LMFDB - Embedded newform 85.2.e.a.81.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(21,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.3
Root			$3.48265i$ of defining polynomial
Character	$\chi$	$=$	85.81
Dual form			85.2.e.a.21.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.12708i q^{2} +(-1.75550 - 1.75550i) q^{3} +0.729699 q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.97858 + 1.97858i) q^{6} +(-1.72715 + 1.72715i) q^{7} -3.07658i q^{8} +3.16356i q^{9} +(-0.796963 + 0.796963i) q^{10} +(2.57251 - 2.57251i) q^{11} +(-1.28099 - 1.28099i) q^{12} +3.64168 q^{13} +(1.94663 + 1.94663i) q^{14} +2.48265i q^{15} -2.00814 q^{16} +(3.03394 + 2.79199i) q^{17} +3.56558 q^{18} +2.61358i q^{19} +(-0.515975 - 0.515975i) q^{20} +6.06403 q^{21} +(-2.89941 - 2.89941i) q^{22} +(0.993850 - 0.993850i) q^{23} +(-5.40094 + 5.40094i) q^{24} +1.00000i q^{25} -4.10445i q^{26} +(0.287137 - 0.287137i) q^{27} +(-1.26030 + 1.26030i) q^{28} +(0.601589 + 0.601589i) q^{29} +2.79814 q^{30} +(-6.67744 - 6.67744i) q^{31} -3.88983i q^{32} -9.03208 q^{33} +(3.14678 - 3.41948i) q^{34} +2.44256 q^{35} +2.30845i q^{36} +(7.78199 + 7.78199i) q^{37} +2.94570 q^{38} +(-6.39297 - 6.39297i) q^{39} +(-2.17547 + 2.17547i) q^{40} +(-6.74550 + 6.74550i) q^{41} -6.83463i q^{42} +7.47280i q^{43} +(1.87716 - 1.87716i) q^{44} +(2.23698 - 2.23698i) q^{45} +(-1.12014 - 1.12014i) q^{46} -5.42683 q^{47} +(3.52529 + 3.52529i) q^{48} +1.03389i q^{49} +1.12708 q^{50} +(-0.424747 - 10.2274i) q^{51} +2.65733 q^{52} -12.9453i q^{53} +(-0.323626 - 0.323626i) q^{54} -3.63808 q^{55} +(5.31372 + 5.31372i) q^{56} +(4.58814 - 4.58814i) q^{57} +(0.678037 - 0.678037i) q^{58} +1.40270i q^{59} +1.81159i q^{60} +(0.804485 - 0.804485i) q^{61} +(-7.52598 + 7.52598i) q^{62} +(-5.46396 - 5.46396i) q^{63} -8.40042 q^{64} +(-2.57506 - 2.57506i) q^{65} +10.1798i q^{66} -2.07908 q^{67} +(2.21387 + 2.03731i) q^{68} -3.48941 q^{69} -2.75295i q^{70} +(8.69168 + 8.69168i) q^{71} +9.73296 q^{72} +(1.04359 + 1.04359i) q^{73} +(8.77090 - 8.77090i) q^{74} +(1.75550 - 1.75550i) q^{75} +1.90713i q^{76} +8.88623i q^{77} +(-7.20536 + 7.20536i) q^{78} +(6.34470 - 6.34470i) q^{79} +(1.41997 + 1.41997i) q^{80} +8.48255 q^{81} +(7.60269 + 7.60269i) q^{82} +2.52680i q^{83} +4.42492 q^{84} +(-0.171086 - 4.11955i) q^{85} +8.42242 q^{86} -2.11218i q^{87} +(-7.91453 - 7.91453i) q^{88} -1.66373 q^{89} +(-2.52124 - 2.52124i) q^{90} +(-6.28973 + 6.28973i) q^{91} +(0.725212 - 0.725212i) q^{92} +23.4445i q^{93} +6.11645i q^{94} +(1.84808 - 1.84808i) q^{95} +(-6.82860 + 6.82860i) q^{96} +(-8.67432 - 8.67432i) q^{97} +1.16527 q^{98} +(8.13830 + 8.13830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.12708i		−	0.796963i	−0.917176	−	0.398482i	$-0.869537\pi$
$2$		−	1.12708i		−	0.796963i	0.917176	−	0.398482i	$-0.130463\pi$
$3$	−1.75550	−	1.75550i	−1.01354	−	1.01354i	−0.999907	−	0.0136316i	$-0.995661\pi$
$3$	−1.75550	−	1.75550i	−1.01354	−	1.01354i	−0.0136316	−	0.999907i	$-0.504339\pi$
$4$	0.729699			0.364850
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.97858	+	1.97858i	−0.807753	+	0.807753i
$7$	−1.72715	+	1.72715i	−0.652802	+	0.652802i	−0.953667	−	0.300865i	$-0.902725\pi$
$7$	−1.72715	+	1.72715i	−0.652802	+	0.652802i	0.300865	+	0.953667i	$0.402725\pi$
$8$		−	3.07658i		−	1.08773i
$9$			3.16356i			1.05452i
$10$	−0.796963	+	0.796963i	−0.252022	+	0.252022i
$11$	2.57251	−	2.57251i	0.775641	−	0.775641i	−0.203446	−	0.979086i	$-0.565214\pi$
$11$	2.57251	−	2.57251i	0.775641	−	0.775641i	0.979086	+	0.203446i	$0.0652140\pi$
$12$	−1.28099	−	1.28099i	−0.369789	−	0.369789i
$13$	3.64168			1.01002			0.505010	−	0.863113i	$-0.331489\pi$
$13$	3.64168			1.01002			0.505010	+	0.863113i	$0.331489\pi$
$14$	1.94663	+	1.94663i	0.520259	+	0.520259i
$15$			2.48265i			0.641018i
$16$	−2.00814			−0.502035
$17$	3.03394	+	2.79199i	0.735839	+	0.677157i
$17$	3.03394	+	2.79199i	0.735839	+	0.677157i
$18$	3.56558			0.840415
$19$			2.61358i			0.599596i	0.954003	+	0.299798i	$0.0969193\pi$
$19$			2.61358i			0.599596i	−0.954003	+	0.299798i	$0.903081\pi$
$20$	−0.515975	−	0.515975i	−0.115376	−	0.115376i
$21$	6.06403			1.32328
$22$	−2.89941	−	2.89941i	−0.618157	−	0.618157i
$23$	0.993850	−	0.993850i	0.207232	−	0.207232i	−0.595858	−	0.803090i	$-0.703188\pi$
$23$	0.993850	−	0.993850i	0.207232	−	0.207232i	0.803090	+	0.595858i	$0.203188\pi$
$24$	−5.40094	+	5.40094i	−1.10246	+	1.10246i
$25$			1.00000i			0.200000i
$26$		−	4.10445i		−	0.804949i
$27$	0.287137	−	0.287137i	0.0552596	−	0.0552596i
$28$	−1.26030	+	1.26030i	−0.238175	+	0.238175i
$29$	0.601589	+	0.601589i	0.111712	+	0.111712i	0.760753	−	0.649041i	$-0.224830\pi$
$29$	0.601589	+	0.601589i	0.111712	+	0.111712i	−0.649041	+	0.760753i	$0.724830\pi$
$30$	2.79814			0.510868
$31$	−6.67744	−	6.67744i	−1.19930	−	1.19930i	−0.974376	−	0.224928i	$-0.927785\pi$
$31$	−6.67744	−	6.67744i	−1.19930	−	1.19930i	−0.224928	−	0.974376i	$-0.572215\pi$
$32$		−	3.88983i		−	0.687632i
$33$	−9.03208			−1.57228
$34$	3.14678	−	3.41948i	0.539669	−	0.586436i
$35$	2.44256			0.412868
$36$			2.30845i			0.384742i
$37$	7.78199	+	7.78199i	1.27935	+	1.27935i	0.941031	+	0.338320i	$0.109859\pi$
$37$	7.78199	+	7.78199i	1.27935	+	1.27935i	0.338320	+	0.941031i	$0.390141\pi$
$38$	2.94570			0.477856
$39$	−6.39297	−	6.39297i	−1.02369	−	1.02369i
$40$	−2.17547	+	2.17547i	−0.343972	+	0.343972i
$41$	−6.74550	+	6.74550i	−1.05347	+	1.05347i	−0.0549831	+	0.998487i	$0.517511\pi$
$41$	−6.74550	+	6.74550i	−1.05347	+	1.05347i	−0.998487	+	0.0549831i	$0.982489\pi$
$42$		−	6.83463i		−	1.05461i
$43$			7.47280i			1.13959i	0.821786	+	0.569796i	$0.192978\pi$
$43$			7.47280i			1.13959i	−0.821786	+	0.569796i	$0.807022\pi$
$44$	1.87716	−	1.87716i	0.282992	−	0.282992i
$45$	2.23698	−	2.23698i	0.333469	−	0.333469i
$46$	−1.12014	−	1.12014i	−0.165156	−	0.165156i
$47$	−5.42683			−0.791585			−0.395792	−	0.918340i	$-0.629530\pi$
$47$	−5.42683			−0.791585			−0.395792	+	0.918340i	$0.629530\pi$
$48$	3.52529	+	3.52529i	0.508832	+	0.508832i
$49$			1.03389i			0.147699i
$50$	1.12708			0.159393
$51$	−0.424747	−	10.2274i	−0.0594765	−	1.43213i
$52$	2.65733			0.368506
$53$		−	12.9453i		−	1.77817i	−0.457737	−	0.889087i	$-0.651340\pi$
$53$		−	12.9453i		−	1.77817i	0.457737	−	0.889087i	$-0.348660\pi$
$54$	−0.323626	−	0.323626i	−0.0440399	−	0.0440399i
$55$	−3.63808			−0.490558
$56$	5.31372	+	5.31372i	0.710076	+	0.710076i
$57$	4.58814	−	4.58814i	0.607714	−	0.607714i
$58$	0.678037	−	0.678037i	0.0890306	−	0.0890306i
$59$			1.40270i			0.182616i	0.995823	+	0.0913081i	$0.0291048\pi$
$59$			1.40270i			0.182616i	−0.995823	+	0.0913081i	$0.970895\pi$
$60$			1.81159i			0.233875i
$61$	0.804485	−	0.804485i	0.103004	−	0.103004i	−0.653727	−	0.756731i	$-0.726795\pi$
$61$	0.804485	−	0.804485i	0.103004	−	0.103004i	0.756731	+	0.653727i	$0.226795\pi$
$62$	−7.52598	+	7.52598i	−0.955800	+	0.955800i
$63$	−5.46396	−	5.46396i	−0.688394	−	0.688394i
$64$	−8.40042			−1.05005
$65$	−2.57506	−	2.57506i	−0.319396	−	0.319396i
$66$			10.1798i			1.25305i
$67$	−2.07908			−0.254000			−0.127000	−	0.991903i	$-0.540535\pi$
$67$	−2.07908			−0.254000			−0.127000	+	0.991903i	$0.540535\pi$
$68$	2.21387	+	2.03731i	0.268471	+	0.247060i
$69$	−3.48941			−0.420076
$70$		−	2.75295i		−	0.329041i
$71$	8.69168	+	8.69168i	1.03151	+	1.03151i	0.999487	+	0.0320251i	$0.0101957\pi$
$71$	8.69168	+	8.69168i	1.03151	+	1.03151i	0.0320251	+	0.999487i	$0.489804\pi$
$72$	9.73296			1.14704
$73$	1.04359	+	1.04359i	0.122143	+	0.122143i	0.765536	−	0.643393i	$-0.222474\pi$
$73$	1.04359	+	1.04359i	0.122143	+	0.122143i	−0.643393	+	0.765536i	$0.722474\pi$
$74$	8.77090	−	8.77090i	1.01960	−	1.01960i
$75$	1.75550	−	1.75550i	0.202708	−	0.202708i
$76$			1.90713i			0.218762i
$77$			8.88623i			1.01268i
$78$	−7.20536	+	7.20536i	−0.815847	+	0.815847i
$79$	6.34470	−	6.34470i	0.713834	−	0.713834i	−0.253501	−	0.967335i	$-0.581582\pi$
$79$	6.34470	−	6.34470i	0.713834	−	0.713834i	0.967335	+	0.253501i	$0.0815821\pi$
$80$	1.41997	+	1.41997i	0.158757	+	0.158757i
