LMFDB - Embedded newform 425.2.e.f.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(251,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("425.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.4
Root			$-3.48265i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.f.276.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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	$0.130463\pi$
$2$			1.12708i			0.796963i	−0.917176	+	0.398482i	$0.869537\pi$
$3$	1.75550	+	1.75550i	1.01354	+	1.01354i	0.999907	+	0.0136316i	$0.00433922\pi$
$3$	1.75550	+	1.75550i	1.01354	+	1.01354i	0.0136316	+	0.999907i	$0.495661\pi$
$4$	0.729699			0.364850
$5$		0			0
$5$		0			0
$6$	−1.97858	+	1.97858i	−0.807753	+	0.807753i
$7$	1.72715	−	1.72715i	0.652802	−	0.652802i	−0.300865	−	0.953667i	$-0.597275\pi$
$7$	1.72715	−	1.72715i	0.652802	−	0.652802i	0.953667	+	0.300865i	$0.0972753\pi$
$8$			3.07658i			1.08773i
$9$			3.16356i			1.05452i
$10$		0			0
$11$	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	$-0.668511\pi$
$13$	−3.64168			−1.01002			−0.505010	+	0.863113i	$0.668511\pi$
$14$	1.94663	+	1.94663i	0.520259	+	0.520259i
$15$		0			0
$16$	−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			0
$21$	6.06403			1.32328
$22$	2.89941	+	2.89941i	0.618157	+	0.618157i
$23$	−0.993850	+	0.993850i	−0.207232	+	0.207232i	−0.803090	−	0.595858i	$-0.796812\pi$
$23$	−0.993850	+	0.993850i	−0.207232	+	0.207232i	0.595858	+	0.803090i	$0.296812\pi$
$24$	−5.40094	+	5.40094i	−1.10246	+	1.10246i
$25$		0			0
$26$		−	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	$0.724830\pi$
$30$		0			0
$31$	−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
$35$		0			0
$36$			2.30845i			0.384742i
$37$	−7.78199	−	7.78199i	−1.27935	−	1.27935i	−0.941031	−	0.338320i	$-0.890141\pi$
$37$	−7.78199	−	7.78199i	−1.27935	−	1.27935i	−0.338320	−	0.941031i	$-0.609859\pi$
$38$	−2.94570			−0.477856
$39$	−6.39297	−	6.39297i	−1.02369	−	1.02369i
$40$		0			0
$41$	−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	$-0.807022\pi$
$43$		−	7.47280i		−	1.13959i	0.821786	−	0.569796i	$-0.192978\pi$
$44$	1.87716	−	1.87716i	0.282992	−	0.282992i
$45$		0			0
$46$	−1.12014	−	1.12014i	−0.165156	−	0.165156i
$47$	5.42683			0.791585			0.395792	−	0.918340i	$-0.370470\pi$
$47$	5.42683			0.791585			0.395792	+	0.918340i	$0.370470\pi$
$48$	−3.52529	−	3.52529i	−0.508832	−	0.508832i
$49$			1.03389i			0.147699i
$50$		0			0
$51$	−0.424747	−	10.2274i	−0.0594765	−	1.43213i
$52$	−2.65733			−0.368506
$53$			12.9453i			1.77817i	0.457737	+	0.889087i	$0.348660\pi$
$53$			12.9453i			1.77817i	−0.457737	+	0.889087i	$0.651340\pi$
$54$	−0.323626	−	0.323626i	−0.0440399	−	0.0440399i
$55$		0			0
$56$	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	$0.970895\pi$
$60$		0			0
$61$	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
$65$		0			0
$66$			10.1798i			1.25305i
$67$	2.07908			0.254000			0.127000	−	0.991903i	$-0.459465\pi$
$67$	2.07908			0.254000			0.127000	+	0.991903i	$0.459465\pi$
$68$	−2.21387	−	2.03731i	−0.268471	−	0.247060i
$69$	−3.48941			−0.420076
$70$		0			0
$71$	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	0.643393	−	0.765536i	$-0.277526\pi$
$73$	−1.04359	−	1.04359i	−0.122143	−	0.122143i	−0.765536	+	0.643393i	$0.777526\pi$
$74$	8.77090	−	8.77090i	1.01960	−	1.01960i
$75$		0			0
$76$			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	$0.0815821\pi$
$80$		0			0
$81$	8.48255			0.942506
$82$	−7.60269	−	7.60269i	−0.839577	−	0.839577i
$83$		−	2.52680i		−	0.277353i	−0.990338	−	0.138676i	$-0.955715\pi$
$83$		−	2.52680i		−	0.277353i	0.990338	−	0.138676i	$-0.0442848\pi$
$84$	4.42492			0.482799
$85$		0			0
$86$	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	$0.528104\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−6.82860	+	6.82860i	−0.696941	+	0.696941i
$97$	8.67432	+	8.67432i	0.880744	+	0.880744i	0.993610	−	0.112867i	$-0.0360032\pi$
$97$	8.67432	+	8.67432i	0.880744	+	0.880744i	−0.112867	+	0.993610i	$0.536003\pi$
$98$	−1.16527			−0.117710
$99$	8.13830	+	8.13830i	0.817930	+	0.817930i
$100$		0			0
$101$	−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	$-0.630392\pi$
