$		0			0
$201$	27.1130	−	15.6537i	1.91240	−	1.10413i
$202$		0			0
$203$		−	7.16581i		−	0.502941i
$204$		0			0
$205$	4.54370	−	7.86992i	0.317346	−	0.549659i
$206$		0			0
$207$	−5.16658			−0.359102
$208$		0			0
$209$	−12.0421			−0.832969
$210$		0			0
$211$	1.40805	−	2.43882i	0.0969345	−	0.167895i	−0.813480	−	0.581593i	$-0.802430\pi$
$211$	1.40805	−	2.43882i	0.0969345	−	0.167895i	0.910414	+	0.413698i	$0.135763\pi$
$212$		0			0
$213$		−	4.93901i		−	0.338415i
$214$		0			0
$215$	7.24968	−	4.18560i	0.494424	−	0.285456i
$216$		0			0
$217$	−7.54426	−	13.0670i	−0.512138	−	0.887049i
$218$		0			0
$219$	−22.1486	−	12.7875i	−1.49667	−	0.864101i
$220$		0			0
$221$	5.75034	+	1.07895i	0.386810	+	0.0725780i
$222$		0			0
$223$	−1.26128	−	0.728200i	−0.0844615	−	0.0487639i	0.457174	−	0.889377i	$-0.348862\pi$
$223$	−1.26128	−	0.728200i	−0.0844615	−	0.0487639i	−0.541636	+	0.840613i	$0.682195\pi$
$224$		0			0
$225$	0.511370	+	0.885719i	0.0340914	+	0.0590480i
$226$		0			0
$227$	−2.55700	+	1.47629i	−0.169714	+	0.0979845i	−0.582451	−	0.812866i	$-0.697906\pi$
$227$	−2.55700	+	1.47629i	−0.169714	+	0.0979845i	0.412737	+	0.910850i	$0.364573\pi$
$228$		0			0
$229$		−	11.4087i		−	0.753906i	−0.926232	−	0.376953i	$-0.876972\pi$
$229$		−	11.4087i		−	0.753906i	0.926232	−	0.376953i	$-0.123028\pi$
$230$		0			0
$231$	9.12574	−	15.8063i	0.600430	−	1.03998i
$232$		0			0
$233$	−20.9789			−1.37438			−0.687188	−	0.726480i	$-0.741155\pi$
$233$	−20.9789			−1.37438			−0.687188	+	0.726480i	$0.741155\pi$
$234$		0			0
$235$	−2.45297			−0.160014
$236$		0			0
$237$	0.704834	−	1.22081i	0.0457839	−	0.0793001i
$238$		0			0
$239$			18.5331i			1.19881i	0.800447	+	0.599403i	$0.204595\pi$
$239$			18.5331i			1.19881i	−0.800447	+	0.599403i	$0.795405\pi$
$240$		0			0
$241$	15.0668	−	8.69885i	0.970541	−	0.560342i	0.0711396	−	0.997466i	$-0.477336\pi$
$241$	15.0668	−	8.69885i	0.970541	−	0.560342i	0.899401	+	0.437124i	$0.144003\pi$
$242$		0			0
$243$	5.10489	+	8.84194i	0.327479	+	0.567211i
$244$		0			0
$245$	3.51144	+	2.02733i	0.224338	+	0.129522i
$246$		0			0
$247$	−1.51007	+	8.04804i	−0.0960836	+	0.512085i
$248$		0			0
$249$	6.20153	+	3.58045i	0.393006	+	0.226902i
$250$		0			0
$251$	−2.59642	−	4.49713i	−0.163885	−	0.283857i	0.772374	−	0.635168i	$-0.219069\pi$
$251$	−2.59642	−	4.49713i	−0.163885	−	0.283857i	−0.936259	+	0.351311i	$0.885736\pi$
$252$		0			0
$253$	23.1974	−	13.3930i	1.45841	−	0.842011i
$254$		0			0
$255$			3.25459i			0.203810i
$256$		0			0
$257$	−8.06865	+	13.9753i	−0.503309	+	0.871756i	0.496684	+	0.867932i	$0.334551\pi$
$257$	−8.06865	+	13.9753i	−0.503309	+	0.871756i	−0.999993	+	0.00382494i	$0.998782\pi$
$258$		0			0
$259$	1.86787			0.116064
$260$		0			0
$261$	4.27035			0.264328
$262$		0			0
$263$	2.08186	−	3.60589i	0.128373	−	0.222349i	−0.794673	−	0.607037i	$-0.792358\pi$
$263$	2.08186	−	3.60589i	0.128373	−	0.222349i	0.923046	+	0.384689i	$0.125691\pi$
$264$		0			0
$265$			5.54358i			0.340540i
$266$		0			0
$267$	−19.9317	+	11.5076i	−1.21980	+	0.704251i
$268$		0			0
$269$	−14.1797	−	24.5599i	−0.864550	−	1.49744i	−0.867493	−	0.497449i	$-0.834270\pi$
$269$	−14.1797	−	24.5599i	−0.864550	−	1.49744i	0.00294289	−	0.999996i	$-0.499063\pi$
$270$		0			0
$271$	17.1277	+	9.88867i	1.04043	+	0.600694i	0.919956	−	0.392023i	$-0.128224\pi$
$271$	17.1277	+	9.88867i	1.04043	+	0.600694i	0.120476	+	0.992716i	$0.461558\pi$
$272$		0			0
$273$	−9.41936	−	8.08107i	−0.570086	−	0.489088i
$274$		0			0
$275$	−4.59199	−	2.65119i	−0.276907	−	0.159872i
$276$		0			0
$277$	13.9236	+	24.1164i	0.836589	+	1.44901i	0.892730	+	0.450592i	$0.148787\pi$
$277$	13.9236	+	24.1164i	0.836589	+	1.44901i	−0.0561409	+	0.998423i	$0.517880\pi$
$278$		0			0
$279$	7.78710	−	4.49588i	0.466201	−	0.269161i
$280$		0			0
$281$		−	23.0773i		−	1.37668i	−0.725390	−	0.688338i	$-0.758341\pi$
$281$		−	23.0773i		−	1.37668i	0.725390	−	0.688338i	$-0.241659\pi$
$282$		0			0
$283$	−10.7995	+	18.7053i	−0.641963	+	1.11191i	0.343031	+	0.939324i	$0.388546\pi$
$283$	−10.7995	+	18.7053i	−0.641963	+	1.11191i	−0.984994	+	0.172588i	$0.944787\pi$
$284$		0			0
$285$	−4.55505			−0.269818
$286$		0			0
$287$	−15.5958			−0.920590
$288$		0			0
$289$	7.18344	−	12.4421i	0.422555	−	0.731887i
$290$		0			0
$291$			28.2319i			1.65498i
$292$		0			0
$293$	11.0994	−	6.40827i	0.648437	−	0.374375i	−0.139420	−	0.990233i	$-0.544524\pi$
$293$	11.0994	−	6.40827i	0.648437	−	0.374375i	0.787857	+	0.615858i	$0.211191\pi$
$294$		0			0
$295$	4.94988	+	8.57344i	0.288193	+	0.499165i
$296$		0			0
$297$	−18.2106	−	10.5139i	−1.05669	−	0.610080i
$298$		0			0
$299$	−6.04195	−	17.1829i	−0.349415	−	0.993711i
$300$		0			0
$301$	−12.4419	−	7.18332i	−0.717138	−	0.414040i
$302$		0			0
$303$	−9.86587	−	17.0882i	−0.566780	−	0.981691i
$304$		0			0
$305$	0.646589	−	0.373308i	0.0370236	−	0.0213756i