$81$	8.48255			0.942506
$82$	7.60269	+	7.60269i	0.839577	+	0.839577i
$83$			2.52680i			0.277353i	0.990338	+	0.138676i	$0.0442848\pi$
$83$			2.52680i			0.277353i	−0.990338	+	0.138676i	$0.955715\pi$
$84$	4.42492			0.482799
$85$	−0.171086	−	4.11955i	−0.0185569	−	0.446828i
$86$	8.42242			0.908213
$87$		−	2.11218i		−	0.226449i
$88$	−7.91453	−	7.91453i	−0.843691	−	0.843691i
$89$	−1.66373			−0.176355			−0.0881775	−	0.996105i	$-0.528104\pi$
$89$	−1.66373			−0.176355			−0.0881775	+	0.996105i	$0.528104\pi$
$90$	−2.52124	−	2.52124i	−0.265762	−	0.265762i
$91$	−6.28973	+	6.28973i	−0.659343	+	0.659343i
$92$	0.725212	−	0.725212i	0.0756086	−	0.0756086i
$93$			23.4445i			2.43108i
$94$			6.11645i			0.630864i
$95$	1.84808	−	1.84808i	0.189609	−	0.189609i
$96$	−6.82860	+	6.82860i	−0.696941	+	0.696941i
$97$	−8.67432	−	8.67432i	−0.880744	−	0.880744i	0.112867	−	0.993610i	$-0.463997\pi$
$97$	−8.67432	−	8.67432i	−0.880744	−	0.880744i	−0.993610	+	0.112867i	$0.963997\pi$
$98$	1.16527			0.117710
$99$	8.13830	+	8.13830i	0.817930	+	0.817930i
$100$			0.729699i			0.0729699i
$101$	−4.18131			−0.416056			−0.208028	−	0.978123i	$-0.566704\pi$
$101$	−4.18131			−0.416056			−0.208028	+	0.978123i	$0.566704\pi$
$102$	−11.5271	+	0.478722i	−1.14135	+	0.0474006i
$103$	8.08417			0.796557			0.398279	−	0.917265i	$-0.369608\pi$
$103$	8.08417			0.796557			0.398279	+	0.917265i	$0.369608\pi$
$104$		−	11.2039i		−	1.09863i
$105$	−4.28792	−	4.28792i	−0.418458	−	0.418458i
$106$	−14.5903			−1.41714
$107$	−6.22304	−	6.22304i	−0.601604	−	0.601604i	0.339134	−	0.940738i	$-0.389866\pi$
$107$	−6.22304	−	6.22304i	−0.601604	−	0.601604i	−0.940738	+	0.339134i	$0.889866\pi$
$108$	0.209524	−	0.209524i	0.0201615	−	0.0201615i
$109$	10.1218	−	10.1218i	0.969496	−	0.969496i	−0.0300524	−	0.999548i	$-0.509567\pi$
$109$	10.1218	−	10.1218i	0.969496	−	0.969496i	0.999548	+	0.0300524i	$0.00956740\pi$
$110$			4.10039i			0.390957i
$111$		−	27.3226i		−	2.59334i
$112$	3.46836	−	3.46836i	0.327730	−	0.327730i
$113$	−8.10334	+	8.10334i	−0.762298	+	0.762298i	−0.976737	−	0.214440i	$-0.931208\pi$
$113$	−8.10334	+	8.10334i	−0.762298	+	0.762298i	0.214440	+	0.976737i	$0.431208\pi$
$114$	−5.17118	−	5.17118i	−0.484325	−	0.484325i
$115$	−1.40552			−0.131065
$116$	0.438979	+	0.438979i	0.0407582	+	0.0407582i
$117$			11.5207i			1.06509i
$118$	1.58095			0.145538
$119$	−10.0623	+	0.417888i	−0.922407	+	0.0383077i
$120$	7.63808			0.697258
$121$		−	2.23561i		−	0.203237i
$122$	−0.906716	−	0.906716i	−0.0820902	−	0.0820902i
$123$	23.6835			2.13547
$124$	−4.87252	−	4.87252i	−0.437565	−	0.437565i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−6.15830	+	6.15830i	−0.548625	+	0.548625i
$127$		−	2.51562i		−	0.223225i	−0.993752	−	0.111613i	$-0.964398\pi$
$127$		−	2.51562i		−	0.223225i	0.993752	−	0.111613i	$-0.0356015\pi$
$128$			1.68825i			0.149221i
$129$	13.1185	−	13.1185i	1.15502	−	1.15502i
$130$	−2.90228	+	2.90228i	−0.254547	+	0.254547i
$131$	−1.57140	−	1.57140i	−0.137294	−	0.137294i	0.635120	−	0.772414i	$-0.280951\pi$
$131$	−1.57140	−	1.57140i	−0.137294	−	0.137294i	−0.772414	+	0.635120i	$0.780951\pi$
$132$	−6.59071			−0.573647
$133$	−4.51405	−	4.51405i	−0.391417	−	0.391417i
$134$			2.34328i			0.202428i
$135$	−0.406074			−0.0349493
$136$	8.58977	−	9.33416i	0.736567	−	0.800398i
$137$	−22.1633			−1.89354			−0.946771	−	0.321908i	$-0.895676\pi$
$137$	−22.1633			−1.89354			−0.946771	+	0.321908i	$0.895676\pi$
$138$			3.93283i			0.334785i
$139$	9.81865	+	9.81865i	0.832807	+	0.832807i	0.987900	−	0.155093i	$-0.0495676\pi$
$139$	9.81865	+	9.81865i	0.832807	+	0.832807i	−0.155093	+	0.987900i	$0.549568\pi$
$140$	1.78234			0.150635
$141$	9.52680	+	9.52680i	0.802302	+	0.802302i
$142$	9.79618	−	9.79618i	0.822077	−	0.822077i
$143$	9.36825	−	9.36825i	0.783413	−	0.783413i
$144$		−	6.35288i		−	0.529407i
$145$		−	0.850775i		−	0.0706530i
$146$	1.17621	−	1.17621i	0.0973438	−	0.0973438i
$147$	1.81500	−	1.81500i	0.149698	−	0.149698i
$148$	5.67851	+	5.67851i	0.466771	+	0.466771i
$149$	−11.6461			−0.954087			−0.477044	−	0.878880i	$-0.658292\pi$
$149$	−11.6461			−0.954087			−0.477044	+	0.878880i	$0.658292\pi$
$150$	−1.97858	−	1.97858i	−0.161551	−	0.161551i
$151$		−	2.82731i		−	0.230083i	−0.993361	−	0.115042i	$-0.963300\pi$
$151$		−	2.82731i		−	0.230083i	0.993361	−	0.115042i	$-0.0367002\pi$
$152$	8.04088			0.652201
$153$	−8.83264	+	9.59807i	−0.714076	+	0.775958i
$154$	10.0155			0.807068
$155$			9.44332i			0.758506i
$156$	−4.66495	−	4.66495i	−0.373495	−	0.373495i
$157$	1.36913			0.109268			0.0546342	−	0.998506i	$-0.482601\pi$
$157$	1.36913			0.109268			0.0546342	+	0.998506i	$0.482601\pi$
$158$	−7.15096	−	7.15096i	−0.568900	−	0.568900i
$159$	−22.7255	+	22.7255i	−1.80225	+	1.80225i
$160$	−2.75053	+	2.75053i	−0.217448	+	0.217448i
$161$			3.43306i			0.270563i
$162$		−	9.56048i		−	0.751143i
$163$	−8.54984	+	8.54984i	−0.669675	+	0.669675i	−0.957641	−	0.287966i	$-0.907021\pi$
$163$	−8.54984	+	8.54984i	−0.669675	+	0.669675i	0.287966	+	0.957641i	$0.407021\pi$
$164$	−4.92219	+	4.92219i	−0.384358	+	0.384358i
$165$	6.38665	+	6.38665i	0.497200	+	0.497200i
$166$	2.84790			0.221040
$167$	4.16611	+	4.16611i	0.322383	+	0.322383i	0.849681	−	0.527297i	$-0.176795\pi$
$167$	4.16611	+	4.16611i	0.322383	+	0.322383i	−0.527297	+	0.849681i	$0.676795\pi$
$168$		−	18.6565i		−	1.43938i
$169$	0.261831			0.0201408
$170$	−4.64305	+	0.192827i	−0.356106	+	0.0147892i
$171$	−8.26822			−0.632287
$172$			5.45290i			0.415780i
$173$	1.46761	+	1.46761i	0.111580	+	0.111580i	0.760693	−	0.649112i	$-0.224859\pi$
$173$	1.46761	+	1.46761i	0.111580	+	0.111580i	−0.649112	+	0.760693i	$0.724859\pi$
$174$	−2.38059			−0.180472
$175$	−1.72715	−	1.72715i	−0.130560	−	0.130560i
$176$	−5.16596	+	5.16596i	−0.389399	+	0.389399i
$177$	2.46244	−	2.46244i	0.185089	−	0.185089i
$178$			1.87515i			0.140548i
$179$			10.5373i			0.787597i	0.919197	+	0.393799i	$0.128839\pi$
$179$			10.5373i			0.787597i	−0.919197	+	0.393799i	$0.871161\pi$
$180$	1.63232	−	1.63232i	0.121666	−	0.121666i
$181$	−2.39758	+	2.39758i	−0.178210	+	0.178210i	−0.790575	−	0.612365i	$-0.790218\pi$
$181$	−2.39758	+	2.39758i	−0.178210	+	0.178210i	0.612365	+	0.790575i	$0.290218\pi$
$182$	7.08901	+	7.08901i	0.525472	+	0.525472i
$183$	−2.82455			−0.208797
$184$	−3.05766	−	3.05766i	−0.225414	−	0.225414i
$185$		−	11.0054i		−	0.809133i
$186$	26.4237			1.93748
$187$	14.9873	−	0.622424i	1.09598	−	0.0455162i
$188$	−3.95995			−0.288809
$189$			0.991860i			0.0721472i
$190$	−2.08293	−	2.08293i	−0.151111	−	0.151111i
$191$	−12.3426			−0.893077			−0.446538	−	0.894764i	$-0.647343\pi$
$191$	−12.3426			−0.893077			−0.446538	+	0.894764i	$0.647343\pi$
$192$	14.7469	+	14.7469i	1.06427	+	1.06427i
$193$	8.45396	−	8.45396i	0.608529	−	0.608529i	−0.334032	−	0.942562i	$-0.608409\pi$
$193$	8.45396	−	8.45396i	0.608529	−	0.608529i	0.942562	+	0.334032i	$0.108409\pi$
$194$	−9.77662	+	9.77662i	−0.701920	+	0.701920i
$195$			9.04103i			0.647441i
$196$			0.754430i			0.0538878i
$197$	0.864156	−	0.864156i	0.0615686	−	0.0615686i	−0.675652	−	0.737221i	$-0.736138\pi$
$197$	0.864156	−	0.864156i	0.0615686	−	0.0615686i	0.737221	+	0.675652i	$0.236138\pi$
$198$	9.17248	−	9.17248i	0.651860	−	0.651860i
$199$	15.3689	+	15.3689i	1.08947	+	1.08947i	0.995583	+	0.0938906i	$0.0299304\pi$
$199$	15.3689	+	15.3689i	1.08947	+	1.08947i	0.0938906	+	0.995583i	$0.470070\pi$
$200$	3.07658			0.217547
$201$	3.64982	+	3.64982i	0.257438	+	0.257438i
$202$			4.71265i			0.331581i
$203$	−2.07807			−0.145852
$204$	−0.309938	−	7.46294i	−0.0217000	−	0.522511i
$205$	9.53958			0.666273
$206$		−	9.11148i		−	0.634827i
$207$	3.14411	+	3.14411i	0.218531	+	0.218531i
$208$	−7.31300			−0.507065
$209$	6.72345	+	6.72345i	0.465071	+	0.465071i
$210$	−4.83281	+	4.83281i	−0.333496	+	0.333496i
$211$	−11.9397	+	11.9397i	−0.821965	+	0.821965i	−0.986390	−	0.164425i	$-0.947423\pi$
$211$	−11.9397	+	11.9397i	−0.821965	+	0.821965i	0.164425	+	0.986390i	$0.447423\pi$
$212$		−	9.44618i		−	0.648767i
$213$		−	30.5165i		−	2.09096i