$103$	−8.08417			−0.796557			−0.398279	+	0.917265i	$0.630392\pi$
$104$		−	11.2039i		−	1.09863i
$105$		0			0
$106$	−14.5903			−1.41714
$107$	6.22304	+	6.22304i	0.601604	+	0.601604i	0.940738	−	0.339134i	$-0.110134\pi$
$107$	6.22304	+	6.22304i	0.601604	+	0.601604i	−0.339134	+	0.940738i	$0.610134\pi$
$108$	−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	$0.00956740\pi$
$110$		0			0
$111$		−	27.3226i		−	2.59334i
$112$	−3.46836	+	3.46836i	−0.327730	+	0.327730i
$113$	8.10334	−	8.10334i	0.762298	−	0.762298i	−0.214440	−	0.976737i	$-0.568792\pi$
$113$	8.10334	−	8.10334i	0.762298	−	0.762298i	0.976737	+	0.214440i	$0.0687925\pi$
$114$	−5.17118	−	5.17118i	−0.484325	−	0.484325i
$115$		0			0
$116$	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
$120$		0			0
$121$		−	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			0
$126$	−6.15830	+	6.15830i	−0.548625	+	0.548625i
$127$			2.51562i			0.223225i	0.993752	+	0.111613i	$0.0356015\pi$
$127$			2.51562i			0.223225i	−0.993752	+	0.111613i	$0.964398\pi$
$128$		−	1.68825i		−	0.149221i
$129$	13.1185	−	13.1185i	1.15502	−	1.15502i
$130$		0			0
$131$	−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			0
$136$	8.58977	−	9.33416i	0.736567	−	0.800398i
$137$	22.1633			1.89354			0.946771	−	0.321908i	$-0.104324\pi$
$137$	22.1633			1.89354			0.946771	+	0.321908i	$0.104324\pi$
$138$		−	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	$0.549568\pi$
$140$		0			0
$141$	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			0
$146$	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	$0.658292\pi$
$150$		0			0
$151$		−	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
$155$		0			0
$156$	−4.66495	−	4.66495i	−0.373495	−	0.373495i
$157$	−1.36913			−0.109268			−0.0546342	−	0.998506i	$-0.517399\pi$
$157$	−1.36913			−0.109268			−0.0546342	+	0.998506i	$0.517399\pi$
$158$	7.15096	+	7.15096i	0.568900	+	0.568900i
$159$	−22.7255	+	22.7255i	−1.80225	+	1.80225i
$160$		0			0
$161$			3.43306i			0.270563i
$162$			9.56048i			0.751143i
$163$	8.54984	−	8.54984i	0.669675	−	0.669675i	−0.287966	−	0.957641i	$-0.592979\pi$
$163$	8.54984	−	8.54984i	0.669675	−	0.669675i	0.957641	+	0.287966i	$0.0929789\pi$
$164$	−4.92219	+	4.92219i	−0.384358	+	0.384358i
$165$		0			0
$166$	2.84790			0.221040
$167$	−4.16611	−	4.16611i	−0.322383	−	0.322383i	0.527297	−	0.849681i	$-0.323205\pi$
$167$	−4.16611	−	4.16611i	−0.322383	−	0.322383i	−0.849681	+	0.527297i	$0.823205\pi$
$168$			18.6565i			1.43938i
$169$	0.261831			0.0201408
$170$		0			0
$171$	−8.26822			−0.632287
$172$		−	5.45290i		−	0.415780i
$173$	−1.46761	−	1.46761i	−0.111580	−	0.111580i	0.649112	−	0.760693i	$-0.275141\pi$
$173$	−1.46761	−	1.46761i	−0.111580	−	0.111580i	−0.760693	+	0.649112i	$0.775141\pi$
$174$	−2.38059			−0.180472
$175$		0			0
$176$	−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	$0.871161\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	26.4237			1.93748
$187$	−14.9873	+	0.622424i	−1.09598	+	0.0455162i
$188$	3.95995			0.288809
$189$			0.991860i			0.0721472i
$190$		0			0
$191$	−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	−0.942562	−	0.334032i	$-0.891591\pi$
$193$	−8.45396	+	8.45396i	−0.608529	+	0.608529i	0.334032	+	0.942562i	$0.391591\pi$
$194$	−9.77662	+	9.77662i	−0.701920	+	0.701920i
$195$		0			0
$196$			0.754430i			0.0538878i
$197$	−0.864156	+	0.864156i	−0.0615686	+	0.0615686i	−0.737221	−	0.675652i	$-0.763862\pi$
$197$	−0.864156	+	0.864156i	−0.0615686	+	0.0615686i	0.675652	+	0.737221i	$0.263862\pi$
$198$	−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	$0.470070\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$		−	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
$210$		0			0
$211$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$	11.0486	+	10.1675i	0.743212	+	0.683942i
$222$	30.7946			2.06680
$223$			9.61320i			0.643748i	0.946783	+	0.321874i	$0.104313\pi$
$223$			9.61320i			0.643748i	−0.946783	+	0.321874i	$0.895687\pi$
$224$	6.71833	+	6.71833i	0.448887	+	0.448887i
$225$		0			0
$226$	9.13308	+	9.13308i	0.607523	+	0.607523i
$227$	−1.25815	+	1.25815i	−0.0835064	+	0.0835064i	−0.747626	−	0.664120i	$-0.768806\pi$
$227$	−1.25815	+	1.25815i	−0.0835064	+	0.0835064i	0.664120	+	0.747626i	$0.268806\pi$