$306$		0			0
$307$		−	6.39172i		−	0.364795i	−0.983225	−	0.182397i	$-0.941614\pi$
$307$		−	6.39172i		−	0.364795i	0.983225	−	0.182397i	$-0.0583858\pi$
$308$		0			0
$309$	−9.27623	+	16.0669i	−0.527707	+	0.914014i
$310$		0			0
$311$	20.3701			1.15508			0.577540	−	0.816362i	$-0.304013\pi$
$311$	20.3701			1.15508			0.577540	+	0.816362i	$0.304013\pi$
$312$		0			0
$313$	−1.16374			−0.0657786			−0.0328893	−	0.999459i	$-0.510471\pi$
$313$	−1.16374			−0.0657786			−0.0328893	+	0.999459i	$0.510471\pi$
$314$		0			0
$315$	0.877612	−	1.52007i	0.0494479	−	0.0856462i
$316$		0			0
$317$		−	2.24705i		−	0.126207i	−0.998007	−	0.0631033i	$-0.979900\pi$
$317$		−	2.24705i		−	0.126207i	0.998007	−	0.0631033i	$-0.0200998\pi$
$318$		0			0
$319$	−19.1734	+	11.0698i	−1.07350	+	0.619787i
$320$		0			0
$321$	−0.523356	−	0.906480i	−0.0292109	−	0.0505948i
$322$		0			0
$323$	−3.19152	−	1.84262i	−0.177581	−	0.102526i
$324$		0			0
$325$	−2.34769	+	2.73649i	−0.130226	+	0.151793i
$326$		0			0
$327$	9.47081	+	5.46797i	0.523737	+	0.302380i
$328$		0			0
$329$	2.10489	+	3.64577i	0.116046	+	0.200998i
$330$		0			0
$331$	14.2060	−	8.20183i	0.780832	−	0.450813i	−0.0558933	−	0.998437i	$-0.517801\pi$
$331$	14.2060	−	8.20183i	0.780832	−	0.450813i	0.836725	+	0.547623i	$0.184467\pi$
$332$		0			0
$333$			1.11313i			0.0609990i
$334$		0			0
$335$	−7.80468	+	13.5181i	−0.426415	+	0.738573i
$336$		0			0
$337$	0.463522			0.0252497			0.0126248	−	0.999920i	$-0.495981\pi$
$337$	0.463522			0.0252497			0.0126248	+	0.999920i	$0.495981\pi$
$338$		0			0
$339$	−24.1641			−1.31241
$340$		0			0
$341$	−23.3088	+	40.3720i	−1.26224	+	2.18627i
$342$		0			0
$343$		−	18.9720i		−	1.02439i
$344$		0			0
$345$	8.77464	−	5.06604i	0.472411	−	0.272747i
$346$		0			0
$347$	8.94212	+	15.4882i	0.480038	+	0.831451i	0.999738	−	0.0228985i	$-0.00728947\pi$
$347$	8.94212	+	15.4882i	0.480038	+	0.831451i	−0.519700	+	0.854349i	$0.673956\pi$
$348$		0			0
$349$	−11.7299	−	6.77227i	−0.627888	−	0.362511i	0.152046	−	0.988373i	$-0.451414\pi$
$349$	−11.7299	−	6.77227i	−0.627888	−	0.362511i	−0.779934	+	0.625862i	$0.784747\pi$
$350$		0			0
$351$	−9.31033	+	10.8522i	−0.496949	+	0.579248i
$352$		0			0
$353$	−30.3096	−	17.4992i	−1.61322	−	0.931390i	−0.988619	−	0.150443i	$-0.951930\pi$
$353$	−30.3096	−	17.4992i	−1.61322	−	0.931390i	−0.624597	−	0.780947i	$-0.714737\pi$
$354$		0			0
$355$	1.23126	+	2.13260i	0.0653483	+	0.113187i
$356$		0			0
$357$	4.83720	−	2.79276i	0.256012	−	0.147808i
$358$		0			0
$359$		−	32.9967i		−	1.74150i	−0.491725	−	0.870750i	$-0.663634\pi$
$359$		−	32.9967i		−	1.74150i	0.491725	−	0.870750i	$-0.336366\pi$
$360$		0			0
$361$	−6.92110	+	11.9877i	−0.364269	+	0.630932i
$362$		0			0
$363$	−34.3274			−1.80172
$364$		0			0
$365$	12.7513			0.667435
$366$		0			0
$367$	13.5804	−	23.5219i	0.708889	−	1.22783i	−0.256380	−	0.966576i	$-0.582530\pi$
$367$	13.5804	−	23.5219i	0.708889	−	1.22783i	0.965270	−	0.261256i	$-0.0841367\pi$
$368$		0			0
$369$		−	9.29406i		−	0.483829i
$370$		0			0
$371$	8.23926	−	4.75694i	0.427761	−	0.246968i
$372$		0			0
$373$	6.94659	+	12.0319i	0.359681	+	0.622986i	0.987907	−	0.155045i	$-0.0495522\pi$
$373$	6.94659	+	12.0319i	0.359681	+	0.622986i	−0.628226	+	0.778031i	$0.716219\pi$
$374$		0			0
$375$	−1.73697	−	1.00284i	−0.0896966	−	0.0517864i
$376$		0			0
$377$	4.99387	+	14.2022i	0.257197	+	0.731451i
$378$		0			0
$379$	7.37323	+	4.25694i	0.378738	+	0.218664i	0.677269	−	0.735736i	$-0.263163\pi$
$379$	7.37323	+	4.25694i	0.378738	+	0.218664i	−0.298531	+	0.954400i	$0.596497\pi$
$380$		0			0
$381$	4.94962	+	8.57298i	0.253576	+	0.439207i
$382$		0			0
$383$	−15.0492	+	8.68865i	−0.768977	+	0.443969i	−0.832510	−	0.554011i	$-0.813097\pi$
$383$	−15.0492	+	8.68865i	−0.768977	+	0.443969i	0.0635326	+	0.997980i	$0.479763\pi$
$384$		0			0
$385$			9.09991i			0.463775i
$386$		0			0
$387$	4.28079	−	7.41454i	0.217605	−	0.376902i
$388$		0			0
$389$	−0.820966			−0.0416246			−0.0208123	−	0.999783i	$-0.506625\pi$
$389$	−0.820966			−0.0416246			−0.0208123	+	0.999783i	$0.506625\pi$
$390$		0			0
$391$	8.19734			0.414557
$392$		0			0
$393$	12.0232	−	20.8248i	0.606490	−	1.05047i
$394$		0			0
$395$			0.702839i			0.0353637i
$396$		0			0
$397$	−27.9339	+	16.1276i	−1.40196	+	0.809422i	−0.994594	−	0.103842i	$-0.966886\pi$
$397$	−27.9339	+	16.1276i	−1.40196	+	0.809422i	−0.407367	+	0.913265i	$0.633553\pi$
$398$		0			0
$399$	3.90868	+	6.77003i	0.195679	+	0.338926i
$400$		0			0
$401$	−31.9989	−	18.4746i	−1.59795	−	0.922577i	−0.991882	−	0.127165i	$-0.959412\pi$
$401$	−31.9989	−	18.4746i	−1.59795	−	0.922577i	−0.606069	−	0.795412i	$-0.707254\pi$
$402$		0			0
$403$	24.0587	+	20.6405i	1.19845	+	1.02818i
$404$		0			0
$405$	−9.54553	−	5.51111i	−0.474321	−	0.273849i
$406$		0			0
$407$	−2.88549	−	4.99782i	−0.143028	−	0.247733i