$214$	−7.01384	+	7.01384i	−0.479456	+	0.479456i
$215$	5.28407	−	5.28407i	0.360371	−	0.360371i
$216$	−0.883401	−	0.883401i	−0.0601078	−	0.0601078i
$217$	23.0659			1.56582
$218$	−11.4081	−	11.4081i	−0.772653	−	0.772653i
$219$		−	3.66406i		−	0.247594i
$220$	−2.65470			−0.178980
$221$	11.0486	+	10.1675i	0.743212	+	0.683942i
$222$	−30.7946			−2.06680
$223$		−	9.61320i		−	0.643748i	−0.946783	−	0.321874i	$-0.895687\pi$
$223$		−	9.61320i		−	0.643748i	0.946783	−	0.321874i	$-0.104313\pi$
$224$	6.71833	+	6.71833i	0.448887	+	0.448887i
$225$	−3.16356			−0.210904
$226$	9.13308	+	9.13308i	0.607523	+	0.607523i
$227$	1.25815	−	1.25815i	0.0835064	−	0.0835064i	−0.664120	−	0.747626i	$-0.731194\pi$
$227$	1.25815	−	1.25815i	0.0835064	−	0.0835064i	0.747626	+	0.664120i	$0.231194\pi$
$228$	3.34796	−	3.34796i	0.221724	−	0.221724i
$229$		−	16.7429i		−	1.10640i	−0.833048	−	0.553201i	$-0.813406\pi$
$229$		−	16.7429i		−	1.10640i	0.833048	−	0.553201i	$-0.186594\pi$
$230$			1.58412i			0.104454i
$231$	15.5998	−	15.5998i	1.02639	−	1.02639i
$232$	1.85084	−	1.85084i	0.121513	−	0.121513i
$233$	9.25323	+	9.25323i	0.606199	+	0.606199i	0.941951	−	0.335751i	$-0.108990\pi$
$233$	9.25323	+	9.25323i	0.606199	+	0.606199i	−0.335751	+	0.941951i	$0.608990\pi$
$234$	12.9847			0.848836
$235$	3.83735	+	3.83735i	0.250321	+	0.250321i
$236$			1.02355i			0.0666275i
$237$	−22.2762			−1.44700
$238$	0.470992	+	11.3409i	0.0305299	+	0.735124i
$239$	−23.9469			−1.54900			−0.774498	−	0.632577i	$-0.781997\pi$
$239$	−23.9469			−1.54900			−0.774498	+	0.632577i	$0.781997\pi$
$240$		−	4.98551i		−	0.321814i
$241$	−12.2266	−	12.2266i	−0.787587	−	0.787587i	0.193511	−	0.981098i	$-0.438012\pi$
$241$	−12.2266	−	12.2266i	−0.787587	−	0.787587i	−0.981098	+	0.193511i	$0.938012\pi$
$242$	−2.51970			−0.161972
$243$	−15.7525	−	15.7525i	−1.01053	−	1.01053i
$244$	0.587032	−	0.587032i	0.0375809	−	0.0375809i
$245$	0.731071	−	0.731071i	0.0467064	−	0.0467064i
$246$		−	26.6931i		−	1.70189i
$247$			9.51781i			0.605604i
$248$	−20.5437	+	20.5437i	−1.30452	+	1.30452i
$249$	4.43581	−	4.43581i	0.281108	−	0.281108i
$250$	−0.796963	−	0.796963i	−0.0504044	−	0.0504044i
$251$	18.2106			1.14944			0.574722	−	0.818349i	$-0.305110\pi$
$251$	18.2106			1.14944			0.574722	+	0.818349i	$0.305110\pi$
$252$	−3.98705	−	3.98705i	−0.251160	−	0.251160i
$253$		−	5.11338i		−	0.321475i
$254$	−2.83529			−0.177902
$255$	−6.93154	+	7.53222i	−0.434070	+	0.471686i
$256$	−14.8981			−0.931128
$257$		−	2.58018i		−	0.160947i	−0.996757	−	0.0804735i	$-0.974357\pi$
$257$		−	2.58018i		−	0.160947i	0.996757	−	0.0804735i	$-0.0256432\pi$
$258$	−14.7856	−	14.7856i	−0.920509	−	0.920509i
$259$	−26.8814			−1.67033
$260$	−1.87902	−	1.87902i	−0.116532	−	0.116532i
$261$	−1.90317	+	1.90317i	−0.117803	+	0.117803i
$262$	−1.77109	+	1.77109i	−0.109418	+	0.109418i
$263$			9.58787i			0.591213i	0.955310	+	0.295607i	$0.0955218\pi$
$263$			9.58787i			0.591213i	−0.955310	+	0.295607i	$0.904478\pi$
$264$			27.7879i			1.71023i
$265$	−9.15372	+	9.15372i	−0.562308	+	0.562308i
$266$	−5.08767	+	5.08767i	−0.311945	+	0.311945i
$267$	2.92068	+	2.92068i	0.178743	+	0.178743i
$268$	−1.51710			−0.0926717
$269$	−5.01049	−	5.01049i	−0.305495	−	0.305495i	0.537664	−	0.843159i	$-0.319307\pi$
$269$	−5.01049	−	5.01049i	−0.305495	−	0.305495i	−0.843159	+	0.537664i	$0.819307\pi$
$270$			0.457676i			0.0278533i
$271$	−13.7773			−0.836909			−0.418454	−	0.908238i	$-0.637428\pi$
$271$	−13.7773			−0.836909			−0.418454	+	0.908238i	$0.637428\pi$
$272$	−6.09258	−	5.60670i	−0.369417	−	0.339956i
$273$	22.0833			1.33654
$274$			24.9798i			1.50908i
$275$	2.57251	+	2.57251i	0.155128	+	0.155128i
$276$	−2.54622			−0.153264
$277$	3.19263	+	3.19263i	0.191827	+	0.191827i	0.796485	−	0.604658i	$-0.206690\pi$
$277$	3.19263	+	3.19263i	0.191827	+	0.191827i	−0.604658	+	0.796485i	$0.706690\pi$
$278$	11.0664	−	11.0664i	0.663717	−	0.663717i
$279$	21.1245	−	21.1245i	1.26469	−	1.26469i
$280$		−	7.51473i		−	0.449091i
$281$		−	3.44172i		−	0.205316i	−0.994717	−	0.102658i	$-0.967265\pi$
$281$		−	3.44172i		−	0.205316i	0.994717	−	0.102658i	$-0.0327347\pi$
$282$	10.7374	−	10.7374i	0.639405	−	0.639405i
$283$	16.6458	−	16.6458i	0.989493	−	0.989493i	−0.0104528	−	0.999945i	$-0.503327\pi$
$283$	16.6458	−	16.6458i	0.989493	−	0.989493i	0.999945	+	0.0104528i	$0.00332730\pi$
$284$	6.34231	+	6.34231i	0.376347	+	0.376347i
$285$	−6.48861			−0.384352
$286$	−10.5587	−	10.5587i	−0.624351	−	0.624351i
$287$		−	23.3010i		−	1.37542i
$288$	12.3057			0.725122
$289$	1.40960	+	16.9415i	0.0829174	+	0.996556i
$290$	−0.958888			−0.0563079
$291$			30.4555i			1.78534i
$292$	0.761510	+	0.761510i	0.0445640	+	0.0445640i
$293$	15.5924			0.910918			0.455459	−	0.890257i	$-0.349475\pi$
$293$	15.5924			0.910918			0.455459	+	0.890257i	$0.349475\pi$
$294$	−2.04564	−	2.04564i	−0.119304	−	0.119304i
$295$	0.991860	−	0.991860i	0.0577483	−	0.0577483i
$296$	23.9419	−	23.9419i	1.39160	−	1.39160i
$297$		−	1.47733i		−	0.0857232i
$298$			13.1261i			0.760372i
$299$	3.61928	−	3.61928i	0.209309	−	0.209309i
$300$	1.28099	−	1.28099i	0.0739579	−	0.0739579i
$301$	−12.9067	−	12.9067i	−0.743928	−	0.743928i
$302$	−3.18660			−0.183368
$303$	7.34029	+	7.34029i	0.421688	+	0.421688i
$304$		−	5.24843i		−	0.301018i
$305$	−1.13771			−0.0651453
$306$	10.8178	+	9.95505i	0.618410	+	0.569093i
$307$	21.6549			1.23591			0.617955	−	0.786214i	$-0.287962\pi$
$307$	21.6549			1.23591			0.617955	+	0.786214i	$0.287962\pi$
$308$			6.48428i			0.369476i
$309$	−14.1918	−	14.1918i	−0.807341	−	0.807341i
$310$	10.6433			0.604501
$311$	−6.26814	−	6.26814i	−0.355434	−	0.355434i	0.506693	−	0.862127i	$-0.330868\pi$
$311$	−6.26814	−	6.26814i	−0.355434	−	0.355434i	−0.862127	+	0.506693i	$0.830868\pi$
$312$	−19.6685	+	19.6685i	−1.11351	+	1.11351i
$313$	−12.1015	+	12.1015i	−0.684016	+	0.684016i	−0.960903	−	0.276887i	$-0.910697\pi$
$313$	−12.1015	+	12.1015i	−0.684016	+	0.684016i	0.276887	+	0.960903i	$0.410697\pi$
$314$		−	1.54311i		−	0.0870828i
$315$			7.72720i			0.435379i
$316$	4.62972	−	4.62972i	0.260442	−	0.260442i
$317$	7.30027	−	7.30027i	0.410024	−	0.410024i	−0.471723	−	0.881747i	$-0.656368\pi$
$317$	7.30027	−	7.30027i	0.410024	−	0.410024i	0.881747	+	0.471723i	$0.156368\pi$
$318$	25.6134	+	25.6134i	1.43633	+	1.43633i
$319$	3.09519			0.173297
$320$	5.93999	+	5.93999i	0.332056	+	0.332056i
$321$			21.8491i			1.21950i
$322$	3.86932			0.215629
$323$	−7.29708	+	7.92944i	−0.406020	+	0.441206i
$324$	6.18971			0.343873
$325$			3.64168i			0.202004i
$326$	9.63632	+	9.63632i	0.533706	+	0.533706i
$327$	−35.5378			−1.96524
$328$	20.7531	+	20.7531i	1.14590	+	1.14590i
$329$	9.37296	−	9.37296i	0.516748	−	0.516748i
$330$	7.19824	−	7.19824i	0.396250	−	0.396250i
$331$		−	6.56727i		−	0.360970i	−0.983578	−	0.180485i	$-0.942233\pi$
$331$		−	6.56727i		−	0.360970i	0.983578	−	0.180485i	$-0.0577667\pi$
$332$			1.84381i			0.101192i
$333$	−24.6188	+	24.6188i	−1.34910	+	1.34910i
$334$	4.69553	−	4.69553i	0.256928	−	0.256928i
$335$	1.47013	+	1.47013i	0.0803217	+	0.0803217i
$336$	−12.1774			−0.664333
$337$	−21.3377	−	21.3377i	−1.16234	−	1.16234i	−0.983962	−	0.178379i	$-0.942915\pi$
$337$	−21.3377	−	21.3377i	−1.16234	−	1.16234i	−0.178379	−	0.983962i	$-0.557085\pi$
$338$		−	0.295103i		−	0.0160515i
$339$	28.4508			1.54524
$340$	−0.124841	−	3.00604i	−0.00677047	−	0.163025i
$341$	−34.3555			−1.86046
$342$			9.31892i			0.503909i
$343$	−13.8758	−	13.8758i	−0.749220	−	0.749220i
$344$	22.9907			1.23957
$345$	2.46739	+	2.46739i	0.132840	+	0.132840i
$346$	1.65411	−	1.65411i	0.0889254	−	0.0889254i
$347$	4.97815	−	4.97815i	0.267241	−	0.267241i	−0.560746	−	0.827988i	$-0.689486\pi$
$347$	4.97815	−	4.97815i	0.267241	−	0.267241i	0.827988	+	0.560746i	$0.189486\pi$
$348$		−	1.54126i		−	0.0826200i
$349$		−	35.4396i		−	1.89704i	−0.316723	−	0.948518i	$-0.602583\pi$
$349$		−	35.4396i		−	1.89704i	0.316723	−	0.948518i	$-0.397417\pi$
$350$	−1.94663	+	1.94663i	−0.104052	+	0.104052i
$351$	1.04566	−	1.04566i	0.0558133	−	0.0558133i
$352$	−10.0066	−	10.0066i	−0.533355	−	0.533355i