$228$	−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	$-0.186594\pi$
$230$		0			0
$231$	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	0.335751	−	0.941951i	$-0.391010\pi$
$233$	−9.25323	−	9.25323i	−0.606199	−	0.606199i	−0.941951	+	0.335751i	$0.891010\pi$
$234$	12.9847			0.848836
$235$		0			0
$236$			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	$0.781997\pi$
$240$		0			0
$241$	−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			0
$246$		−	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			0
$251$	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
$255$		0			0
$256$	−14.8981			−0.931128
$257$			2.58018i			0.160947i	0.996757	+	0.0804735i	$0.0256432\pi$
$257$			2.58018i			0.160947i	−0.996757	+	0.0804735i	$0.974357\pi$
$258$	14.7856	+	14.7856i	0.920509	+	0.920509i
$259$	−26.8814			−1.67033
$260$		0			0
$261$	−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	$-0.904478\pi$
$263$		−	9.58787i		−	0.591213i	0.955310	−	0.295607i	$-0.0955218\pi$
$264$			27.7879i			1.71023i
$265$		0			0
$266$	−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			0
$271$	−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
$275$		0			0
$276$	−2.54622			−0.153264
$277$	−3.19263	−	3.19263i	−0.191827	−	0.191827i	0.604658	−	0.796485i	$-0.293310\pi$
$277$	−3.19263	−	3.19263i	−0.191827	−	0.191827i	−0.796485	+	0.604658i	$0.793310\pi$
$278$	−11.0664	+	11.0664i	−0.663717	+	0.663717i
$279$	21.1245	−	21.1245i	1.26469	−	1.26469i
$280$		0			0
$281$		−	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	−0.999945	−	0.0104528i	$-0.996673\pi$
$283$	−16.6458	+	16.6458i	−0.989493	+	0.989493i	0.0104528	+	0.999945i	$0.496673\pi$
$284$	6.34231	+	6.34231i	0.376347	+	0.376347i
$285$		0			0
$286$	−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			0
$291$			30.4555i			1.78534i
$292$	−0.761510	−	0.761510i	−0.0445640	−	0.0445640i
$293$	−15.5924			−0.910918			−0.455459	−	0.890257i	$-0.650525\pi$
$293$	−15.5924			−0.910918			−0.455459	+	0.890257i	$0.650525\pi$
$294$	−2.04564	−	2.04564i	−0.119304	−	0.119304i
$295$		0			0
$296$	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
$300$		0			0
$301$	−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
$305$		0			0
$306$	10.8178	+	9.95505i	0.618410	+	0.569093i
$307$	−21.6549			−1.23591			−0.617955	−	0.786214i	$-0.712038\pi$
$307$	−21.6549			−1.23591			−0.617955	+	0.786214i	$0.712038\pi$
$308$		−	6.48428i		−	0.369476i
$309$	−14.1918	−	14.1918i	−0.807341	−	0.807341i
$310$		0			0
$311$	−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	−0.276887	−	0.960903i	$-0.589303\pi$
$313$	12.1015	−	12.1015i	0.684016	−	0.684016i	0.960903	+	0.276887i	$0.0893026\pi$
$314$		−	1.54311i		−	0.0870828i
$315$		0			0
$316$	4.62972	−	4.62972i	0.260442	−	0.260442i
$317$	−7.30027	+	7.30027i	−0.410024	+	0.410024i	−0.881747	−	0.471723i	$-0.843632\pi$
$317$	−7.30027	+	7.30027i	−0.410024	+	0.410024i	0.471723	+	0.881747i	$0.343632\pi$
$318$	−25.6134	−	25.6134i	−1.43633	−	1.43633i
$319$	3.09519			0.173297
$320$		0			0
$321$			21.8491i			1.21950i
$322$	−3.86932			−0.215629
$323$	7.29708	−	7.92944i	0.406020	−	0.441206i
$324$	6.18971			0.343873
$325$		0			0
$326$	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
$330$		0			0
$331$		−	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
$335$		0			0
$336$	−12.1774			−0.664333
$337$	21.3377	+	21.3377i	1.16234	+	1.16234i	0.983962	+	0.178379i	$0.0570852\pi$
$337$	21.3377	+	21.3377i	1.16234	+	1.16234i	0.178379	+	0.983962i	$0.442915\pi$
$338$			0.295103i			0.0160515i
$339$	28.4508			1.54524
$340$		0			0
$341$	−34.3555			−1.86046
$342$		−	9.31892i		−	0.503909i
$343$	13.8758	+	13.8758i	0.749220	+	0.749220i
$344$	22.9907			1.23957
$345$		0			0
$346$	1.65411	−	1.65411i	0.0889254	−	0.0889254i
$347$	−4.97815	+	4.97815i	−0.267241	+	0.267241i	−0.827988	−	0.560746i	$-0.810514\pi$
$347$	−4.97815	+	4.97815i	−0.267241	+	0.267241i	0.560746	+	0.827988i	$0.310514\pi$
$348$			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	$-0.397417\pi$
$350$		0			0
$351$	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	$-0.426962\pi$