$408$		0			0
$409$	1.04612	−	0.603980i	0.0517275	−	0.0298649i	−0.473913	−	0.880572i	$-0.657159\pi$
$409$	1.04612	−	0.603980i	0.0517275	−	0.0298649i	0.525641	+	0.850707i	$0.323826\pi$
$410$		0			0
$411$		−	15.0315i		−	0.741450i
$412$		0			0
$413$	8.49497	−	14.7137i	0.418010	−	0.724015i
$414$		0			0
$415$	−3.57032			−0.175260
$416$		0			0
$417$	−2.89206			−0.141625
$418$		0			0
$419$	16.9479	−	29.3547i	0.827960	−	1.43407i	−0.0716752	−	0.997428i	$-0.522835\pi$
$419$	16.9479	−	29.3547i	0.827960	−	1.43407i	0.899636	−	0.436641i	$-0.143832\pi$
$420$		0			0
$421$			9.03483i			0.440330i	0.975463	+	0.220165i	$0.0706597\pi$
$421$			9.03483i			0.440330i	−0.975463	+	0.220165i	$0.929340\pi$
$422$		0			0
$423$	−2.17264	+	1.25437i	−0.105637	+	0.0609898i
$424$		0			0
$425$	−0.811344	−	1.40529i	−0.0393560	−	0.0681665i
$426$		0			0
$427$	−1.10967	−	0.640671i	−0.0537009	−	0.0310042i
$428$		0			0
$429$	−7.07126	+	37.6868i	−0.341404	+	1.81954i
$430$		0			0
$431$	2.41688	+	1.39539i	0.116417	+	0.0672135i	0.557078	−	0.830460i	$-0.311922\pi$
$431$	2.41688	+	1.39539i	0.116417	+	0.0672135i	−0.440661	+	0.897674i	$0.645256\pi$
$432$		0			0
$433$	7.74573	+	13.4160i	0.372236	+	0.644731i	0.989909	−	0.141703i	$-0.0452579\pi$
$433$	7.74573	+	13.4160i	0.372236	+	0.644731i	−0.617673	+	0.786435i	$0.711925\pi$
$434$		0			0
$435$	−7.25253	+	4.18725i	−0.347732	+	0.200763i
$436$		0			0
$437$			11.4728i			0.548819i
$438$		0			0
$439$	−2.88191	+	4.99161i	−0.137546	+	0.238236i	−0.926567	−	0.376129i	$-0.877255\pi$
$439$	−2.88191	+	4.99161i	−0.137546	+	0.238236i	0.789021	+	0.614366i	$0.210588\pi$
$440$		0			0
$441$	4.14687			0.197470
$442$		0			0
$443$	8.98705			0.426987			0.213494	−	0.976944i	$-0.431516\pi$
$443$	8.98705			0.426987			0.213494	+	0.976944i	$0.431516\pi$
$444$		0			0
$445$	5.73750	−	9.93763i	0.271983	−	0.471089i
$446$		0			0
$447$			4.76410i			0.225334i
$448$		0			0
$449$	23.9604	−	13.8336i	1.13076	−	0.652846i	0.186635	−	0.982429i	$-0.440242\pi$
$449$	23.9604	−	13.8336i	1.13076	−	0.652846i	0.944126	+	0.329584i	$0.106908\pi$
$450$		0			0
$451$	24.0924	+	41.7292i	1.13447	+	1.96495i
$452$		0			0
$453$	38.9119	+	22.4658i	1.82824	+	1.05554i
$454$		0			0
$455$	6.08171	+	1.14112i	0.285115	+	0.0534967i
$456$		0			0
$457$	33.8839	+	19.5629i	1.58502	+	0.915112i	0.994110	+	0.108374i	$0.0345645\pi$
$457$	33.8839	+	19.5629i	1.58502	+	0.915112i	0.590910	+	0.806737i	$0.298769\pi$
$458$		0			0
$459$	−3.21758	−	5.57302i	−0.150184	−	0.260126i
$460$		0			0
$461$	−2.48917	+	1.43712i	−0.115932	+	0.0669334i	−0.556845	−	0.830617i	$-0.687988\pi$
$461$	−2.48917	+	1.43712i	−0.115932	+	0.0669334i	0.440913	+	0.897550i	$0.354655\pi$
$462$		0			0
$463$		−	21.5250i		−	1.00035i	−0.865924	−	0.500176i	$-0.833269\pi$
$463$		−	21.5250i		−	1.00035i	0.865924	−	0.500176i	$-0.166731\pi$
$464$		0			0
$465$	−8.81679	+	15.2711i	−0.408869	+	0.708181i
$466$		0			0
$467$	−27.3600			−1.26607			−0.633035	−	0.774123i	$-0.718191\pi$
$467$	−27.3600			−1.26607			−0.633035	+	0.774123i	$0.718191\pi$
$468$		0			0
$469$	26.7888			1.23699
$470$		0			0
$471$	−4.87176	+	8.43813i	−0.224479	+	0.388809i
$472$		0			0
$473$			44.3872i			2.04093i
$474$		0			0
$475$	1.96681	−	1.13554i	0.0902435	−	0.0521021i
$476$		0			0
$477$	2.83482	+	4.91006i	0.129798	+	0.224816i
$478$		0			0
$479$	25.4251	+	14.6792i	1.16170	+	0.670708i	0.951711	−	0.306995i	$-0.0993236\pi$
$479$	25.4251	+	14.6792i	1.16170	+	0.670708i	0.209990	+	0.977704i	$0.432657\pi$
$480$		0			0
$481$	−3.70201	+	1.30172i	−0.168797	+	0.0593535i
$482$		0			0
$483$	−15.0590	−	8.69433i	−0.685209	−	0.395606i
$484$		0			0
$485$	−7.03799	−	12.1902i	−0.319579	−	0.553527i
$486$		0			0
$487$	5.39501	−	3.11481i	0.244471	−	0.141146i	−0.372759	−	0.927928i	$-0.621588\pi$
$487$	5.39501	−	3.11481i	0.244471	−	0.141146i	0.617230	+	0.786783i	$0.288255\pi$
$488$		0			0
$489$			43.4956i			1.96694i
$490$		0			0
$491$	−7.30361	+	12.6502i	−0.329607	+	0.570897i	−0.982434	−	0.186611i	$-0.940250\pi$
$491$	−7.30361	+	12.6502i	−0.329607	+	0.570897i	0.652827	+	0.757507i	$0.273583\pi$
$492$		0			0
$493$	−6.77537			−0.305147
$494$		0			0
$495$	−5.42295			−0.243743
$496$		0			0
$497$	2.11308	−	3.65996i	0.0947846	−	0.164172i
$498$		0			0
$499$		−	0.958620i		−	0.0429137i	−0.999770	−	0.0214569i	$-0.993170\pi$
$499$		−	0.958620i		−	0.0429137i	0.999770	−	0.0214569i	$-0.00683046\pi$
$500$		0			0
$501$	−13.5110	+	7.80055i	−0.603625	+	0.348503i
$502$		0			0
$503$	−10.8418	−	18.7786i	−0.483413	−	0.837295i	0.516406	−	0.856344i	$-0.327270\pi$
$503$	−10.8418	−	18.7786i	−0.483413	−	0.837295i	−0.999819	+	0.0190488i	$0.993936\pi$
$504$		0			0
$505$	8.51991	+	4.91897i	0.379131	+	0.218891i
$506$		0			0
$507$	24.3003	+	9.45181i	1.07922	+	0.419770i
$508$		0			0
$509$	−24.6912	−	14.2554i	−1.09442	−	0.631862i	−0.159668	−	0.987171i	$-0.551042\pi$