$353$	−8.54669			−0.454895			−0.227447	−	0.973790i	$-0.573038\pi$
$353$	−8.54669			−0.454895			−0.227447	+	0.973790i	$0.573038\pi$
$354$	−2.77536	−	2.77536i	−0.147509	−	0.147509i
$355$		−	12.2919i		−	0.652386i
$356$	−1.21402			−0.0643430
$357$	18.3979	+	16.9307i	0.973721	+	0.896068i
$358$	11.8764			0.627686
$359$			20.2839i			1.07054i	0.844681	+	0.535271i	$0.179790\pi$
$359$			20.2839i			1.07054i	−0.844681	+	0.535271i	$0.820210\pi$
$360$	−6.88224	−	6.88224i	−0.362726	−	0.362726i
$361$	12.1692			0.640485
$362$	2.70225	+	2.70225i	0.142027	+	0.142027i
$363$	−3.92461	+	3.92461i	−0.205988	+	0.205988i
$364$	−4.58962	+	4.58962i	−0.240561	+	0.240561i
$365$		−	1.47586i		−	0.0772503i
$366$			3.18348i			0.166403i
$367$	−8.99600	+	8.99600i	−0.469587	+	0.469587i	−0.901781	−	0.432193i	$-0.857740\pi$
$367$	−8.99600	+	8.99600i	−0.469587	+	0.469587i	0.432193	+	0.901781i	$0.357740\pi$
$368$	−1.99579	+	1.99579i	−0.104038	+	0.104038i
$369$	−21.3398	−	21.3398i	−1.11091	−	1.11091i
$370$	−12.4039			−0.644849
$371$	22.3585	+	22.3585i	1.16080	+	1.16080i
$372$			17.1074i			0.886979i
$373$	−11.1454			−0.577086			−0.288543	−	0.957467i	$-0.593171\pi$
$373$	−11.1454			−0.577086			−0.288543	+	0.957467i	$0.593171\pi$
$374$	−0.701519	−	16.8918i	−0.0362747	−	0.873453i
$375$	−2.48265			−0.128204
$376$			16.6961i			0.861034i
$377$	2.19079	+	2.19079i	0.112832	+	0.112832i
$378$	1.11790			0.0574987
$379$	8.96691	+	8.96691i	0.460599	+	0.460599i	0.898852	−	0.438253i	$-0.144402\pi$
$379$	8.96691	+	8.96691i	0.460599	+	0.460599i	−0.438253	+	0.898852i	$0.644402\pi$
$380$	1.34854	−	1.34854i	0.0691787	−	0.0691787i
$381$	−4.41617	+	4.41617i	−0.226247	+	0.226247i
$382$			13.9110i			0.711749i
$383$			17.3523i			0.886661i	0.896358	+	0.443331i	$0.146203\pi$
$383$			17.3523i			0.886661i	−0.896358	+	0.443331i	$0.853797\pi$
$384$	2.96372	−	2.96372i	0.151241	−	0.151241i
$385$	6.28351	−	6.28351i	0.320237	−	0.320237i
$386$	−9.52825	−	9.52825i	−0.484975	−	0.484975i
$387$	−23.6407			−1.20172
$388$	−6.32965	−	6.32965i	−0.321339	−	0.321339i
$389$		−	19.4510i		−	0.986205i	−0.869971	−	0.493103i	$-0.835863\pi$
$389$		−	19.4510i		−	0.986205i	0.869971	−	0.493103i	$-0.164137\pi$
$390$	10.1899			0.515987
$391$	5.79010	−	0.240464i	0.292818	−	0.0121608i
$392$	3.18085			0.160657
$393$			5.51720i			0.278306i
$394$	−0.973970	−	0.973970i	−0.0490679	−	0.0490679i
$395$	−8.97276			−0.451468
$396$	5.93851	+	5.93851i	0.298421	+	0.298421i
$397$	−3.36574	+	3.36574i	−0.168922	+	0.168922i	−0.786505	−	0.617584i	$-0.788112\pi$
$397$	−3.36574	+	3.36574i	−0.168922	+	0.168922i	0.617584	+	0.786505i	$0.288112\pi$
$398$	17.3219	−	17.3219i	0.868270	−	0.868270i
$399$			15.8488i			0.793434i
$400$		−	2.00814i		−	0.100407i
$401$	17.1148	−	17.1148i	0.854672	−	0.854672i	−0.136032	−	0.990704i	$-0.543435\pi$
$401$	17.1148	−	17.1148i	0.854672	−	0.854672i	0.990704	+	0.136032i	$0.0434350\pi$
$402$	4.11362	−	4.11362i	0.205169	−	0.205169i
$403$	−24.3171	−	24.3171i	−1.21132	−	1.21132i
$404$	−3.05110			−0.151798
$405$	−5.99807	−	5.99807i	−0.298047	−	0.298047i
$406$			2.34214i			0.116239i
$407$	40.0385			1.98463
$408$	−31.4655	+	1.30677i	−1.55777	+	0.0646947i
$409$	18.2463			0.902221			0.451111	−	0.892468i	$-0.351028\pi$
$409$	18.2463			0.902221			0.451111	+	0.892468i	$0.351028\pi$
$410$		−	10.7518i		−	0.530995i
$411$	38.9078	+	38.9078i	1.91918	+	1.91918i
$412$	5.89901			0.290624
$413$	−2.42268	−	2.42268i	−0.119212	−	0.119212i
$414$	3.54365	−	3.54365i	0.174161	−	0.174161i
$415$	1.78672	−	1.78672i	0.0877066	−	0.0877066i
$416$		−	14.1655i		−	0.694522i
$417$		−	34.4733i		−	1.68816i
$418$	7.57784	−	7.57784i	0.370644	−	0.370644i
$419$	1.23229	−	1.23229i	0.0602015	−	0.0602015i	−0.676365	−	0.736567i	$-0.736446\pi$
$419$	1.23229	−	1.23229i	0.0602015	−	0.0602015i	0.736567	+	0.676365i	$0.236446\pi$
$420$	−3.12889	−	3.12889i	−0.152674	−	0.152674i
$421$	−37.0251			−1.80449			−0.902247	−	0.431220i	$-0.858083\pi$
$421$	−37.0251			−1.80449			−0.902247	+	0.431220i	$0.858083\pi$
$422$	13.4570	+	13.4570i	0.655076	+	0.655076i
$423$		−	17.1681i		−	0.834743i
$424$	−39.8273			−1.93418
$425$	−2.79199	+	3.03394i	−0.135431	+	0.147168i
$426$	−34.3944			−1.66641
$427$			2.77894i			0.134482i
$428$	−4.54095	−	4.54095i	−0.219495	−	0.219495i
$429$	−32.8920			−1.58804
$430$	−5.95555	−	5.95555i	−0.287202	−	0.287202i
$431$	21.4877	−	21.4877i	1.03503	−	1.03503i	0.0356645	−	0.999364i	$-0.488645\pi$
$431$	21.4877	−	21.4877i	1.03503	−	1.03503i	0.999364	−	0.0356645i	$-0.0113548\pi$
$432$	−0.576612	+	0.576612i	−0.0277423	+	0.0277423i
$433$			15.8246i			0.760483i	0.924887	+	0.380242i	$0.124159\pi$
$433$			15.8246i			0.760483i	−0.924887	+	0.380242i	$0.875841\pi$
$434$		−	25.9970i		−	1.24790i
$435$	−1.49354	+	1.49354i	−0.0716096	+	0.0716096i
$436$	7.38590	−	7.38590i	0.353720	−	0.353720i
$437$	2.59751	+	2.59751i	0.124256	+	0.124256i
$438$	−4.12967			−0.197323
$439$	−2.94661	−	2.94661i	−0.140634	−	0.140634i	0.633285	−	0.773919i	$-0.281706\pi$
$439$	−2.94661	−	2.94661i	−0.140634	−	0.140634i	−0.773919	+	0.633285i	$0.781706\pi$
$440$			11.1928i			0.533597i
$441$	−3.27078			−0.155751
$442$	11.4596	−	12.4527i	0.545077	−	0.592313i
$443$	15.7201			0.746884			0.373442	−	0.927654i	$-0.378177\pi$
$443$	15.7201			0.746884			0.373442	+	0.927654i	$0.378177\pi$
$444$		−	19.9373i		−	0.946181i
$445$	1.17643	+	1.17643i	0.0557683	+	0.0557683i
$446$	−10.8348			−0.513043
$447$	20.4448	+	20.4448i	0.967004	+	0.967004i
$448$	14.5088	−	14.5088i	0.685476	−	0.685476i
$449$	−11.7004	+	11.7004i	−0.552176	+	0.552176i	−0.927068	−	0.374892i	$-0.877680\pi$
$449$	−11.7004	+	11.7004i	−0.552176	+	0.552176i	0.374892	+	0.927068i	$0.377680\pi$
$450$			3.56558i			0.168083i
$451$			34.7057i			1.63423i
$452$	−5.91300	+	5.91300i	−0.278124	+	0.278124i
$453$	−4.96335	+	4.96335i	−0.233199	+	0.233199i
$454$	−1.41803	−	1.41803i	−0.0665515	−	0.0665515i
$455$	8.89503			0.417005
$456$	−14.1158	−	14.1158i	−0.661031	−	0.661031i
$457$			1.42830i			0.0668131i	0.999442	+	0.0334066i	$0.0106356\pi$
$457$			1.42830i			0.0668131i	−0.999442	+	0.0334066i	$0.989364\pi$
$458$	−18.8705			−0.881761
$459$	1.67284	−	0.0694735i	0.0780816	−	0.00324275i
$460$	−1.02560			−0.0478191
$461$		−	11.1662i		−	0.520062i	−0.965600	−	0.260031i	$-0.916267\pi$
$461$		−	11.1662i		−	0.520062i	0.965600	−	0.260031i	$-0.0837327\pi$
$462$	−17.5821	−	17.5821i	−0.817995	−	0.817995i
$463$	−29.2204			−1.35799			−0.678994	−	0.734144i	$-0.737584\pi$
$463$	−29.2204			−1.35799			−0.678994	+	0.734144i	$0.737584\pi$
$464$	−1.20807	−	1.20807i	−0.0560835	−	0.0560835i
$465$	16.5778	−	16.5778i	0.768775	−	0.768775i
$466$	10.4291	−	10.4291i	0.483119	−	0.483119i
$467$		−	10.9388i		−	0.506187i	−0.967442	−	0.253093i	$-0.918552\pi$
$467$		−	10.9388i		−	0.506187i	0.967442	−	0.253093i	$-0.0814480\pi$
$468$			8.40664i			0.388597i
$469$	3.59088	−	3.59088i	0.165811	−	0.165811i
$470$	4.32498	−	4.32498i	0.199497	−	0.199497i
$471$	−2.40351	−	2.40351i	−0.110748	−	0.110748i
$472$	4.31552			0.198638
$473$	19.2239	+	19.2239i	0.883914	+	0.883914i
$474$			25.1070i			1.15320i
$475$	−2.61358			−0.119919
$476$	−7.34243	+	0.304933i	−0.336540	+	0.0139766i
$477$	40.9533			1.87512
$478$			26.9900i			1.23449i
$479$	−12.1620	−	12.1620i	−0.555695	−	0.555695i	0.372384	−	0.928079i	$-0.378540\pi$
$479$	−12.1620	−	12.1620i	−0.555695	−	0.555695i	−0.928079	+	0.372384i	$0.878540\pi$
$480$	9.65710			0.440784
$481$	28.3395	+	28.3395i	1.29217	+	1.29217i
$482$	−13.7803	+	13.7803i	−0.627678	+	0.627678i
$483$	6.02674	−	6.02674i	0.274226	−	0.274226i
$484$		−	1.63132i		−	0.0741509i
$485$			12.2673i			0.557031i
$486$	−17.7543	+	17.7543i	−0.805352	+	0.805352i
$487$	−18.2749	+	18.2749i	−0.828113	+	0.828113i	−0.987256	−	0.159143i	$-0.949127\pi$
$487$	−18.2749	+	18.2749i	−0.828113	+	0.828113i	0.159143	+	0.987256i	$0.449127\pi$
$488$	−2.47506	−	2.47506i	−0.112041	−	0.112041i
$489$	30.0185			1.35748
$490$	−0.823973	−	0.823973i	−0.0372233	−	0.0372233i
$491$		−	12.2373i		−	0.552261i	−0.961120	−	0.276131i	$-0.910948\pi$