$353$	8.54669			0.454895			0.227447	+	0.973790i	$0.426962\pi$
$354$	−2.77536	−	2.77536i	−0.147509	−	0.147509i
$355$		0			0
$356$	−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	$0.820210\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$			3.18348i			0.166403i
$367$	8.99600	−	8.99600i	0.469587	−	0.469587i	−0.432193	−	0.901781i	$-0.642260\pi$
$367$	8.99600	−	8.99600i	0.469587	−	0.469587i	0.901781	+	0.432193i	$0.142260\pi$
$368$	1.99579	−	1.99579i	0.104038	−	0.104038i
$369$	−21.3398	−	21.3398i	−1.11091	−	1.11091i
$370$		0			0
$371$	22.3585	+	22.3585i	1.16080	+	1.16080i
$372$		−	17.1074i		−	0.886979i
$373$	11.1454			0.577086			0.288543	−	0.957467i	$-0.406829\pi$
$373$	11.1454			0.577086			0.288543	+	0.957467i	$0.406829\pi$
$374$	−0.701519	−	16.8918i	−0.0362747	−	0.873453i
$375$		0			0
$376$			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	$0.644402\pi$
$380$		0			0
$381$	−4.41617	+	4.41617i	−0.226247	+	0.226247i
$382$		−	13.9110i		−	0.711749i
$383$		−	17.3523i		−	0.886661i	−0.896358	−	0.443331i	$-0.853797\pi$
$383$		−	17.3523i		−	0.886661i	0.896358	−	0.443331i	$-0.146203\pi$
$384$	2.96372	−	2.96372i	0.151241	−	0.151241i
$385$		0			0
$386$	−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	$-0.164137\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	5.93851	+	5.93851i	0.298421	+	0.298421i
$397$	3.36574	−	3.36574i	0.168922	−	0.168922i	−0.617584	−	0.786505i	$-0.711888\pi$
$397$	3.36574	−	3.36574i	0.168922	−	0.168922i	0.786505	+	0.617584i	$0.211888\pi$
$398$	−17.3219	+	17.3219i	−0.868270	+	0.868270i
$399$			15.8488i			0.793434i
$400$		0			0
$401$	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
$405$		0			0
$406$			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	$0.351028\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$		−	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	$0.236446\pi$
$420$		0			0
$421$	−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
$425$		0			0
$426$	−34.3944			−1.66641
$427$		−	2.77894i		−	0.134482i
$428$	4.54095	+	4.54095i	0.219495	+	0.219495i
$429$	−32.8920			−1.58804
$430$		0			0
$431$	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	$-0.875841\pi$
$433$		−	15.8246i		−	0.760483i	0.924887	−	0.380242i	$-0.124159\pi$
$434$		−	25.9970i		−	1.24790i
$435$		0			0
$436$	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	$0.781706\pi$
$440$		0			0
$441$	−3.27078			−0.155751
$442$	−11.4596	+	12.4527i	−0.545077	+	0.592313i
$443$	−15.7201			−0.746884			−0.373442	−	0.927654i	$-0.621823\pi$
$443$	−15.7201			−0.746884			−0.373442	+	0.927654i	$0.621823\pi$
$444$		−	19.9373i		−	0.946181i
$445$		0			0
$446$	−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	$0.377680\pi$
$450$		0			0
$451$			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
$455$		0			0
$456$	−14.1158	−	14.1158i	−0.661031	−	0.661031i
$457$		−	1.42830i		−	0.0668131i	−0.999442	−	0.0334066i	$-0.989364\pi$
$457$		−	1.42830i		−	0.0668131i	0.999442	−	0.0334066i	$-0.0106356\pi$
$458$	18.8705			0.881761
$459$	1.67284	−	0.0694735i	0.0780816	−	0.00324275i
$460$		0			0
$461$		−	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	$-0.262416\pi$
$463$	29.2204			1.35799			0.678994	+	0.734144i	$0.262416\pi$
$464$	−1.20807	−	1.20807i	−0.0560835	−	0.0560835i
$465$		0			0
$466$	10.4291	−	10.4291i	0.483119	−	0.483119i
$467$			10.9388i			0.506187i	0.967442	+	0.253093i	$0.0814480\pi$
$467$			10.9388i			0.506187i	−0.967442	+	0.253093i	$0.918552\pi$
$468$		−	8.40664i		−	0.388597i
$469$	3.59088	−	3.59088i	0.165811	−	0.165811i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	$0.878540\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−17.7543	+	17.7543i	−0.805352	+	0.805352i
$487$	18.2749	−	18.2749i	0.828113	−	0.828113i	−0.159143	−	0.987256i	$-0.550873\pi$
$487$	18.2749	−	18.2749i	0.828113	−	0.828113i	0.987256	+	0.159143i	$0.0508730\pi$
$488$	2.47506	+	2.47506i	0.112041	+	0.112041i
$489$	30.0185			1.35748
$490$		0			0
$491$		−	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
$495$		0			0
$496$	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			0
$501$		−	14.6272i		−	0.653496i
$502$			20.5248i			0.916065i