$509$	−24.6912	−	14.2554i	−1.09442	−	0.631862i	−0.934749	+	0.355309i	$0.884376\pi$
$510$		0			0
$511$	−10.9419	−	18.9519i	−0.484041	−	0.838384i
$512$		0			0
$513$	7.79987	−	4.50325i	0.344373	−	0.198824i
$514$		0			0
$515$		−	9.24998i		−	0.407603i
$516$		0			0
$517$	6.50327	−	11.2640i	0.286013	−	0.495390i
$518$		0			0
$519$	−18.3194			−0.804134
$520$		0			0
$521$	7.39789			0.324107			0.162054	−	0.986782i	$-0.448188\pi$
$521$	7.39789			0.324107			0.162054	+	0.986782i	$0.448188\pi$
$522$		0			0
$523$	5.27191	−	9.13121i	0.230524	−	0.399280i	−0.727438	−	0.686173i	$-0.759289\pi$
$523$	5.27191	−	9.13121i	0.230524	−	0.399280i	0.957963	+	0.286893i	$0.0926225\pi$
$524$		0			0
$525$			3.44214i			0.150227i
$526$		0			0
$527$	−12.3551	+	7.13320i	−0.538195	+	0.310727i
$528$		0			0
$529$	−1.25985	−	2.18213i	−0.0547763	−	0.0948753i
$530$		0			0
$531$	8.76841	+	5.06244i	0.380516	+	0.219691i
$532$		0			0
$533$	30.9099	−	10.8687i	1.33886	−	0.470777i
$534$		0			0
$535$	0.451957	+	0.260938i	0.0195398	+	0.0112813i
$536$		0			0
$537$	12.4154	+	21.5041i	0.535765	+	0.927972i
$538$		0			0
$539$	−18.6190	+	10.7497i	−0.801976	+	0.463021i
$540$		0			0
$541$		−	37.8467i		−	1.62715i	−0.581457	−	0.813577i	$-0.697517\pi$
$541$		−	37.8467i		−	1.62715i	0.581457	−	0.813577i	$-0.302483\pi$
$542$		0			0
$543$	−26.0476	+	45.1158i	−1.11781	+	1.93610i
$544$		0			0
$545$	−5.45250			−0.233559
$546$		0			0
$547$	−7.38183			−0.315624			−0.157812	−	0.987469i	$-0.550444\pi$
$547$	−7.38183			−0.315624			−0.157812	+	0.987469i	$0.550444\pi$
$548$		0			0
$549$	0.381798	−	0.661293i	0.0162947	−	0.0282233i
$550$		0			0
$551$		−	9.48265i		−	0.403975i
$552$		0			0
$553$	1.04461	−	0.603105i	0.0444213	−	0.0256467i
$554$		0			0
$555$	−1.09147	−	1.89048i	−0.0463302	−	0.0802462i
$556$		0			0
$557$	16.3597	+	9.44530i	0.693185	+	0.400210i	0.804804	−	0.593541i	$-0.202270\pi$
$557$	16.3597	+	9.44530i	0.693185	+	0.400210i	−0.111619	+	0.993751i	$0.535604\pi$
$558$		0			0
$559$	29.6651	+	5.56614i	1.25470	+	0.235423i
$560$		0			0
$561$	−14.9450	−	8.62852i	−0.630980	−	0.364296i
$562$		0			0
$563$	0.984449	+	1.70512i	0.0414896	+	0.0718620i	0.886024	−	0.463638i	$-0.153456\pi$
$563$	0.984449	+	1.70512i	0.0414896	+	0.0718620i	−0.844535	+	0.535500i	$0.820123\pi$
$564$		0			0
$565$	10.4338	−	6.02393i	0.438951	−	0.253429i
$566$		0			0
$567$			18.9163i			0.794410i
$568$		0			0
$569$	6.74724	−	11.6866i	0.282859	−	0.489926i	−0.689229	−	0.724544i	$-0.742050\pi$
$569$	6.74724	−	11.6866i	0.282859	−	0.489926i	0.972088	+	0.234618i	$0.0753838\pi$
$570$		0			0
$571$	−11.8340			−0.495236			−0.247618	−	0.968858i	$-0.579648\pi$
$571$	−11.8340			−0.495236			−0.247618	+	0.968858i	$0.579648\pi$
$572$		0			0
$573$	−17.3625			−0.725330
$574$		0			0
$575$	−2.52585	+	4.37490i	−0.105335	+	0.182446i
$576$		0			0
$577$			5.86318i			0.244087i	0.992525	+	0.122044i	$0.0389448\pi$
$577$			5.86318i			0.244087i	−0.992525	+	0.122044i	$0.961055\pi$
$578$		0			0
$579$	21.6547	−	12.5024i	0.899939	−	0.519580i
$580$		0			0
$581$	3.06369	+	5.30646i	0.127103	+	0.220149i
$582$		0			0
$583$	−25.4561	−	14.6971i	−1.05428	−	0.608690i
$584$		0			0
$585$	−0.680035	+	3.62430i	−0.0281160	+	0.149846i
$586$		0			0
$587$	34.3418	+	19.8273i	1.41744	+	0.818359i	0.996073	−	0.0885314i	$-0.0282173\pi$
$587$	34.3418	+	19.8273i	1.41744	+	0.818359i	0.421366	+	0.906891i	$0.361551\pi$
$588$		0			0
$589$	−9.98346	−	17.2919i	−0.411361	−	0.712499i
$590$		0			0
$591$	37.6201	−	21.7199i	1.54748	−	0.893439i
$592$		0			0
$593$			9.39484i			0.385800i	0.981218	+	0.192900i	$0.0617893\pi$
$593$			9.39484i			0.385800i	−0.981218	+	0.192900i	$0.938211\pi$
$594$		0			0
$595$	−1.39243	+	2.41175i	−0.0570839	+	0.0988722i
$596$		0			0
$597$	−40.9154			−1.67456
$598$		0			0
$599$	−40.7504			−1.66502			−0.832508	−	0.554013i	$-0.813096\pi$
$599$	−40.7504			−1.66502			−0.832508	+	0.554013i	$0.813096\pi$
$600$		0			0
$601$	−11.9231	+	20.6514i	−0.486353	+	0.842388i	−0.999877	−	0.0156872i	$-0.995006\pi$
$601$	−11.9231	+	20.6514i	−0.486353	+	0.842388i	0.513524	+	0.858075i	$0.328340\pi$
$602$		0			0
$603$			15.9643i			0.650118i
$604$		0			0
$605$	14.8221	−	8.55756i	0.602606	−	0.347914i
$606$		0			0
$607$	−21.5955	−	37.4045i	−0.876535	−	1.51820i	−0.855118	−	0.518433i	$-0.826516\pi$
$607$	−21.5955	−	37.4045i	−0.876535	−	1.51820i	−0.0214172	−	0.999771i	$-0.506818\pi$
$608$		0			0
$609$	12.4468	+	7.18615i	0.504369	+	0.291197i
$610$		0			0
$611$	−6.71251	−	5.75880i	−0.271559	−	0.232976i
$612$		0			0
$613$	−18.1727	−	10.4920i	−0.733990	−	0.423769i	0.0858899	−	0.996305i	$-0.472627\pi$
$613$	−18.1727	−	10.4920i	−0.733990	−	0.423769i	−0.819880	+	0.572535i	$0.805960\pi$
$614$		0			0
$615$	9.11320	+	15.7845i	0.367480	+	0.636494i
$616$		0			0