$491$		−	12.2373i		−	0.552261i	0.961120	−	0.276131i	$-0.0890523\pi$
$492$	17.2818			0.779124
$493$	0.145556	+	3.50481i	0.00655550	+	0.157849i
$494$	10.7273			0.482644
$495$		−	11.5093i		−	0.517304i
$496$	13.4092	+	13.4092i	0.602092	+	0.602092i
$497$	−30.0237			−1.34675
$498$	−4.99949	−	4.99949i	−0.224033	−	0.224033i
$499$	4.53684	−	4.53684i	0.203097	−	0.203097i	−0.598229	−	0.801325i	$-0.704129\pi$
$499$	4.53684	−	4.53684i	0.203097	−	0.203097i	0.801325	+	0.598229i	$0.204129\pi$
$500$	0.515975	−	0.515975i	0.0230751	−	0.0230751i
$501$		−	14.6272i		−	0.653496i
$502$		−	20.5248i		−	0.916065i
$503$	15.0825	−	15.0825i	0.672497	−	0.672497i	−0.285794	−	0.958291i	$-0.592257\pi$
$503$	15.0825	−	15.0825i	0.672497	−	0.672497i	0.958291	+	0.285794i	$0.0922574\pi$
$504$	−16.8103	+	16.8103i	−0.748790	+	0.748790i
$505$	2.95663	+	2.95663i	0.131568	+	0.131568i
$506$	−5.76317			−0.256204
$507$	−0.459644	−	0.459644i	−0.0204135	−	0.0204135i
$508$		−	1.83565i		−	0.0814436i
$509$	14.2265			0.630577			0.315289	−	0.948996i	$-0.397899\pi$
$509$	14.2265			0.630577			0.315289	+	0.948996i	$0.397899\pi$
$510$	8.48939	+	7.81237i	0.375916	+	0.345938i
$511$	−3.60489			−0.159471
$512$			20.1677i			0.891296i
$513$	0.750456	+	0.750456i	0.0331334	+	0.0331334i
$514$	−2.90805			−0.128269
$515$	−5.71637	−	5.71637i	−0.251893	−	0.251893i
$516$	9.57257	−	9.57257i	0.421409	−	0.421409i
$517$	−13.9606	+	13.9606i	−0.613985	+	0.613985i
$518$			30.2973i			1.33119i
$519$		−	5.15278i		−	0.226182i
$520$	−7.92236	+	7.92236i	−0.347419	+	0.347419i
$521$	−17.3636	+	17.3636i	−0.760714	+	0.760714i	−0.976451	−	0.215738i	$-0.930784\pi$
$521$	−17.3636	+	17.3636i	−0.760714	+	0.760714i	0.215738	+	0.976451i	$0.430784\pi$
$522$	2.14501	+	2.14501i	0.0938846	+	0.0938846i
$523$	39.8642			1.74314			0.871570	−	0.490271i	$-0.163102\pi$
$523$	39.8642			1.74314			0.871570	+	0.490271i	$0.163102\pi$
$524$	−1.14665	−	1.14665i	−0.0500917	−	0.0500917i
$525$			6.06403i			0.264656i
$526$	10.8063			0.471175
$527$	−1.61562	−	38.9023i	−0.0703775	−	1.69461i
$528$	18.1377			0.789341
$529$			21.0245i			0.914110i
$530$	10.3169	+	10.3169i	0.448139	+	0.448139i
$531$	−4.43754			−0.192573
$532$	−3.29390	−	3.29390i	−0.142809	−	0.142809i
$533$	−24.5650	+	24.5650i	−1.06403	+	1.06403i
$534$	3.29183	−	3.29183i	0.142451	−	0.142451i
$535$			8.80071i			0.380488i
$536$			6.39644i			0.276284i
$537$	18.4983	−	18.4983i	0.798260	−	0.798260i
$538$	−5.64720	+	5.64720i	−0.243468	+	0.243468i
$539$	2.65969	+	2.65969i	0.114561	+	0.114561i
$540$	−0.296312			−0.0127512
$541$	16.1805	+	16.1805i	0.695654	+	0.695654i	0.963470	−	0.267816i	$-0.0863020\pi$
$541$	16.1805	+	16.1805i	0.695654	+	0.695654i	−0.267816	+	0.963470i	$0.586302\pi$
$542$			15.5280i			0.666985i
$543$	8.41789			0.361246
$544$	10.8604	−	11.8015i	0.465634	−	0.505986i
$545$	−14.3144			−0.613163
$546$		−	24.8895i		−	1.06517i
$547$	10.9849	+	10.9849i	0.469682	+	0.469682i	0.901812	−	0.432130i	$-0.142238\pi$
$547$	10.9849	+	10.9849i	0.469682	+	0.469682i	−0.432130	+	0.901812i	$0.642238\pi$
$548$	−16.1726			−0.690858
$549$	2.54504	+	2.54504i	0.108620	+	0.108620i
$550$	2.89941	−	2.89941i	0.123631	−	0.123631i
$551$	−1.57230	+	1.57230i	−0.0669822	+	0.0669822i
$552$			10.7354i			0.456931i
$553$			21.9165i			0.931985i
$554$	3.59834	−	3.59834i	0.152879	−	0.152879i
$555$	−19.3200	+	19.3200i	−0.820087	+	0.820087i
$556$	7.16467	+	7.16467i	0.303849	+	0.303849i
$557$	−0.980081			−0.0415274			−0.0207637	−	0.999784i	$-0.506610\pi$
$557$	−0.980081			−0.0415274			−0.0207637	+	0.999784i	$0.506610\pi$
$558$	−23.8089	−	23.8089i	−1.00791	−	1.00791i
$559$			27.2136i			1.15101i
$560$	−4.90501			−0.207274
$561$	−27.4028	−	25.2175i	−1.15695	−	1.06468i
$562$	−3.87908			−0.163629
$563$		−	28.8837i		−	1.21730i	−0.793437	−	0.608652i	$-0.791711\pi$
$563$		−	28.8837i		−	1.21730i	0.793437	−	0.608652i	$-0.208289\pi$
$564$	6.95170	+	6.95170i	0.292720	+	0.292720i
$565$	11.4598			0.482119
$566$	−18.7611	−	18.7611i	−0.788589	−	0.788589i
$567$	−14.6507	+	14.6507i	−0.615270	+	0.615270i
$568$	26.7406	−	26.7406i	1.12201	−	1.12201i
$569$			18.2893i			0.766729i	0.923597	+	0.383365i	$0.125235\pi$
$569$			18.2893i			0.766729i	−0.923597	+	0.383365i	$0.874765\pi$
$570$			7.31315i			0.306314i
$571$	−7.35702	+	7.35702i	−0.307882	+	0.307882i	−0.844087	−	0.536206i	$-0.819857\pi$
$571$	−7.35702	+	7.35702i	−0.307882	+	0.307882i	0.536206	+	0.844087i	$0.319857\pi$
$572$	6.83601	−	6.83601i	0.285828	−	0.285828i
$573$	21.6674	+	21.6674i	0.905168	+	0.905168i
$574$	−26.2620			−1.09616
$575$	0.993850	+	0.993850i	0.0414464	+	0.0414464i
$576$		−	26.5753i		−	1.10730i
$577$	−28.3066			−1.17842			−0.589209	−	0.807980i	$-0.700561\pi$
$577$	−28.3066			−1.17842			−0.589209	+	0.807980i	$0.700561\pi$
$578$	19.0943	−	1.58872i	0.794219	−	0.0660821i
$579$	−29.6819			−1.23354
$580$		−	0.620810i		−	0.0257777i
$581$	−4.36417	−	4.36417i	−0.181056	−	0.181056i
$582$	34.3257			1.42285
$583$	−33.3019	−	33.3019i	−1.37922	−	1.37922i
$584$	3.21070	−	3.21070i	0.132860	−	0.132860i
$585$	8.14636	−	8.14636i	0.336810	−	0.336810i
$586$		−	17.5738i		−	0.725968i
$587$			2.68137i			0.110672i	0.998468	+	0.0553360i	$0.0176230\pi$
$587$			2.68137i			0.110672i	−0.998468	+	0.0553360i	$0.982377\pi$
$588$	1.32440	−	1.32440i	0.0546174	−	0.0546174i
$589$	17.4520	−	17.4520i	0.719097	−	0.719097i
$590$	−1.11790	−	1.11790i	−0.0460233	−	0.0460233i
$591$	−3.03405			−0.124804
$592$	−15.6273	−	15.6273i	−0.642279	−	0.642279i
$593$			15.3155i			0.628934i	0.949268	+	0.314467i	$0.101826\pi$
$593$			15.3155i			0.628934i	−0.949268	+	0.314467i	$0.898174\pi$
$594$	−1.66506			−0.0683183
$595$	7.41059	+	6.81961i	0.303805	+	0.279577i
$596$	−8.49817			−0.348098
$597$		−	53.9603i		−	2.20845i
$598$	−4.07921	−	4.07921i	−0.166811	−	0.166811i
$599$	43.5243			1.77836			0.889178	−	0.457561i	$-0.151277\pi$
$599$	43.5243			1.77836			0.889178	+	0.457561i	$0.151277\pi$
$600$	−5.40094	−	5.40094i	−0.220492	−	0.220492i
$601$	21.7299	−	21.7299i	0.886381	−	0.886381i	−0.107792	−	0.994173i	$-0.534378\pi$
$601$	21.7299	−	21.7299i	0.886381	−	0.886381i	0.994173	+	0.107792i	$0.0343782\pi$
$602$	−14.5468	+	14.5468i	−0.592883	+	0.592883i
$603$		−	6.57729i		−	0.267848i
$604$		−	2.06309i		−	0.0839459i
$605$	−1.58081	+	1.58081i	−0.0642692	+	0.0642692i
$606$	8.27306	−	8.27306i	0.336070	−	0.336070i
$607$	−10.3997	−	10.3997i	−0.422112	−	0.422112i	0.463818	−	0.885930i	$-0.346479\pi$
$607$	−10.3997	−	10.3997i	−0.422112	−	0.422112i	−0.885930	+	0.463818i	$0.846479\pi$
$608$	10.1664			0.412301
$609$	3.64806	+	3.64806i	0.147827	+	0.147827i
$610$			1.28229i			0.0519184i
$611$	−19.7628			−0.799516
$612$	−6.44517	+	7.00370i	−0.260531	+	0.283108i
$613$	23.6535			0.955354			0.477677	−	0.878535i	$-0.341479\pi$
$613$	23.6535			0.955354			0.477677	+	0.878535i	$0.341479\pi$
$614$		−	24.4067i		−	0.984974i
$615$	−16.7467	−	16.7467i	−0.675294	−	0.675294i
$616$	27.3392			1.10153
$617$	7.10492	+	7.10492i	0.286033	+	0.286033i	0.835509	−	0.549476i	$-0.185173\pi$
$617$	7.10492	+	7.10492i	0.286033	+	0.286033i	−0.549476	+	0.835509i	$0.685173\pi$
$618$	−15.9952	+	15.9952i	−0.643421	+	0.643421i
$619$	−24.3145	+	24.3145i	−0.977281	+	0.977281i	−0.999748	−	0.0224668i	$-0.992848\pi$
$619$	−24.3145	+	24.3145i	−0.977281	+	0.977281i	0.0224668	+	0.999748i	$0.492848\pi$
$620$			6.89079i			0.276741i
$621$		−	0.570743i		−	0.0229031i
$622$	−7.06467	+	7.06467i	−0.283268	+	0.283268i
$623$	2.87351	−	2.87351i	0.115125	−	0.115125i
$624$	12.8380	+	12.8380i	0.513930	+	0.513930i
$625$	−1.00000			−0.0400000
$626$	13.6393	+	13.6393i	0.545136	+	0.545136i
$627$		−	23.6060i		−	0.942735i
$628$	0.999052			0.0398665
$629$	1.88287	+	45.3373i	0.0750749	+	1.80772i
$630$	8.70915			0.346981
$631$		−	8.25061i		−	0.328451i	−0.986423	−	0.164226i	$-0.947487\pi$
$631$		−	8.25061i		−	0.328451i	0.986423	−	0.164226i	$-0.0525125\pi$
$632$	−19.5200	−	19.5200i	−0.776462	−	0.776462i
$633$	41.9204			1.66619
$634$	−8.22796	−	8.22796i	−0.326774	−	0.326774i
$635$	−1.77881	+	1.77881i	−0.0705900	+	0.0705900i