$503$	−15.0825	+	15.0825i	−0.672497	+	0.672497i	−0.958291	−	0.285794i	$-0.907743\pi$
$503$	−15.0825	+	15.0825i	−0.672497	+	0.672497i	0.285794	+	0.958291i	$0.407743\pi$
$504$	−16.8103	+	16.8103i	−0.748790	+	0.748790i
$505$		0			0
$506$	−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	$0.397899\pi$
$510$		0			0
$511$	−3.60489			−0.159471
$512$		−	20.1677i		−	0.891296i
$513$	−0.750456	−	0.750456i	−0.0331334	−	0.0331334i
$514$	−2.90805			−0.128269
$515$		0			0
$516$	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
$520$		0			0
$521$	−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	$-0.836898\pi$
$523$	−39.8642			−1.74314			−0.871570	+	0.490271i	$0.836898\pi$
$524$	−1.14665	−	1.14665i	−0.0500917	−	0.0500917i
$525$		0			0
$526$	10.8063			0.471175
$527$	1.61562	+	38.9023i	0.0703775	+	1.69461i
$528$	−18.1377			−0.789341
$529$			21.0245i			0.914110i
$530$		0			0
$531$	−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
$535$		0			0
$536$			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			0
$541$	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
$545$		0			0
$546$		−	24.8895i		−	1.06517i
$547$	−10.9849	−	10.9849i	−0.469682	−	0.469682i	0.432130	−	0.901812i	$-0.357762\pi$
$547$	−10.9849	−	10.9849i	−0.469682	−	0.469682i	−0.901812	+	0.432130i	$0.857762\pi$
$548$	16.1726			0.690858
$549$	2.54504	+	2.54504i	0.108620	+	0.108620i
$550$		0			0
$551$	−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
$555$		0			0
$556$	7.16467	+	7.16467i	0.303849	+	0.303849i
$557$	0.980081			0.0415274			0.0207637	−	0.999784i	$-0.493390\pi$
$557$	0.980081			0.0415274			0.0207637	+	0.999784i	$0.493390\pi$
$558$	23.8089	+	23.8089i	1.00791	+	1.00791i
$559$			27.2136i			1.15101i
$560$		0			0
$561$	−27.4028	−	25.2175i	−1.15695	−	1.06468i
$562$	3.87908			0.163629
$563$			28.8837i			1.21730i	0.793437	+	0.608652i	$0.208289\pi$
$563$			28.8837i			1.21730i	−0.793437	+	0.608652i	$0.791711\pi$
$564$	6.95170	+	6.95170i	0.292720	+	0.292720i
$565$		0			0
$566$	−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	$0.874765\pi$
$570$		0			0
$571$	−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			0
$576$		−	26.5753i		−	1.10730i
$577$	28.3066			1.17842			0.589209	−	0.807980i	$-0.299439\pi$
$577$	28.3066			1.17842			0.589209	+	0.807980i	$0.299439\pi$
$578$	−19.0943	+	1.58872i	−0.794219	+	0.0660821i
$579$	−29.6819			−1.23354
$580$		0			0
$581$	−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
$585$		0			0
$586$		−	17.5738i		−	0.725968i
$587$		−	2.68137i		−	0.110672i	−0.998468	−	0.0553360i	$-0.982377\pi$
$587$		−	2.68137i		−	0.110672i	0.998468	−	0.0553360i	$-0.0176230\pi$
$588$	−1.32440	+	1.32440i	−0.0546174	+	0.0546174i
$589$	17.4520	−	17.4520i	0.719097	−	0.719097i
$590$		0			0
$591$	−3.03405			−0.124804
$592$	15.6273	+	15.6273i	0.642279	+	0.642279i
$593$		−	15.3155i		−	0.628934i	−0.949268	−	0.314467i	$-0.898174\pi$
$593$		−	15.3155i		−	0.628934i	0.949268	−	0.314467i	$-0.101826\pi$
$594$	−1.66506			−0.0683183
$595$		0			0
$596$	−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	$0.151277\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	8.27306	−	8.27306i	0.336070	−	0.336070i
$607$	10.3997	+	10.3997i	0.422112	+	0.422112i	0.885930	−	0.463818i	$-0.153521\pi$
$607$	10.3997	+	10.3997i	0.422112	+	0.422112i	−0.463818	+	0.885930i	$0.653521\pi$
$608$	−10.1664			−0.412301
$609$	3.64806	+	3.64806i	0.147827	+	0.147827i
$610$		0			0
$611$	−19.7628			−0.799516
$612$	6.44517	−	7.00370i	0.260531	−	0.283108i
$613$	−23.6535			−0.955354			−0.477677	−	0.878535i	$-0.658521\pi$
$613$	−23.6535			−0.955354			−0.477677	+	0.878535i	$0.658521\pi$
$614$		−	24.4067i		−	0.984974i
$615$		0			0
$616$	27.3392			1.10153
$617$	−7.10492	−	7.10492i	−0.286033	−	0.286033i	0.549476	−	0.835509i	$-0.314827\pi$
$617$	−7.10492	−	7.10492i	−0.286033	−	0.286033i	−0.835509	+	0.549476i	$0.814827\pi$
$618$	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	$0.492848\pi$
$620$		0			0
$621$		−	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
$625$		0			0
$626$	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
$630$		0			0
$631$		−	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	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	0.860192	−	0.509971i	$-0.170344\pi$