$617$	−36.5250	+	21.0877i	−1.47044	+	0.848960i	−0.999449	−	0.0331780i	$-0.989437\pi$
$617$	−36.5250	+	21.0877i	−1.47044	+	0.848960i	−0.470992	+	0.882138i	$0.656104\pi$
$618$		0			0
$619$		−	0.238595i		−	0.00958994i	−0.999989	−	0.00479497i	$-0.998474\pi$
$619$		−	0.238595i		−	0.00958994i	0.999989	−	0.00479497i	$-0.00152629\pi$
$620$		0			0
$621$	−10.0169	+	17.3497i	−0.401964	+	0.696221i
$622$		0			0
$623$	−19.6933			−0.788997
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	12.0763	−	20.9167i	0.482280	−	0.835333i
$628$		0			0
$629$		−	1.76610i		−	0.0704189i
$630$		0			0
$631$	−6.56681	+	3.79135i	−0.261420	+	0.150931i	−0.624982	−	0.780639i	$-0.714894\pi$
$631$	−6.56681	+	3.79135i	−0.261420	+	0.150931i	0.363562	+	0.931570i	$0.381561\pi$
$632$		0			0
$633$	2.82410	+	4.89149i	0.112248	+	0.194419i
$634$		0			0
$635$	−4.27436	−	2.46780i	−0.169623	−	0.0979318i
$636$		0			0
$637$	4.84947	+	13.7915i	0.192143	+	0.546441i
$638$		0			0
$639$	2.18110	+	1.25926i	0.0862828	+	0.0498154i
$640$		0			0
$641$	18.0317	+	31.2318i	0.712210	+	1.23358i	0.964026	+	0.265808i	$0.0856388\pi$
$641$	18.0317	+	31.2318i	0.712210	+	1.23358i	−0.251816	+	0.967775i	$0.581028\pi$
$642$		0			0
$643$	−10.7462	+	6.20431i	−0.423788	+	0.244674i	−0.696697	−	0.717366i	$-0.745348\pi$
$643$	−10.7462	+	6.20431i	−0.423788	+	0.244674i	0.272909	+	0.962040i	$0.412014\pi$
$644$		0			0
$645$			16.7899i			0.661103i
$646$		0			0
$647$	−3.66854	+	6.35409i	−0.144225	+	0.249805i	−0.929084	−	0.369870i	$-0.879402\pi$
$647$	−3.66854	+	6.35409i	−0.144225	+	0.249805i	0.784858	+	0.619675i	$0.212736\pi$
$648$		0			0
$649$	−52.4922			−2.06050
$650$		0			0
$651$	30.2627			1.18609
$652$		0			0
$653$	−6.04754	+	10.4746i	−0.236659	+	0.409905i	−0.959753	−	0.280844i	$-0.909386\pi$
$653$	−6.04754	+	10.4746i	−0.236659	+	0.409905i	0.723095	+	0.690749i	$0.242719\pi$
$654$		0			0
$655$			11.9892i			0.468456i
$656$		0			0
$657$	11.2941	−	6.52065i	0.440625	−	0.254395i
$658$		0			0
$659$	−10.9871	−	19.0302i	−0.427997	−	0.741313i	0.568698	−	0.822547i	$-0.307447\pi$
$659$	−10.9871	−	19.0302i	−0.427997	−	0.741313i	−0.996695	+	0.0812334i	$0.974114\pi$
$660$		0			0
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634817i	−0.163436	−	0.986554i	$-0.552258\pi$
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634817i	−0.936099	+	0.351737i	$0.885591\pi$
$662$		0			0
$663$	−7.64076	+	8.90614i	−0.296743	+	0.345886i
$664$		0			0
$665$	−3.37543	−	1.94881i	−0.130894	−	0.0755715i
$666$		0			0
$667$	10.5464	+	18.2670i	0.408360	+	0.707300i
$668$		0			0
$669$	2.52972	−	1.46053i	0.0978046	−	0.0564675i
$670$		0			0
$671$			3.95884i			0.152829i
$672$		0			0
$673$	22.2921	−	38.6111i	0.859299	−	1.48835i	−0.0133002	−	0.999912i	$-0.504234\pi$
$673$	22.2921	−	38.6111i	0.859299	−	1.48835i	0.872599	−	0.488437i	$-0.162433\pi$
$674$		0			0
$675$	3.96574			0.152642
$676$		0			0
$677$	21.1348			0.812275			0.406138	−	0.913812i	$-0.366875\pi$
$677$	21.1348			0.812275			0.406138	+	0.913812i	$0.366875\pi$
$678$		0			0
$679$	−12.0786	+	20.9207i	−0.463533	+	0.802864i
$680$		0			0
$681$		−	5.92190i		−	0.226928i
$682$		0			0
$683$	8.54278	−	4.93218i	0.326881	−	0.188725i	−0.327575	−	0.944825i	$-0.606231\pi$
$683$	8.54278	−	4.93218i	0.326881	−	0.188725i	0.654455	+	0.756101i	$0.272898\pi$
$684$		0			0
$685$	3.74724	+	6.49042i	0.143175	+	0.247986i
$686$		0			0
$687$	19.8165	+	11.4410i	0.756046	+	0.436503i
$688$		0			0
$689$	−13.0146	+	15.1699i	−0.495817	+	0.577929i
$690$		0			0
$691$	0.654092	+	0.377640i	0.0248828	+	0.0143661i	0.512390	−	0.858753i	$-0.328760\pi$
$691$	0.654092	+	0.377640i	0.0248828	+	0.0143661i	−0.487507	+	0.873119i	$0.662094\pi$
$692$		0			0
$693$	4.65343	+	8.05997i	0.176769	+	0.306173i
$694$		0			0
$695$	1.24876	−	0.720969i	0.0473680	−	0.0273479i
$696$		0			0
$697$			14.7460i			0.558545i
$698$		0			0
$699$	21.0385	−	36.4397i	0.795749	−	1.37828i
$700$		0			0
$701$	−29.9381			−1.13075			−0.565373	−	0.824835i	$-0.691268\pi$
$701$	−29.9381			−1.13075			−0.565373	+	0.824835i	$0.691268\pi$
$702$		0			0
$703$	2.47179			0.0932253
$704$		0			0
$705$	2.45993	−	4.26072i	0.0926463	−	0.160468i
$706$		0			0
$707$		−	16.8839i		−	0.634983i
$708$		0			0
$709$	6.46114	−	3.73034i	0.242653	−	0.140096i	−0.373742	−	0.927533i	$-0.621926\pi$
$709$	6.46114	−	3.73034i	0.242653	−	0.140096i	0.616395	+	0.787437i	$0.288592\pi$
$710$		0			0
$711$	0.359411	+	0.622518i	0.0134790	+	0.0233463i
$712$		0			0
$713$	38.4634	+	22.2069i	1.44047	+	0.831654i
$714$		0			0
$715$	−6.34175	−	18.0355i	−0.237168	−	0.674489i
$716$		0			0
$717$	−32.1914	−	18.5857i	−1.20221	−	0.694095i
$718$		0			0
$719$	22.7263	+	39.3631i	0.847547	+	1.46799i	0.883391	+	0.468637i	$0.155255\pi$
$719$	22.7263	+	39.3631i	0.847547	+	1.46799i	−0.0358435	+	0.999357i	$0.511412\pi$
$720$		0			0