$636$	−16.5828	+	16.5828i	−0.657550	+	0.657550i
$637$			3.76510i			0.149179i
$638$		−	3.48851i		−	0.138111i
$639$	−27.4967	+	27.4967i	−1.08775	+	1.08775i
$640$	1.19377	−	1.19377i	0.0471879	−	0.0471879i
$641$	12.1786	+	12.1786i	0.481024	+	0.481024i	0.905459	−	0.424434i	$-0.139527\pi$
$641$	12.1786	+	12.1786i	0.481024	+	0.481024i	−0.424434	+	0.905459i	$0.639527\pi$
$642$	24.6256			0.971895
$643$	−8.88071	−	8.88071i	−0.350221	−	0.350221i	0.509971	−	0.860192i	$-0.329656\pi$
$643$	−8.88071	−	8.88071i	−0.350221	−	0.350221i	−0.860192	+	0.509971i	$0.829656\pi$
$644$			2.50510i			0.0987149i
$645$	−18.5524			−0.730499
$646$	8.93708	+	8.22436i	0.351625	+	0.323583i
$647$	−3.62337			−0.142449			−0.0712247	−	0.997460i	$-0.522691\pi$
$647$	−3.62337			−0.142449			−0.0712247	+	0.997460i	$0.522691\pi$
$648$		−	26.0972i		−	1.02520i
$649$	3.60846	+	3.60846i	0.141645	+	0.141645i
$650$	4.10445			0.160990
$651$	−40.4922	−	40.4922i	−1.58701	−	1.58701i
$652$	−6.23881	+	6.23881i	−0.244331	+	0.244331i
$653$	6.89142	−	6.89142i	0.269682	−	0.269682i	−0.559290	−	0.828972i	$-0.688926\pi$
$653$	6.89142	−	6.89142i	0.269682	−	0.269682i	0.828972	+	0.559290i	$0.188926\pi$
$654$			40.0538i			1.56623i
$655$			2.22230i			0.0868325i
$656$	13.5459	−	13.5459i	0.528879	−	0.528879i
$657$	−3.30148	+	3.30148i	−0.128803	+	0.128803i
$658$	−10.5640	−	10.5640i	−0.411829	−	0.411829i
$659$	−7.19930			−0.280445			−0.140222	−	0.990120i	$-0.544782\pi$
$659$	−7.19930			−0.280445			−0.140222	+	0.990120i	$0.544782\pi$
$660$	4.66033	+	4.66033i	0.181403	+	0.181403i
$661$			11.0362i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$661$			11.0362i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$662$	−7.40181			−0.287680
$663$	−1.54679	−	37.2450i	−0.0600725	−	1.44648i
$664$	7.77391			0.301686
$665$			6.38383i			0.247554i
$666$	27.7473	+	27.7473i	1.07519	+	1.07519i
$667$	1.19578			0.0463007
$668$	3.04001	+	3.04001i	0.117621	+	0.117621i
$669$	−16.8760	+	16.8760i	−0.652463	+	0.652463i
$670$	1.65695	−	1.65695i	0.0640135	−	0.0640135i
$671$		−	4.13909i		−	0.159788i
$672$		−	23.5881i		−	0.909929i
$673$	20.8675	−	20.8675i	0.804382	−	0.804382i	−0.179395	−	0.983777i	$-0.557414\pi$
$673$	20.8675	−	20.8675i	0.804382	−	0.804382i	0.983777	+	0.179395i	$0.0574141\pi$
$674$	−24.0493	+	24.0493i	−0.926343	+	0.926343i
$675$	0.287137	+	0.287137i	0.0110519	+	0.0110519i
$676$	0.191058			0.00734837
$677$	0.394531	+	0.394531i	0.0151631	+	0.0151631i	0.714648	−	0.699485i	$-0.246587\pi$
$677$	0.394531	+	0.394531i	0.0151631	+	0.0151631i	−0.699485	+	0.714648i	$0.746587\pi$
$678$		−	32.0662i		−	1.23150i
$679$	29.9637			1.14990
$680$	−12.6741	+	0.526360i	−0.486031	+	0.0201850i
$681$	−4.41737			−0.169274
$682$			38.7213i			1.48272i
$683$	−25.5664	−	25.5664i	−0.978272	−	0.978272i	0.0214974	−	0.999769i	$-0.493157\pi$
$683$	−25.5664	−	25.5664i	−0.978272	−	0.978272i	−0.999769	+	0.0214974i	$0.993157\pi$
$684$	−6.03332			−0.230690
$685$	15.6718	+	15.6718i	0.598790	+	0.598790i
$686$	−15.6390	+	15.6390i	−0.597101	+	0.597101i
$687$	−29.3922	+	29.3922i	−1.12138	+	1.12138i
$688$		−	15.0064i		−	0.572115i
$689$		−	47.1427i		−	1.79599i
$690$	2.78093	−	2.78093i	0.105868	−	0.105868i
$691$	28.1588	−	28.1588i	1.07121	−	1.07121i	0.0739501	−	0.997262i	$-0.476439\pi$
$691$	28.1588	−	28.1588i	1.07121	−	1.07121i	0.997262	−	0.0739501i	$-0.0235606\pi$
$692$	1.07091	+	1.07091i	0.0407100	+	0.0407100i
$693$	−28.1122			−1.06789
$694$	−5.61075	−	5.61075i	−0.212981	−	0.212981i
$695$		−	13.8857i		−	0.526714i
$696$	−6.49829			−0.246317
$697$	−39.2988	+	1.63209i	−1.48855	+	0.0618198i
$698$	−39.9431			−1.51187
$699$		−	32.4881i		−	1.22881i
$700$	−1.26030	−	1.26030i	−0.0476349	−	0.0476349i
$701$	20.0299			0.756520			0.378260	−	0.925699i	$-0.376522\pi$
$701$	20.0299			0.756520			0.378260	+	0.925699i	$0.376522\pi$
$702$	−1.17854	−	1.17854i	−0.0444812	−	0.0444812i
$703$	−20.3388	+	20.3388i	−0.767094	+	0.767094i
$704$	−21.6101	+	21.6101i	−0.814463	+	0.814463i
$705$		−	13.4729i		−	0.507420i
$706$			9.63277i			0.362534i
$707$	7.22175	−	7.22175i	0.271602	−	0.271602i
$708$	1.79684	−	1.79684i	0.0675295	−	0.0675295i
$709$	−6.86493	−	6.86493i	−0.257818	−	0.257818i	0.566348	−	0.824166i	$-0.308356\pi$
$709$	−6.86493	−	6.86493i	−0.257818	−	0.257818i	−0.824166	+	0.566348i	$0.808356\pi$
$710$	−13.8539			−0.519927
$711$	20.0719	+	20.0719i	0.752753	+	0.752753i
$712$			5.11859i			0.191827i
$713$	−13.2727			−0.497068
$714$	19.0822	−	20.7359i	0.714133	−	0.776020i
$715$	−13.2487			−0.495474
$716$			7.68909i			0.287355i
$717$	42.0388	+	42.0388i	1.56997	+	1.56997i
$718$	22.8615			0.853182
$719$	14.7143	+	14.7143i	0.548750	+	0.548750i	0.926079	−	0.377329i	$-0.123157\pi$
$719$	14.7143	+	14.7143i	0.548750	+	0.548750i	−0.377329	+	0.926079i	$0.623157\pi$
$720$	−4.49216	+	4.49216i	−0.167413	+	0.167413i
$721$	−13.9626	+	13.9626i	−0.519994	+	0.519994i
$722$		−	13.7156i		−	0.510443i
$723$			42.9277i			1.59650i
$724$	−1.74951	+	1.74951i	−0.0650200	+	0.0650200i
$725$	−0.601589	+	0.601589i	−0.0223425	+	0.0223425i
$726$	4.42333	+	4.42333i	0.164165	+	0.164165i
$727$	39.1557			1.45220			0.726102	−	0.687587i	$-0.241330\pi$
$727$	39.1557			1.45220			0.726102	+	0.687587i	$0.241330\pi$
$728$	19.3509	+	19.3509i	0.717191	+	0.717191i
$729$			29.8595i			1.10591i
$730$	−1.66341			−0.0615656
$731$	−20.8640	+	22.6720i	−0.771682	+	0.838556i
$732$	−2.06107			−0.0761793
$733$		−	12.9215i		−	0.477265i	−0.971110	−	0.238633i	$-0.923301\pi$
$733$		−	12.9215i		−	0.477265i	0.971110	−	0.238633i	$-0.0766992\pi$
$734$	10.1392	+	10.1392i	0.374244	+	0.374244i
$735$	−2.56679			−0.0946776
$736$	−3.86591	−	3.86591i	−0.142499	−	0.142499i
$737$	−5.34844	+	5.34844i	−0.197012	+	0.197012i
$738$	−24.0516	+	24.0516i	−0.885352	+	0.885352i
$739$		−	37.9866i		−	1.39736i	−0.715434	−	0.698680i	$-0.753771\pi$
$739$		−	37.9866i		−	1.39736i	0.715434	−	0.698680i	$-0.246229\pi$
$740$		−	8.03063i		−	0.295212i
$741$	16.7085	−	16.7085i	0.613803	−	0.613803i
$742$	25.1998	−	25.1998i	0.925112	−	0.925112i
$743$	8.65513	+	8.65513i	0.317526	+	0.317526i	0.847816	−	0.530290i	$-0.177917\pi$
$743$	8.65513	+	8.65513i	0.317526	+	0.317526i	−0.530290	+	0.847816i	$0.677917\pi$
$744$	72.1288			2.64437
$745$	8.23505	+	8.23505i	0.301709	+	0.301709i
$746$			12.5617i			0.459916i
$747$	−7.99371			−0.292474
$748$	10.9362	−	0.454183i	0.399867	−	0.0166066i
$749$	21.4963			0.785457
$750$			2.79814i			0.102174i
$751$	−9.97504	−	9.97504i	−0.363995	−	0.363995i	0.501287	−	0.865281i	$-0.332860\pi$
$751$	−9.97504	−	9.97504i	−0.363995	−	0.363995i	−0.865281	+	0.501287i	$0.832860\pi$
$752$	10.8978			0.397403
$753$	−31.9688	−	31.9688i	−1.16501	−	1.16501i
$754$	2.46919	−	2.46919i	0.0899227	−	0.0899227i
$755$	−1.99921	+	1.99921i	−0.0727588	+	0.0727588i
$756$			0.723760i			0.0263229i
$757$		−	0.782070i		−	0.0284248i	−0.999899	−	0.0142124i	$-0.995476\pi$
$757$		−	0.782070i		−	0.0284248i	0.999899	−	0.0142124i	$-0.00452410\pi$
$758$	10.1064	−	10.1064i	0.367081	−	0.367081i
$759$	−8.97654	+	8.97654i	−0.325828	+	0.325828i
$760$	−5.68576	−	5.68576i	−0.206244	−	0.206244i
$761$	2.86350			0.103802			0.0519009	−	0.998652i	$-0.483472\pi$
$761$	2.86350			0.103802			0.0519009	+	0.998652i	$0.483472\pi$
$762$	4.97736	+	4.97736i	0.180311	+	0.180311i
$763$			34.9639i			1.26578i
$764$	−9.00636			−0.325839
$765$	13.0325	−	0.541242i	0.471190	−	0.0195686i
$766$	19.5574			0.706636
$767$			5.10819i			0.184446i
$768$	26.1535	+	26.1535i	0.943734	+	0.943734i
$769$	38.6633			1.39423			0.697117	−	0.716957i	$-0.254466\pi$
$769$	38.6633			1.39423			0.697117	+	0.716957i	$0.254466\pi$
$770$	−7.08200	−	7.08200i	−0.255217	−	0.255217i
$771$	−4.52950	+	4.52950i	−0.163126	+	0.163126i
$772$	6.16885	−	6.16885i	0.222022	−	0.222022i
$773$		−	37.9989i		−	1.36672i	−0.730080	−	0.683362i	$-0.760517\pi$
$773$		−	37.9989i		−	1.36672i	0.730080	−	0.683362i	$-0.239483\pi$
$774$			26.6449i			0.957730i
$775$	6.67744	−	6.67744i	0.239861	−	0.239861i
$776$	−26.6872	+	26.6872i	−0.958016	+	0.958016i