$643$	8.88071	+	8.88071i	0.350221	+	0.350221i	−0.509971	+	0.860192i	$0.670344\pi$
$644$			2.50510i			0.0987149i
$645$		0			0
$646$	8.93708	+	8.22436i	0.351625	+	0.323583i
$647$	3.62337			0.142449			0.0712247	−	0.997460i	$-0.477309\pi$
$647$	3.62337			0.142449			0.0712247	+	0.997460i	$0.477309\pi$
$648$			26.0972i			1.02520i
$649$	3.60846	+	3.60846i	0.141645	+	0.141645i
$650$		0			0
$651$	−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	−0.828972	−	0.559290i	$-0.811074\pi$
$653$	−6.89142	+	6.89142i	−0.269682	+	0.269682i	0.559290	+	0.828972i	$0.311074\pi$
$654$			40.0538i			1.56623i
$655$		0			0
$656$	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	$0.544782\pi$
$660$		0			0
$661$			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
$665$		0			0
$666$	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
$670$		0			0
$671$		−	4.13909i		−	0.159788i
$672$			23.5881i			0.909929i
$673$	−20.8675	+	20.8675i	−0.804382	+	0.804382i	−0.983777	−	0.179395i	$-0.942586\pi$
$673$	−20.8675	+	20.8675i	−0.804382	+	0.804382i	0.179395	+	0.983777i	$0.442586\pi$
$674$	−24.0493	+	24.0493i	−0.926343	+	0.926343i
$675$		0			0
$676$	0.191058			0.00734837
$677$	−0.394531	−	0.394531i	−0.0151631	−	0.0151631i	0.699485	−	0.714648i	$-0.253413\pi$
$677$	−0.394531	−	0.394531i	−0.0151631	−	0.0151631i	−0.714648	+	0.699485i	$0.753413\pi$
$678$			32.0662i			1.23150i
$679$	29.9637			1.14990
$680$		0			0
$681$	−4.41737			−0.169274
$682$		−	38.7213i		−	1.48272i
$683$	25.5664	+	25.5664i	0.978272	+	0.978272i	0.999769	−	0.0214974i	$-0.00684335\pi$
$683$	25.5664	+	25.5664i	0.978272	+	0.978272i	−0.0214974	+	0.999769i	$0.506843\pi$
$684$	−6.03332			−0.230690
$685$		0			0
$686$	−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
$690$		0			0
$691$	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
$695$		0			0
$696$	−6.49829			−0.246317
$697$	39.2988	−	1.63209i	1.48855	−	0.0618198i
$698$	39.9431			1.51187
$699$		−	32.4881i		−	1.22881i
$700$		0			0
$701$	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
$705$		0			0
$706$			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	$0.808356\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$			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	$0.623157\pi$
$720$		0			0
$721$	−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			0
$726$	4.42333	+	4.42333i	0.164165	+	0.164165i
$727$	−39.1557			−1.45220			−0.726102	−	0.687587i	$-0.758670\pi$
$727$	−39.1557			−1.45220			−0.726102	+	0.687587i	$0.758670\pi$
$728$	−19.3509	−	19.3509i	−0.717191	−	0.717191i
$729$			29.8595i			1.10591i
$730$		0			0
$731$	−20.8640	+	22.6720i	−0.771682	+	0.838556i
$732$	2.06107			0.0761793
$733$			12.9215i			0.477265i	0.971110	+	0.238633i	$0.0766992\pi$
$733$			12.9215i			0.477265i	−0.971110	+	0.238633i	$0.923301\pi$
$734$	10.1392	+	10.1392i	0.374244	+	0.374244i
$735$		0			0
$736$	−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	$-0.246229\pi$
$740$		0			0
$741$	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	0.530290	−	0.847816i	$-0.322083\pi$
$743$	−8.65513	−	8.65513i	−0.317526	−	0.317526i	−0.847816	+	0.530290i	$0.822083\pi$
$744$	72.1288			2.64437
$745$		0			0
$746$			12.5617i			0.459916i
$747$	7.99371			0.292474
$748$	−10.9362	+	0.454183i	−0.399867	+	0.0166066i
$749$	21.4963			0.785457
$750$		0			0
$751$	−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
$755$		0			0
$756$			0.723760i			0.0263229i
$757$			0.782070i			0.0284248i	0.999899	+	0.0142124i	$0.00452410\pi$
$757$			0.782070i			0.0284248i	−0.999899	+	0.0142124i	$0.995476\pi$
$758$	−10.1064	+	10.1064i	−0.367081	+	0.367081i
$759$	−8.97654	+	8.97654i	−0.325828	+	0.325828i
$760$		0			0
$761$	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
$765$		0			0
$766$	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	$0.254466\pi$
$770$		0			0
$771$	−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	$0.239483\pi$
$773$			37.9989i			1.36672i	−0.730080	+	0.683362i	$0.760517\pi$
$774$			26.6449i			0.957730i
$775$		0			0
$776$	−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
$780$		0			0