$721$	−13.7480	+	7.93739i	−0.512001	+	0.295604i
$722$		0			0
$723$			34.8942i			1.29773i
$724$		0			0
$725$	2.08770	−	3.61600i	0.0775352	−	0.134295i
$726$		0			0
$727$	−16.8996			−0.626770			−0.313385	−	0.949626i	$-0.601463\pi$
$727$	−16.8996			−0.626770			−0.313385	+	0.949626i	$0.601463\pi$
$728$		0			0
$729$	12.5891			0.466264
$730$		0			0
$731$	−6.79193	+	11.7640i	−0.251209	+	0.435106i
$732$		0			0
$733$		−	15.8306i		−	0.584716i	−0.956309	−	0.292358i	$-0.905560\pi$
$733$		−	15.8306i		−	0.584716i	0.956309	−	0.292358i	$-0.0944399\pi$
$734$		0			0
$735$	−7.04282	+	4.06618i	−0.259778	+	0.149983i
$736$		0			0
$737$	−41.3833	−	71.6780i	−1.52437	−	2.64029i
$738$		0			0
$739$	25.9335	+	14.9727i	0.953980	+	0.550781i	0.894315	−	0.447438i	$-0.147663\pi$
$739$	25.9335	+	14.9727i	0.953980	+	0.550781i	0.0596653	+	0.998218i	$0.480997\pi$
$740$		0			0
$741$	−12.4648	−	10.6938i	−0.457907	−	0.392848i
$742$		0			0
$743$	22.3811	+	12.9217i	0.821083	+	0.474052i	0.850790	−	0.525506i	$-0.176124\pi$
$743$	22.3811	+	12.9217i	0.821083	+	0.474052i	−0.0297071	+	0.999559i	$0.509457\pi$
$744$		0			0
$745$	−1.18765	−	2.05708i	−0.0435123	−	0.0753655i
$746$		0			0
$747$	−3.16230	+	1.82576i	−0.115703	+	0.0668009i
$748$		0			0
$749$		−	0.895641i		−	0.0327260i
$750$		0			0
$751$	8.27217	−	14.3278i	0.301856	−	0.522830i	−0.674701	−	0.738092i	$-0.735727\pi$
$751$	8.27217	−	14.3278i	0.301856	−	0.522830i	0.976556	+	0.215262i	$0.0690605\pi$
$752$		0			0
$753$	10.4152			0.379550
$754$		0			0
$755$	−22.4022			−0.815300
$756$		0			0
$757$	8.82115	−	15.2787i	0.320610	−	0.555313i	−0.660004	−	0.751262i	$-0.729445\pi$
$757$	8.82115	−	15.2787i	0.320610	−	0.555313i	0.980614	+	0.195949i	$0.0627787\pi$
$758$		0			0
$759$			53.7241i			1.95006i
$760$		0			0
$761$	28.8019	−	16.6288i	1.04407	−	0.602794i	0.123086	−	0.992396i	$-0.460721\pi$
$761$	28.8019	−	16.6288i	1.04407	−	0.602794i	0.920983	+	0.389602i	$0.127387\pi$
$762$		0			0
$763$	4.67878	+	8.10388i	0.169383	+	0.293380i
$764$		0			0
$765$	−1.43725	−	0.829794i	−0.0519637	−	0.0300013i
$766$		0			0
$767$	−6.58249	+	35.0819i	−0.237680	+	1.26673i
$768$		0			0
$769$	34.7652	+	20.0717i	1.25367	+	0.723804i	0.971836	−	0.235660i	$-0.0757252\pi$
$769$	34.7652	+	20.0717i	1.25367	+	0.723804i	0.281830	+	0.959464i	$0.409059\pi$
$770$		0			0
$771$	−16.1831	−	28.0300i	−0.582821	−	1.00948i
$772$		0			0
$773$	13.7243	−	7.92372i	0.493628	−	0.284996i	−0.232450	−	0.972608i	$-0.574674\pi$
$773$	13.7243	−	7.92372i	0.493628	−	0.284996i	0.726078	+	0.687612i	$0.241341\pi$
$774$		0			0
$775$		−	8.79183i		−	0.315812i
$776$		0			0
$777$	−1.87317	+	3.24443i	−0.0671997	+	0.116393i
$778$		0			0
$779$	−20.6382			−0.739440
$780$		0			0
$781$	−13.0572			−0.467222
$782$		0			0
$783$	8.27928	−	14.3401i	0.295877	−	0.512475i
$784$		0			0
$785$		−	4.85797i		−	0.173388i
$786$		0			0
$787$	1.79404	−	1.03579i	0.0639508	−	0.0369220i	−0.467684	−	0.883896i	$-0.654911\pi$
$787$	1.79404	−	1.03579i	0.0639508	−	0.0369220i	0.531634	+	0.846974i	$0.321578\pi$
$788$		0			0
$789$	4.17554	+	7.23225i	0.148653	+	0.257475i
$790$		0			0
$791$	−17.9064	−	10.3383i	−0.636678	−	0.367586i
$792$		0			0
$793$	2.64579	+	0.496436i	0.0939549	+	0.0176290i
$794$		0			0
$795$	−9.62902	−	5.55932i	−0.341506	−	0.197169i
$796$		0			0
$797$	−22.0448	−	38.1826i	−0.780865	−	1.35250i	−0.931438	−	0.363899i	$-0.881445\pi$
$797$	−22.0448	−	38.1826i	−0.780865	−	1.35250i	0.150573	−	0.988599i	$-0.451888\pi$
$798$		0			0
$799$	3.44713	−	1.99020i	0.121951	−	0.0704082i
$800$		0			0
$801$		−	11.7359i		−	0.414669i
$802$		0			0
$803$	−33.8061	+	58.5539i	−1.19299	+	2.06632i
$804$		0			0
$805$	8.66972			0.305567
$806$		0			0
$807$	56.8797			2.00226
$808$		0			0
$809$	16.6772	−	28.8858i	0.586340	−	1.01557i	−0.408367	−	0.912818i	$-0.633902\pi$
$809$	16.6772	−	28.8858i	0.586340	−	1.01557i	0.994707	−	0.102753i	$-0.0327652\pi$
$810$		0			0
$811$		−	20.4619i		−	0.718516i	−0.933238	−	0.359258i	$-0.883030\pi$
$811$		−	20.4619i		−	0.718516i	0.933238	−	0.359258i	$-0.116970\pi$
$812$		0			0
$813$	−34.3526	+	19.8335i	−1.20480	+	0.695590i
$814$		0			0
$815$	−10.8431	−	18.7808i	−0.379818	−	0.657864i
$816$		0			0
$817$	−16.4646	−	9.50583i	−0.576023	−	0.332567i
$818$		0			0
$819$	5.97022	−	2.09929i	0.208616	−	0.0733551i
$820$		0			0
$821$	29.9808	+	17.3094i	1.04634	+	0.604104i	0.921622	−	0.388089i	$-0.126865\pi$
$821$	29.9808	+	17.3094i	1.04634	+	0.604104i	0.124716	+	0.992192i	$0.460198\pi$
$822$		0			0
$823$	−26.4524	−	45.8169i	−0.922072	−	1.59708i	−0.796204	−	0.605029i	$-0.793162\pi$
$823$	−26.4524	−	45.8169i	−0.922072	−	1.59708i	−0.125868	−	0.992047i	$-0.540172\pi$
$824$		0			0
$825$	9.21004	−	5.31742i	0.320653	−	0.185129i
$826$		0			0
$827$		−	37.3082i		−	1.29733i	−0.761073	−	0.648666i	$-0.775327\pi$