$777$	47.1902	+	47.1902i	1.69294	+	1.69294i
$778$	−21.9228			−0.785969
$779$	−17.6299	−	17.6299i	−0.631656	−	0.631656i
$780$			6.59723i			0.236219i
$781$	44.7188			1.60017
$782$	−0.271021	−	6.52589i	−0.00969171	−	0.233365i
$783$	0.345477			0.0123464
$784$		−	2.07620i		−	0.0741499i
$785$	−0.968120	−	0.968120i	−0.0345537	−	0.0345537i
$786$	6.21831			0.221800
$787$	−25.0127	−	25.0127i	−0.891606	−	0.891606i	0.103068	−	0.994674i	$-0.467134\pi$
$787$	−25.0127	−	25.0127i	−0.891606	−	0.891606i	−0.994674	+	0.103068i	$0.967134\pi$
$788$	0.630574	−	0.630574i	0.0224633	−	0.0224633i
$789$	16.8315	−	16.8315i	0.599217	−	0.599217i
$790$			10.1130i			0.359804i
$791$		−	27.9914i		−	0.995259i
$792$	25.0381	−	25.0381i	0.889691	−	0.889691i
$793$	2.92968	−	2.92968i	0.104036	−	0.104036i
$794$	3.79344	+	3.79344i	0.134624	+	0.134624i
$795$	32.1387			1.13984
$796$	11.2147	+	11.2147i	0.397494	+	0.397494i
$797$			26.7826i			0.948688i	0.880340	+	0.474344i	$0.157315\pi$
$797$			26.7826i			0.948688i	−0.880340	+	0.474344i	$0.842685\pi$
$798$	17.8628			0.632337
$799$	−16.4647	−	15.1516i	−0.582479	−	0.536027i
$800$	3.88983			0.137526
$801$		−	5.26331i		−	0.185970i
$802$	−19.2897	−	19.2897i	−0.681142	−	0.681142i
$803$	5.36931			0.189479
$804$	2.66327	+	2.66327i	0.0939263	+	0.0939263i
$805$	2.42754	−	2.42754i	0.0855596	−	0.0855596i
$806$	−27.4072	+	27.4072i	−0.965378	+	0.965378i
$807$			17.5918i			0.619262i
$808$			12.8641i			0.452558i
$809$	−38.1898	+	38.1898i	−1.34268	+	1.34268i	−0.449303	+	0.893379i	$0.648328\pi$
$809$	−38.1898	+	38.1898i	−1.34268	+	1.34268i	−0.893379	+	0.449303i	$0.851672\pi$
$810$	−6.76028	+	6.76028i	−0.237532	+	0.237532i
$811$	−37.3327	−	37.3327i	−1.31093	−	1.31093i	−0.920730	−	0.390200i	$-0.872406\pi$
$811$	−37.3327	−	37.3327i	−1.31093	−	1.31093i	−0.390200	−	0.920730i	$-0.627594\pi$
$812$	−1.51637			−0.0532141
$813$	24.1860	+	24.1860i	0.848239	+	0.848239i
$814$		−	45.1264i		−	1.58168i
$815$	12.0913			0.423540
$816$	0.852952	+	20.5381i	0.0298593	+	0.718977i
$817$	−19.5308			−0.683295
$818$		−	20.5650i		−	0.719037i
$819$	−19.8980	−	19.8980i	−0.695292	−	0.695292i
$820$	6.96103			0.243090
$821$	−8.42042	−	8.42042i	−0.293875	−	0.293875i	0.544734	−	0.838609i	$-0.316631\pi$
$821$	−8.42042	−	8.42042i	−0.293875	−	0.293875i	−0.838609	+	0.544734i	$0.816631\pi$
$822$	43.8520	−	43.8520i	1.52951	−	1.52951i
$823$	−27.9601	+	27.9601i	−0.974627	+	0.974627i	−0.999686	−	0.0250590i	$-0.992023\pi$
$823$	−27.9601	+	27.9601i	−0.974627	+	0.974627i	0.0250590	+	0.999686i	$0.492023\pi$
$824$		−	24.8716i		−	0.866443i
$825$		−	9.03208i		−	0.314457i
$826$	−2.73054	+	2.73054i	−0.0950078	+	0.0950078i
$827$	−12.9612	+	12.9612i	−0.450704	+	0.450704i	−0.895588	−	0.444884i	$-0.853245\pi$
$827$	−12.9612	+	12.9612i	−0.450704	+	0.450704i	0.444884	+	0.895588i	$0.353245\pi$
$828$	2.29425	+	2.29425i	0.0797309	+	0.0797309i
$829$	−39.4065			−1.36864			−0.684322	−	0.729180i	$-0.739902\pi$
$829$	−39.4065			−1.36864			−0.684322	+	0.729180i	$0.739902\pi$
$830$	−2.01377	−	2.01377i	−0.0698990	−	0.0698990i
$831$		−	11.2093i		−	0.388847i
$832$	−30.5916			−1.06057
$833$	−2.88661	+	3.13676i	−0.100015	+	0.108682i
$834$	−38.8540			−1.34541
$835$		−	5.89177i		−	0.203893i
$836$	4.90610	+	4.90610i	0.169681	+	0.169681i
$837$	−3.83468			−0.132546
$838$	−1.38889	−	1.38889i	−0.0479783	−	0.0479783i
$839$	−14.5709	+	14.5709i	−0.503043	+	0.503043i	−0.912382	−	0.409339i	$-0.865759\pi$
$839$	−14.5709	+	14.5709i	−0.503043	+	0.503043i	0.409339	+	0.912382i	$0.365759\pi$
$840$	−13.1921	+	13.1921i	−0.455171	+	0.455171i
$841$		−	28.2762i		−	0.975041i
$842$			41.7301i			1.43812i
$843$	−6.04194	+	6.04194i	−0.208095	+	0.208095i
$844$	−8.71241	+	8.71241i	−0.299894	+	0.299894i
$845$	−0.185142	−	0.185142i	−0.00636909	−	0.00636909i
$846$	−19.3498			−0.665259
$847$	3.86123	+	3.86123i	0.132673	+	0.132673i
$848$			25.9960i			0.892706i
$849$	−58.4436			−2.00578
$850$	3.41948	+	3.14678i	0.117287	+	0.107934i
$851$	15.4683			0.530245
$852$		−	22.2679i		−	0.762884i
$853$	5.82880	+	5.82880i	0.199574	+	0.199574i	0.799817	−	0.600243i	$-0.204930\pi$
$853$	5.82880	+	5.82880i	0.199574	+	0.199574i	−0.600243	+	0.799817i	$0.704930\pi$
$854$	3.13207			0.107177
$855$	5.84652	+	5.84652i	0.199947	+	0.199947i
$856$	−19.1457	+	19.1457i	−0.654386	+	0.654386i
$857$	19.6053	−	19.6053i	0.669703	−	0.669703i	−0.287944	−	0.957647i	$-0.592972\pi$
$857$	19.6053	−	19.6053i	0.669703	−	0.669703i	0.957647	+	0.287944i	$0.0929716\pi$
$858$			37.0717i			1.26561i
$859$		−	7.00671i		−	0.239066i	−0.992830	−	0.119533i	$-0.961860\pi$
$859$		−	7.00671i		−	0.239066i	0.992830	−	0.119533i	$-0.0381397\pi$
$860$	3.85578	−	3.85578i	0.131481	−	0.131481i
$861$	−40.9049	+	40.9049i	−1.39404	+	1.39404i
$862$	−24.2183	−	24.2183i	−0.824879	−	0.824879i
$863$	29.4176			1.00139			0.500693	−	0.865625i	$-0.333079\pi$
$863$	29.4176			1.00139			0.500693	+	0.865625i	$0.333079\pi$
$864$	−1.11692	−	1.11692i	−0.0379983	−	0.0379983i
$865$		−	2.07551i		−	0.0705696i
$866$	17.8356			0.606077
$867$	27.2662	−	32.2153i	0.926008	−	1.09409i
$868$	16.8312			0.571287
$869$		−	32.6436i		−	1.10736i
$870$	1.68333	+	1.68333i	0.0570702	+	0.0570702i
$871$	−7.57133			−0.256545
$872$	−31.1406	−	31.1406i	−1.05455	−	1.05455i
$873$	27.4418	−	27.4418i	0.928763	−	0.928763i
$874$	2.92759	−	2.92759i	0.0990271	−	0.0990271i
$875$			2.44256i			0.0825737i
$876$		−	2.67366i		−	0.0903347i
$877$	−36.4433	+	36.4433i	−1.23060	+	1.23060i	−0.266872	+	0.963732i	$0.585990\pi$
$877$	−36.4433	+	36.4433i	−1.23060	+	1.23060i	−0.963732	+	0.266872i	$0.914010\pi$
$878$	−3.32106	+	3.32106i	−0.112080	+	0.112080i
$879$	−27.3725	−	27.3725i	−0.923250	−	0.923250i
$880$	7.30577			0.246277
$881$	−33.0055	−	33.0055i	−1.11198	−	1.11198i	−0.992882	−	0.119102i	$-0.961998\pi$
$881$	−33.0055	−	33.0055i	−1.11198	−	1.11198i	−0.119102	−	0.992882i	$-0.538002\pi$
$882$			3.68642i			0.124128i
$883$	9.95880			0.335140			0.167570	−	0.985860i	$-0.446408\pi$
$883$	9.95880			0.335140			0.167570	+	0.985860i	$0.446408\pi$
$884$	8.06219	+	7.41924i	0.271161	+	0.249536i
$885$	−3.48242			−0.117060
$886$		−	17.7177i		−	0.595239i
$887$	13.3201	+	13.3201i	0.447246	+	0.447246i	0.894438	−	0.447192i	$-0.147576\pi$
$887$	13.3201	+	13.3201i	0.447246	+	0.447246i	−0.447192	+	0.894438i	$0.647576\pi$
$888$	−84.0601			−2.82087
$889$	4.34486	+	4.34486i	0.145722	+	0.145722i
$890$	1.32593	−	1.32593i	0.0444453	−	0.0444453i
$891$	21.8214	−	21.8214i	0.731046	−	0.731046i
$892$		−	7.01475i		−	0.234871i
$893$		−	14.1834i		−	0.474631i
$894$	23.0428	−	23.0428i	0.770667	−	0.770667i
$895$	7.45102	−	7.45102i	0.249060	−	0.249060i
$896$	−2.91586	−	2.91586i	−0.0974119	−	0.0974119i
$897$	−12.7073			−0.424285
$898$	13.1872	+	13.1872i	0.440064	+	0.440064i
$899$		−	8.03414i		−	0.267954i
$900$	−2.30845			−0.0769484
$901$	36.1432	−	39.2753i	1.20410	−	1.30845i
$902$	39.1160			1.30242
$903$			45.3153i			1.50800i
$904$	24.9306	+	24.9306i	0.829178	+	0.829178i
$905$	3.39068			0.112710
$906$	5.59407	+	5.59407i	0.185851	+	0.185851i
$907$	18.9094	−	18.9094i	0.627876	−	0.627876i	−0.319658	−	0.947533i	$-0.603568\pi$
$907$	18.9094	−	18.9094i	0.627876	−	0.627876i	0.947533	+	0.319658i	$0.103568\pi$
$908$	0.918072	−	0.918072i	0.0304673	−	0.0304673i
$909$		−	13.2278i		−	0.438740i
$910$		−	10.0254i		−	0.332338i
$911$	7.34196	−	7.34196i	0.243250	−	0.243250i	−0.574943	−	0.818193i	$-0.694976\pi$
$911$	7.34196	−	7.34196i	0.243250	−	0.243250i	0.818193	+	0.574943i	$0.194976\pi$
$912$	−9.21362	+	9.21362i	−0.305093	+	0.305093i
$913$	6.50023	+	6.50023i	0.215126	+	0.215126i
$914$	1.60980			0.0532476
$915$	1.99726	+	1.99726i	0.0660273	+	0.0660273i
$916$		−	12.2173i		−	0.403670i
$917$	5.42811			0.179252
$918$	−0.0783019	−	1.88542i	−0.00258435	−	0.0622282i
$919$	20.4602			0.674919			0.337460	−	0.941340i	$-0.390432\pi$
$919$	20.4602			0.674919			0.337460	+	0.941340i	$0.390432\pi$
$920$			4.32418i			0.142564i
$921$	−38.0151	−	38.0151i	−1.25264	−	1.25264i
$922$	−12.5852			−0.414470
$923$	31.6523	+	31.6523i	1.04185	+	1.04185i