$781$	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			0
$786$	6.21831			0.221800
$787$	25.0127	+	25.0127i	0.891606	+	0.891606i	0.994674	−	0.103068i	$-0.0328659\pi$
$787$	25.0127	+	25.0127i	0.891606	+	0.891606i	−0.103068	+	0.994674i	$0.532866\pi$
$788$	−0.630574	+	0.630574i	−0.0224633	+	0.0224633i
$789$	16.8315	−	16.8315i	0.599217	−	0.599217i
$790$		0			0
$791$		−	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
$795$		0			0
$796$	11.2147	+	11.2147i	0.397494	+	0.397494i
$797$		−	26.7826i		−	0.948688i	−0.880340	−	0.474344i	$-0.842685\pi$
$797$		−	26.7826i		−	0.948688i	0.880340	−	0.474344i	$-0.157315\pi$
$798$	−17.8628			−0.632337
$799$	−16.4647	−	15.1516i	−0.582479	−	0.536027i
$800$		0			0
$801$		−	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
$805$		0			0
$806$	−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	$0.851672\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	−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	−0.0250590	−	0.999686i	$-0.507977\pi$
$823$	27.9601	−	27.9601i	0.974627	−	0.974627i	0.999686	+	0.0250590i	$0.00797737\pi$
$824$		−	24.8716i		−	0.866443i
$825$		0			0
$826$	−2.73054	+	2.73054i	−0.0950078	+	0.0950078i
$827$	12.9612	−	12.9612i	0.450704	−	0.450704i	−0.444884	−	0.895588i	$-0.646755\pi$
$827$	12.9612	−	12.9612i	0.450704	−	0.450704i	0.895588	+	0.444884i	$0.146755\pi$
$828$	−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	$0.739902\pi$
$830$		0			0
$831$		−	11.2093i		−	0.388847i
$832$	30.5916			1.06057
$833$	2.88661	−	3.13676i	0.100015	−	0.108682i
$834$	−38.8540			−1.34541
$835$		0			0
$836$	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	$0.365759\pi$
$840$		0			0
$841$		−	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			0
$846$	−19.3498			−0.665259
$847$	−3.86123	−	3.86123i	−0.132673	−	0.132673i
$848$		−	25.9960i		−	0.892706i
$849$	−58.4436			−2.00578
$850$		0			0
$851$	15.4683			0.530245
$852$			22.2679i			0.762884i
$853$	−5.82880	−	5.82880i	−0.199574	−	0.199574i	0.600243	−	0.799817i	$-0.295070\pi$
$853$	−5.82880	−	5.82880i	−0.199574	−	0.199574i	−0.799817	+	0.600243i	$0.795070\pi$
$854$	3.13207			0.107177
$855$		0			0
$856$	−19.1457	+	19.1457i	−0.654386	+	0.654386i
$857$	−19.6053	+	19.6053i	−0.669703	+	0.669703i	−0.957647	−	0.287944i	$-0.907028\pi$
$857$	−19.6053	+	19.6053i	−0.669703	+	0.669703i	0.287944	+	0.957647i	$0.407028\pi$
$858$		−	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	$-0.0381397\pi$
$860$		0			0
$861$	−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	$-0.666921\pi$
$863$	−29.4176			−1.00139			−0.500693	+	0.865625i	$0.666921\pi$
$864$	−1.11692	−	1.11692i	−0.0379983	−	0.0379983i
$865$		0			0
$866$	17.8356			0.606077
$867$	−27.2662	+	32.2153i	−0.926008	+	1.09409i
$868$	−16.8312			−0.571287
$869$		−	32.6436i		−	1.10736i
$870$		0			0
$871$	−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
$875$		0			0
$876$		−	2.67366i		−	0.0903347i
$877$	36.4433	−	36.4433i	1.23060	−	1.23060i	0.266872	−	0.963732i	$-0.414010\pi$
$877$	36.4433	−	36.4433i	1.23060	−	1.23060i	0.963732	−	0.266872i	$-0.0859900\pi$
$878$	3.32106	−	3.32106i	0.112080	−	0.112080i
$879$	−27.3725	−	27.3725i	−0.923250	−	0.923250i
$880$		0			0
$881$	−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	$-0.553592\pi$
$883$	−9.95880			−0.335140			−0.167570	+	0.985860i	$0.553592\pi$
$884$	8.06219	+	7.41924i	0.271161	+	0.249536i
$885$		0			0
$886$		−	17.7177i		−	0.595239i
$887$	−13.3201	−	13.3201i	−0.447246	−	0.447246i	0.447192	−	0.894438i	$-0.352424\pi$
$887$	−13.3201	−	13.3201i	−0.447246	−	0.447246i	−0.894438	+	0.447192i	$0.852424\pi$
$888$	84.0601			2.82087
$889$	4.34486	+	4.34486i	0.145722	+	0.145722i
$890$		0			0
$891$	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
$895$		0			0
$896$	−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
$900$		0			0
$901$	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
$905$		0			0
$906$	5.59407	+	5.59407i	0.185851	+	0.185851i
$907$	−18.9094	+	18.9094i	−0.627876	+	0.627876i	−0.947533	−	0.319658i	$-0.896432\pi$
$907$	−18.9094	+	18.9094i	−0.627876	+	0.627876i	0.319658	+	0.947533i	$0.396432\pi$
$908$	−0.918072	+	0.918072i	−0.0304673	+	0.0304673i