$827$		−	37.3082i		−	1.29733i	0.761073	−	0.648666i	$-0.224673\pi$
$828$		0			0
$829$	−22.3447	+	38.7022i	−0.776064	+	1.34418i	0.158131	+	0.987418i	$0.449453\pi$
$829$	−22.3447	+	38.7022i	−0.776064	+	1.34418i	−0.934195	+	0.356764i	$0.883880\pi$
$830$		0			0
$831$	−55.8526			−1.93750
$832$		0			0
$833$	−6.57946			−0.227965
$834$		0			0
$835$	3.88924	−	6.73636i	0.134593	−	0.233121i
$836$		0			0
$837$		−	34.8662i		−	1.20515i
$838$		0			0
$839$	−34.3088	+	19.8082i	−1.18447	+	0.683855i	−0.957045	−	0.289940i	$-0.906365\pi$
$839$	−34.3088	+	19.8082i	−1.18447	+	0.683855i	−0.227427	+	0.973795i	$0.573031\pi$
$840$		0			0
$841$	5.78302	+	10.0165i	0.199415	+	0.345396i
$842$		0			0
$843$	40.0845	+	23.1428i	1.38058	+	0.797080i
$844$		0			0
$845$	−12.8488	+	1.97672i	−0.442013	+	0.0680012i
$846$		0			0
$847$	−25.4377	−	14.6865i	−0.874050	−	0.504633i
$848$		0			0
$849$	−21.6603	−	37.5167i	−0.743379	−	1.28757i
$850$		0			0
$851$	−4.76155	+	2.74908i	−0.163224	+	0.0942373i
$852$		0			0
$853$		−	35.0503i		−	1.20010i	−0.799963	−	0.600049i	$-0.795148\pi$
$853$		−	35.0503i		−	1.20010i	0.799963	−	0.600049i	$-0.204852\pi$
$854$		0			0
$855$	1.16136	−	2.01154i	0.0397177	−	0.0687931i
$856$		0			0
$857$	20.9007			0.713955			0.356978	−	0.934113i	$-0.383807\pi$
$857$	20.9007			0.713955			0.356978	+	0.934113i	$0.383807\pi$
$858$		0			0
$859$	35.6838			1.21752			0.608759	−	0.793356i	$-0.291668\pi$
$859$	35.6838			1.21752			0.608759	+	0.793356i	$0.291668\pi$
$860$		0			0
$861$	15.6400	−	27.0894i	0.533011	−	0.923203i
$862$		0			0
$863$		−	7.10800i		−	0.241959i	−0.992655	−	0.120980i	$-0.961396\pi$
$863$		−	7.10800i		−	0.241959i	0.992655	−	0.120980i	$-0.0386036\pi$
$864$		0			0
$865$	7.91010	−	4.56690i	0.268951	−	0.155279i
$866$		0			0
$867$	14.4077	+	24.9548i	0.489310	+	0.847510i
$868$		0			0
$869$	−3.22743	−	1.86336i	−0.109483	−	0.0632101i
$870$		0			0
$871$	−53.0937	+	18.6692i	−1.79901	+	0.632580i
$872$		0			0
$873$	−12.4674	−	7.19804i	−0.421957	−	0.243617i
$874$		0			0
$875$	−0.858099	−	1.48627i	−0.0290090	−	0.0502451i
$876$		0			0
$877$	23.7269	−	13.6987i	0.801199	−	0.462572i	−0.0426913	−	0.999088i	$-0.513593\pi$
$877$	23.7269	−	13.6987i	0.801199	−	0.462572i	0.843890	+	0.536516i	$0.180260\pi$
$878$		0			0
$879$			25.7058i			0.867036i
$880$		0			0
$881$	−0.551145	+	0.954611i	−0.0185685	+	0.0321617i	−0.875160	−	0.483833i	$-0.839244\pi$
$881$	−0.551145	+	0.954611i	−0.0185685	+	0.0321617i	0.856592	+	0.515995i	$0.172578\pi$
$882$		0			0
$883$	45.7344			1.53909			0.769543	−	0.638595i	$-0.220484\pi$
$883$	45.7344			1.53909			0.769543	+	0.638595i	$0.220484\pi$
$884$		0			0
$885$	−19.8557			−0.667443
$886$		0			0
$887$	−14.2456	+	24.6741i	−0.478320	+	0.828475i	−0.999691	−	0.0248550i	$-0.992088\pi$
$887$	−14.2456	+	24.6741i	−0.478320	+	0.828475i	0.521371	+	0.853330i	$0.325421\pi$
$888$		0			0
$889$			8.47047i			0.284091i
$890$		0			0
$891$	50.6139	−	29.2220i	1.69563	−	0.978972i
$892$		0			0
$893$	2.78544	+	4.82452i	0.0932111	+	0.161446i
$894$		0			0
$895$	−10.7216	−	6.19014i	−0.358385	−	0.206914i
$896$		0			0
$897$	35.9052	+	6.73697i	1.19884	+	0.224941i
$898$		0			0
$899$	−31.7913	−	18.3547i	−1.06030	−	0.612164i
$900$		0			0
$901$	−4.49775	−	7.79034i	−0.149842	−	0.259534i
$902$		0			0
$903$	24.9544	−	14.4074i	0.830430	−	0.479449i
$904$		0			0
$905$		−	25.9739i		−	0.863401i
$906$		0			0
$907$	19.1062	−	33.0929i	0.634411	−	1.09883i	−0.352228	−	0.935914i	$-0.614576\pi$
$907$	19.1062	−	33.0929i	0.634411	−	1.09883i	0.986640	−	0.162918i	$-0.0520907\pi$
$908$		0			0
$909$	10.0617			0.333724
$910$		0			0
$911$	−27.1158			−0.898387			−0.449193	−	0.893435i	$-0.648289\pi$
$911$	−27.1158			−0.898387			−0.449193	+	0.893435i	$0.648289\pi$
$912$		0			0
$913$	9.46558	−	16.3949i	0.313265	−	0.542591i
$914$		0			0
$915$			1.49747i			0.0495049i
$916$		0			0
$917$	17.8192	−	10.2879i	0.588440	−	0.339736i
$918$		0			0
$919$	2.99461	+	5.18681i	0.0987830	+	0.171097i	0.911181	−	0.412006i	$-0.135172\pi$
$919$	2.99461	+	5.18681i	0.0987830	+	0.171097i	−0.812398	+	0.583103i	$0.801838\pi$
$920$		0			0
$921$	11.1022	+	6.40987i	0.365830	+	0.211212i
$922$		0			0
$923$	−1.63736	+	8.72644i	−0.0538944	+	0.287234i
$924$		0			0
$925$	0.942563	+	0.544189i	0.0309913	+	0.0178928i
$926$		0			0
$927$	−4.73016	−	8.19288i	−0.155359	−	0.269090i
$928$		0			0
$929$	−25.2421	+	14.5735i	−0.828165	+	0.478141i	−0.853224	−	0.521545i	$-0.825356\pi$
$929$	−25.2421	+	14.5735i	−0.828165	+	0.478141i	0.0250589	+	0.999686i	$0.492023\pi$
$930$		0			0
$931$		−	9.20846i		−	0.301795i
$932$		0			0
$933$	−20.4279	+	35.3821i	−0.668779	+	1.15836i
$934$		0			0
$935$	8.60409			0.281384
$936$		0			0
$937$	5.97773			0.195284			0.0976419	−	0.995222i	$-0.468870\pi$
$937$	5.97773			0.195284			0.0976419	+	0.995222i	$0.468870\pi$
$938$		0			0