$924$	11.3832	−	11.3832i	0.374478	−	0.374478i
$925$	−7.78199	+	7.78199i	−0.255870	+	0.255870i
$926$			32.9337i			1.08227i
$927$			25.5748i			0.839986i
$928$	2.34008	−	2.34008i	0.0768169	−	0.0768169i
$929$	3.22981	−	3.22981i	0.105966	−	0.105966i	−0.652136	−	0.758102i	$-0.726127\pi$
$929$	3.22981	−	3.22981i	0.105966	−	0.105966i	0.758102	+	0.652136i	$0.226127\pi$
$930$	−18.6844	−	18.6844i	−0.612685	−	0.612685i
$931$	−2.70215			−0.0885595
$932$	6.75208	+	6.75208i	0.221172	+	0.221172i
$933$			22.0075i			0.720492i
$934$	−12.3288			−0.403412
$935$	−11.0377	−	10.1575i	−0.360972	−	0.332185i
$936$	35.4443			1.15853
$937$		−	2.90874i		−	0.0950243i	−0.998871	−	0.0475122i	$-0.984871\pi$
$937$		−	2.90874i		−	0.0950243i	0.998871	−	0.0475122i	$-0.0151293\pi$
$938$	−4.04720	−	4.04720i	−0.132146	−	0.132146i
$939$	42.4883			1.38655
$940$	2.80011	+	2.80011i	0.0913296	+	0.0913296i
$941$	−10.8860	+	10.8860i	−0.354872	+	0.354872i	−0.861919	−	0.507046i	$-0.830737\pi$
$941$	−10.8860	+	10.8860i	−0.354872	+	0.354872i	0.507046	+	0.861919i	$0.330737\pi$
$942$	−2.70893	+	2.70893i	−0.0882618	+	0.0882618i
$943$			13.4080i			0.436626i
$944$		−	2.81682i		−	0.0916797i
$945$	0.701351	−	0.701351i	0.0228149	−	0.0228149i
$946$	21.6667	−	21.6667i	0.704447	−	0.704447i
$947$	16.9623	+	16.9623i	0.551200	+	0.551200i	0.926787	−	0.375587i	$-0.122559\pi$
$947$	16.9623	+	16.9623i	0.551200	+	0.551200i	−0.375587	+	0.926787i	$0.622559\pi$
$948$	−16.2550			−0.527937
$949$	3.80043	+	3.80043i	0.123367	+	0.123367i
$950$			2.94570i			0.0955712i
$951$	−25.6313			−0.831151
$952$	1.28567	+	30.9574i	0.0416687	+	1.00333i
$953$	−9.31030			−0.301590			−0.150795	−	0.988565i	$-0.548183\pi$
$953$	−9.31030			−0.301590			−0.150795	+	0.988565i	$0.548183\pi$
$954$		−	46.1575i		−	1.49440i
$955$	8.72751	+	8.72751i	0.282416	+	0.282416i
$956$	−17.4740			−0.565151
$957$	−5.43360	−	5.43360i	−0.175643	−	0.175643i
$958$	−13.7075	+	13.7075i	−0.442868	+	0.442868i
$959$	38.2795	−	38.2795i	1.23611	−	1.23611i
$960$		−	20.8553i		−	0.673102i
$961$			58.1763i			1.87666i
$962$	31.9408	−	31.9408i	1.02981	−	1.02981i
$963$	19.6870	−	19.6870i	0.634404	−	0.634404i
$964$	−8.92177	−	8.92177i	−0.287351	−	0.287351i
$965$	−11.9557			−0.384868
$966$	−6.79260	−	6.79260i	−0.218548	−	0.218548i
$967$			1.29315i			0.0415848i	0.999784	+	0.0207924i	$0.00661890\pi$
$967$			1.29315i			0.0415848i	−0.999784	+	0.0207924i	$0.993381\pi$
$968$	−6.87802			−0.221068
$969$	26.7302	−	1.11011i	0.858697	−	0.0356619i
$970$	13.8262			0.443933
$971$			39.3251i			1.26200i	0.775781	+	0.631002i	$0.217356\pi$
$971$			39.3251i			1.26200i	−0.775781	+	0.631002i	$0.782644\pi$
$972$	−11.4946	−	11.4946i	−0.368690	−	0.368690i
$973$	−33.9166			−1.08732
$974$	20.5972	+	20.5972i	0.659976	+	0.659976i
$975$	6.39297	−	6.39297i	0.204739	−	0.204739i
$976$	−1.61552	+	1.61552i	−0.0517115	+	0.0517115i
$977$			53.3750i			1.70762i	0.520586	+	0.853809i	$0.325714\pi$
$977$			53.3750i			1.70762i	−0.520586	+	0.853809i	$0.674286\pi$
$978$		−	33.8331i		−	1.08186i
$979$	−4.27996	+	4.27996i	−0.136788	+	0.136788i
$980$	0.533462	−	0.533462i	0.0170408	−	0.0170408i
$981$	32.0211	+	32.0211i	1.02235	+	1.02235i
$982$	−13.7924			−0.440132
$983$	−36.1157	−	36.1157i	−1.15191	−	1.15191i	−0.986169	−	0.165742i	$-0.946998\pi$
$983$	−36.1157	−	36.1157i	−1.15191	−	1.15191i	−0.165742	−	0.986169i	$-0.553002\pi$
$984$		−	72.8641i		−	2.32282i
$985$	−1.22210			−0.0389394
$986$	3.95019	−	0.164052i	0.125800	−	0.00522449i
$987$	−32.9085			−1.04749
$988$			6.94514i			0.220954i
$989$	7.42685	+	7.42685i	0.236160	+	0.236160i
$990$	−12.9718			−0.412272
$991$	7.48752	+	7.48752i	0.237849	+	0.237849i	0.815959	−	0.578110i	$-0.196210\pi$
$991$	7.48752	+	7.48752i	0.237849	+	0.237849i	−0.578110	+	0.815959i	$0.696210\pi$
$992$	−25.9741	+	25.9741i	−0.824679	+	0.824679i
$993$	−11.5288	+	11.5288i	−0.365857	+	0.365857i
$994$			33.8390i			1.07331i
$995$		−	21.7349i		−	0.689043i
$996$	3.23680	−	3.23680i	0.102562	−	0.102562i
$997$	−2.43619	+	2.43619i	−0.0771550	+	0.0771550i	−0.744631	−	0.667476i	$-0.767375\pi$
$997$	−2.43619	+	2.43619i	−0.0771550	+	0.0771550i	0.667476	+	0.744631i	$0.267375\pi$
$998$	−5.11336	−	5.11336i	−0.161861	−	0.161861i
$999$	4.46900			0.141393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.e.a.81.3	yes	12
3.2	odd	2		765.2.k.b.676.4		12
4.3	odd	2		1360.2.bt.d.81.6		12
5.2	odd	4		425.2.j.c.149.4		12
5.3	odd	4		425.2.j.b.149.3		12
5.4	even	2		425.2.e.f.251.4		12
17.2	even	8		1445.2.a.o.1.4		6
17.4	even	4	inner	85.2.e.a.21.4	✓	12
17.8	even	8		1445.2.d.g.866.6		12
17.9	even	8		1445.2.d.g.866.5		12
17.15	even	8		1445.2.a.n.1.4		6
51.38	odd	4		765.2.k.b.361.3		12
68.55	odd	4		1360.2.bt.d.1041.6		12
85.4	even	4		425.2.e.f.276.3		12
85.19	even	8		7225.2.a.z.1.3		6
85.38	odd	4		425.2.j.c.174.4		12
85.49	even	8		7225.2.a.bb.1.3		6
85.72	odd	4		425.2.j.b.174.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	17.4	even	4	inner
85.2.e.a.81.3	yes	12	1.1	even	1	trivial
425.2.e.f.251.4		12	5.4	even	2
425.2.e.f.276.3		12	85.4	even	4
425.2.j.b.149.3		12	5.3	odd	4
425.2.j.b.174.3		12	85.72	odd	4
425.2.j.c.149.4		12	5.2	odd	4
425.2.j.c.174.4		12	85.38	odd	4
765.2.k.b.361.3		12	51.38	odd	4
765.2.k.b.676.4		12	3.2	odd	2
1360.2.bt.d.81.6		12	4.3	odd	2
1360.2.bt.d.1041.6		12	68.55	odd	4
1445.2.a.n.1.4		6	17.15	even	8
1445.2.a.o.1.4		6	17.2	even	8
1445.2.d.g.866.5		12	17.9	even	8
1445.2.d.g.866.6		12	17.8	even	8
7225.2.a.z.1.3		6	85.19	even	8
7225.2.a.bb.1.3		6	85.49	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.12708i q^{2} +(-1.75550 - 1.75550i) q^{3} +0.729699 q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.97858 + 1.97858i) q^{6} +(-1.72715 + 1.72715i) q^{7} -3.07658i q^{8} +3.16356i q^{9} +(-0.796963 + 0.796963i) q^{10} +(2.57251 - 2.57251i) q^{11} +(-1.28099 - 1.28099i) q^{12} +3.64168 q^{13} +(1.94663 + 1.94663i) q^{14} +2.48265i q^{15} -2.00814 q^{16} +(3.03394 + 2.79199i) q^{17} +3.56558 q^{18} +2.61358i q^{19} +(-0.515975 - 0.515975i) q^{20} +6.06403 q^{21} +(-2.89941 - 2.89941i) q^{22} +(0.993850 - 0.993850i) q^{23} +(-5.40094 + 5.40094i) q^{24} +1.00000i q^{25} -4.10445i q^{26} +(0.287137 - 0.287137i) q^{27} +(-1.26030 + 1.26030i) q^{28} +(0.601589 + 0.601589i) q^{29} +2.79814 q^{30} +(-6.67744 - 6.67744i) q^{31} -3.88983i q^{32} -9.03208 q^{33} +(3.14678 - 3.41948i) q^{34} +2.44256 q^{35} +2.30845i q^{36} +(7.78199 + 7.78199i) q^{37} +2.94570 q^{38} +(-6.39297 - 6.39297i) q^{39} +(-2.17547 + 2.17547i) q^{40} +(-6.74550 + 6.74550i) q^{41} -6.83463i q^{42} +7.47280i q^{43} +(1.87716 - 1.87716i) q^{44} +(2.23698 - 2.23698i) q^{45} +(-1.12014 - 1.12014i) q^{46} -5.42683 q^{47} +(3.52529 + 3.52529i) q^{48} +1.03389i q^{49} +1.12708 q^{50} +(-0.424747 - 10.2274i) q^{51} +2.65733 q^{52} -12.9453i q^{53} +(-0.323626 - 0.323626i) q^{54} -3.63808 q^{55} +(5.31372 + 5.31372i) q^{56} +(4.58814 - 4.58814i) q^{57} +(0.678037 - 0.678037i) q^{58} +1.40270i q^{59} +1.81159i q^{60} +(0.804485 - 0.804485i) q^{61} +(-7.52598 + 7.52598i) q^{62} +(-5.46396 - 5.46396i) q^{63} -8.40042 q^{64} +(-2.57506 - 2.57506i) q^{65} +10.1798i q^{66} -2.07908 q^{67} +(2.21387 + 2.03731i) q^{68} -3.48941 q^{69} -2.75295i q^{70} +(8.69168 + 8.69168i) q^{71} +9.73296 q^{72} +(1.04359 + 1.04359i) q^{73} +(8.77090 - 8.77090i) q^{74} +(1.75550 - 1.75550i) q^{75} +1.90713i q^{76} +8.88623i q^{77} +(-7.20536 + 7.20536i) q^{78} +(6.34470 - 6.34470i) q^{79} +(1.41997 + 1.41997i) q^{80} +8.48255 q^{81} +(7.60269 + 7.60269i) q^{82} +2.52680i q^{83} +4.42492 q^{84} +(-0.171086 - 4.11955i) q^{85} +8.42242 q^{86} -2.11218i q^{87} +(-7.91453 - 7.91453i) q^{88} -1.66373 q^{89} +(-2.52124 - 2.52124i) q^{90} +(-6.28973 + 6.28973i) q^{91} +(0.725212 - 0.725212i) q^{92} +23.4445i q^{93} +6.11645i q^{94} +(1.84808 - 1.84808i) q^{95} +(-6.82860 + 6.82860i) q^{96} +(-8.67432 - 8.67432i) q^{97} +1.16527 q^{98} +(8.13830 + 8.13830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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