$909$		−	13.2278i		−	0.438740i
$910$		0			0
$911$	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
$915$		0			0
$916$		−	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	$0.390432\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$			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	$0.226127\pi$
$930$		0			0
$931$	−2.70215			−0.0885595
$932$	−6.75208	−	6.75208i	−0.221172	−	0.221172i
$933$		−	22.0075i		−	0.720492i
$934$	−12.3288			−0.403412
$935$		0			0
$936$	35.4443			1.15853
$937$			2.90874i			0.0950243i	0.998871	+	0.0475122i	$0.0151293\pi$
$937$			2.90874i			0.0950243i	−0.998871	+	0.0475122i	$0.984871\pi$
$938$	4.04720	+	4.04720i	0.132146	+	0.132146i
$939$	42.4883			1.38655
$940$		0			0
$941$	−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			0
$946$	21.6667	−	21.6667i	0.704447	−	0.704447i
$947$	−16.9623	−	16.9623i	−0.551200	−	0.551200i	0.375587	−	0.926787i	$-0.377441\pi$
$947$	−16.9623	−	16.9623i	−0.551200	−	0.551200i	−0.926787	+	0.375587i	$0.877441\pi$
$948$	16.2550			0.527937
$949$	3.80043	+	3.80043i	0.123367	+	0.123367i
$950$		0			0
$951$	−25.6313			−0.831151
$952$	−1.28567	−	30.9574i	−0.0416687	−	1.00333i
$953$	9.31030			0.301590			0.150795	−	0.988565i	$-0.451817\pi$
$953$	9.31030			0.301590			0.150795	+	0.988565i	$0.451817\pi$
$954$		−	46.1575i		−	1.49440i
$955$		0			0
$956$	−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
$960$		0			0
$961$			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
$965$		0			0
$966$	−6.79260	−	6.79260i	−0.218548	−	0.218548i
$967$		−	1.29315i		−	0.0415848i	−0.999784	−	0.0207924i	$-0.993381\pi$
$967$		−	1.29315i		−	0.0415848i	0.999784	−	0.0207924i	$-0.00661890\pi$
$968$	6.87802			0.221068
$969$	26.7302	−	1.11011i	0.858697	−	0.0356619i
$970$		0			0
$971$			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
$975$		0			0
$976$	−1.61552	+	1.61552i	−0.0517115	+	0.0517115i
$977$		−	53.3750i		−	1.70762i	−0.520586	−	0.853809i	$-0.674286\pi$
$977$		−	53.3750i		−	1.70762i	0.520586	−	0.853809i	$-0.325714\pi$
$978$			33.8331i			1.08186i
$979$	−4.27996	+	4.27996i	−0.136788	+	0.136788i
$980$		0			0
$981$	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	$0.0530020\pi$
$983$	36.1157	+	36.1157i	1.15191	+	1.15191i	0.165742	+	0.986169i	$0.446998\pi$
$984$		−	72.8641i		−	2.32282i
$985$		0			0
$986$	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
$990$		0			0
$991$	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
$995$		0			0
$996$	3.23680	−	3.23680i	0.102562	−	0.102562i
$997$	2.43619	−	2.43619i	0.0771550	−	0.0771550i	−0.667476	−	0.744631i	$-0.732625\pi$
$997$	2.43619	−	2.43619i	0.0771550	−	0.0771550i	0.744631	+	0.667476i	$0.232625\pi$
$998$	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	425.2.e.f.251.4		12
5.2	odd	4		425.2.j.b.149.3		12
5.3	odd	4		425.2.j.c.149.4		12
5.4	even	2		85.2.e.a.81.3	yes	12
15.14	odd	2		765.2.k.b.676.4		12
17.2	even	8		7225.2.a.z.1.3		6
17.4	even	4	inner	425.2.e.f.276.3		12
17.15	even	8		7225.2.a.bb.1.3		6
20.19	odd	2		1360.2.bt.d.81.6		12
85.4	even	4		85.2.e.a.21.4	✓	12
85.9	even	8		1445.2.d.g.866.5		12
85.19	even	8		1445.2.a.o.1.4		6
85.38	odd	4		425.2.j.b.174.3		12
85.49	even	8		1445.2.a.n.1.4		6
85.59	even	8		1445.2.d.g.866.6		12
85.72	odd	4		425.2.j.c.174.4		12
255.89	odd	4		765.2.k.b.361.3		12
340.259	odd	4		1360.2.bt.d.1041.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	85.4	even	4
85.2.e.a.81.3	yes	12	5.4	even	2
425.2.e.f.251.4		12	1.1	even	1	trivial
425.2.e.f.276.3		12	17.4	even	4	inner
425.2.j.b.149.3		12	5.2	odd	4
425.2.j.b.174.3		12	85.38	odd	4
425.2.j.c.149.4		12	5.3	odd	4
425.2.j.c.174.4		12	85.72	odd	4
765.2.k.b.361.3		12	255.89	odd	4
765.2.k.b.676.4		12	15.14	odd	2
1360.2.bt.d.81.6		12	20.19	odd	2
1360.2.bt.d.1041.6		12	340.259	odd	4
1445.2.a.n.1.4		6	85.49	even	8
1445.2.a.o.1.4		6	85.19	even	8
1445.2.d.g.866.5		12	85.9	even	8
1445.2.d.g.866.6		12	85.59	even	8
7225.2.a.z.1.3		6	17.2	even	8
7225.2.a.bb.1.3		6	17.15	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.e (of order \(4\), degree \(2\), minimal)

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

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