$939$	1.16705	−	2.02138i	0.0380851	−	0.0659653i
$940$		0			0
$941$		−	15.2758i		−	0.497976i	−0.968507	−	0.248988i	$-0.919902\pi$
$941$		−	15.2758i		−	0.497976i	0.968507	−	0.248988i	$-0.0800980\pi$
$942$		0			0
$943$	39.7565	−	22.9534i	1.29465	−	0.747467i
$944$		0			0
$945$	−3.40300	−	5.89417i	−0.110700	−	0.191737i
$946$		0			0
$947$	23.0433	+	13.3041i	0.748807	+	0.432324i	0.825263	−	0.564749i	$-0.191027\pi$
$947$	23.0433	+	13.3041i	0.748807	+	0.432324i	−0.0764555	+	0.997073i	$0.524360\pi$
$948$		0			0
$949$	34.8938	+	29.9361i	1.13270	+	0.971768i
$950$		0			0
$951$	3.90305	+	2.25342i	0.126565	+	0.0730723i
$952$		0			0
$953$	6.61976	+	11.4658i	0.214435	+	0.371412i	0.953098	−	0.302663i	$-0.0978757\pi$
$953$	6.61976	+	11.4658i	0.214435	+	0.371412i	−0.738663	+	0.674075i	$0.764542\pi$
$954$		0			0
$955$	7.49691	−	4.32834i	0.242594	−	0.140062i
$956$		0			0
$957$		−	44.4047i		−	1.43540i
$958$		0			0
$959$	6.43101	−	11.1388i	0.207668	−	0.359692i
$960$		0			0
$961$	−46.2963			−1.49343
$962$		0			0
$963$	0.533743			0.0171996
$964$		0			0
$965$	−6.23348	+	10.7967i	−0.200663	+	0.347558i
$966$		0			0
$967$		−	33.5117i		−	1.07766i	−0.842413	−	0.538832i	$-0.818866\pi$
$967$		−	33.5117i		−	1.07766i	0.842413	−	0.538832i	$-0.181134\pi$
$968$		0			0
$969$	6.40116	−	3.69571i	0.205635	−	0.118723i
$970$		0			0
$971$	19.0618	+	33.0161i	0.611723	+	1.05954i	0.990950	+	0.134232i	$0.0428567\pi$
$971$	19.0618	+	33.0161i	0.611723	+	1.05954i	−0.379227	+	0.925304i	$0.623810\pi$
$972$		0			0
$973$	−2.14311	−	1.23733i	−0.0687050	−	0.0396668i
$974$		0			0
$975$	−2.39884	−	6.82211i	−0.0768242	−	0.218482i
$976$		0			0
$977$	13.3622	+	7.71465i	0.427494	+	0.246814i	0.698278	−	0.715826i	$-0.253950\pi$
$977$	13.3622	+	7.71465i	0.427494	+	0.246814i	−0.270785	+	0.962640i	$0.587283\pi$
$978$		0			0
$979$	30.4223	+	52.6930i	0.972302	+	1.68408i
$980$		0			0
$981$	−4.82938	+	2.78824i	−0.154190	+	0.0890218i
$982$		0			0
$983$			24.0113i			0.765841i	0.923781	+	0.382920i	$0.125082\pi$
$983$			24.0113i			0.765841i	−0.923781	+	0.382920i	$0.874918\pi$
$984$		0			0
$985$	−10.8292	+	18.7568i	−0.345048	+	0.597641i
$986$		0			0
$987$	−8.44345			−0.268758
$988$		0			0
$989$	42.2889			1.34471
$990$		0			0
$991$	−3.46766	+	6.00615i	−0.110154	+	0.190792i	−0.915832	−	0.401561i	$-0.868468\pi$
$991$	−3.46766	+	6.00615i	−0.110154	+	0.190792i	0.805678	+	0.592353i	$0.201801\pi$
$992$		0			0
$993$			32.9004i			1.04406i
$994$		0			0
$995$	17.6668	−	10.1999i	0.560074	−	0.323359i
$996$		0			0
$997$	29.3764	+	50.8814i	0.930360	+	1.61143i	0.782705	+	0.622393i	$0.213839\pi$
$997$	29.3764	+	50.8814i	0.930360	+	1.61143i	0.147655	+	0.989039i	$0.452827\pi$
$998$		0			0
$999$	3.73796	+	2.15811i	0.118264	+	0.0682797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.f.641.2		16
4.3	odd	2		520.2.bu.b.121.7	✓	16
13.10	even	6	inner	1040.2.da.f.881.2		16
52.7	even	12		6760.2.a.bl.1.2		8
52.19	even	12		6760.2.a.bk.1.2		8
52.23	odd	6		520.2.bu.b.361.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.7	✓	16	4.3	odd	2
520.2.bu.b.361.7	yes	16	52.23	odd	6
1040.2.da.f.641.2		16	1.1	even	1	trivial
1040.2.da.f.881.2		16	13.10	even	6	inner
6760.2.a.bk.1.2		8	52.19	even	12
6760.2.a.bl.1.2		8	52.7	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00284 + 1.73697i) q^{3} -1.00000i q^{5} +(-1.48627 + 0.858099i) q^{7} +(-0.511370 - 0.885719i) q^{9} +O(q^{10})\)	\(q+(-1.00284 + 1.73697i) q^{3} -1.00000i q^{5} +(-1.48627 + 0.858099i) q^{7} +(-0.511370 - 0.885719i) q^{9} +(4.59199 + 2.65119i) q^{11} +(2.34769 - 2.73649i) q^{13} +(1.73697 + 1.00284i) q^{15} +(0.811344 + 1.40529i) q^{17} +(-1.96681 + 1.13554i) q^{19} -3.44214i q^{21} +(2.52585 - 4.37490i) q^{23} -1.00000 q^{25} -3.96574 q^{27} +(-2.08770 + 3.61600i) q^{29} +8.79183i q^{31} +(-9.21004 + 5.31742i) q^{33} +(0.858099 + 1.48627i) q^{35} +(-0.942563 - 0.544189i) q^{37} +(2.39884 + 6.82211i) q^{39} +(7.86992 + 4.54370i) q^{41} +(4.18560 + 7.24968i) q^{43} +(-0.885719 + 0.511370i) q^{45} -2.45297i q^{47} +(-2.02733 + 3.51144i) q^{49} -3.25459 q^{51} -5.54358 q^{53} +(2.65119 - 4.59199i) q^{55} -4.55505i q^{57} +(-8.57344 + 4.94988i) q^{59} +(0.373308 + 0.646589i) q^{61} +(1.52007 + 0.877612i) q^{63} +(-2.73649 - 2.34769i) q^{65} +(-13.5181 - 7.80468i) q^{67} +(5.06604 + 8.77464i) q^{69} +(-2.13260 + 1.23126i) q^{71} +12.7513i q^{73} +(1.00284 - 1.73697i) q^{75} -9.09991 q^{77} -0.702839 q^{79} +(5.51111 - 9.54553i) q^{81} -3.57032i q^{83} +(1.40529 - 0.811344i) q^{85} +(-4.18725 - 7.25253i) q^{87} +(9.93763 + 5.73750i) q^{89} +(-1.14112 + 6.08171i) q^{91} +(-15.2711 - 8.81679i) q^{93} +(1.13554 + 1.96681i) q^{95} +(12.1902 - 7.03799i) q^{97} -5.42295i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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