LMFDB - Embedded newform 425.2.e.f.276.3

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			276.3
Root			$3.48265i$ of defining polynomial
Character	$\chi$	$=$	425.276
Dual form			425.2.e.f.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12708i q^{2} +(1.75550 - 1.75550i) q^{3} +0.729699 q^{4} +(-1.97858 - 1.97858i) q^{6} +(1.72715 + 1.72715i) q^{7} -3.07658i q^{8} -3.16356i q^{9} +O(q^{10})$	\(q-1.12708i q^{2} +(1.75550 - 1.75550i) q^{3} +0.729699 q^{4} +(-1.97858 - 1.97858i) q^{6} +(1.72715 + 1.72715i) q^{7} -3.07658i q^{8} -3.16356i q^{9} +(2.57251 + 2.57251i) q^{11} +(1.28099 - 1.28099i) q^{12} -3.64168 q^{13} +(1.94663 - 1.94663i) q^{14} -2.00814 q^{16} +(-3.03394 + 2.79199i) q^{17} -3.56558 q^{18} -2.61358i q^{19} +6.06403 q^{21} +(2.89941 - 2.89941i) q^{22} +(-0.993850 - 0.993850i) q^{23} +(-5.40094 - 5.40094i) q^{24} +4.10445i q^{26} +(-0.287137 - 0.287137i) q^{27} +(1.26030 + 1.26030i) q^{28} +(0.601589 - 0.601589i) q^{29} +(-6.67744 + 6.67744i) q^{31} -3.88983i q^{32} +9.03208 q^{33} +(3.14678 + 3.41948i) q^{34} -2.30845i q^{36} +(-7.78199 + 7.78199i) q^{37} -2.94570 q^{38} +(-6.39297 + 6.39297i) q^{39} +(-6.74550 - 6.74550i) q^{41} -6.83463i q^{42} +7.47280i q^{43} +(1.87716 + 1.87716i) q^{44} +(-1.12014 + 1.12014i) q^{46} +5.42683 q^{47} +(-3.52529 + 3.52529i) q^{48} -1.03389i q^{49} +(-0.424747 + 10.2274i) q^{51} -2.65733 q^{52} -12.9453i q^{53} +(-0.323626 + 0.323626i) q^{54} +(5.31372 - 5.31372i) q^{56} +(-4.58814 - 4.58814i) q^{57} +(-0.678037 - 0.678037i) q^{58} -1.40270i q^{59} +(0.804485 + 0.804485i) q^{61} +(7.52598 + 7.52598i) q^{62} +(5.46396 - 5.46396i) q^{63} -8.40042 q^{64} -10.1798i q^{66} +2.07908 q^{67} +(-2.21387 + 2.03731i) q^{68} -3.48941 q^{69} +(8.69168 - 8.69168i) q^{71} -9.73296 q^{72} +(-1.04359 + 1.04359i) q^{73} +(8.77090 + 8.77090i) q^{74} -1.90713i q^{76} +8.88623i q^{77} +(7.20536 + 7.20536i) q^{78} +(6.34470 + 6.34470i) q^{79} +8.48255 q^{81} +(-7.60269 + 7.60269i) q^{82} +2.52680i q^{83} +4.42492 q^{84} +8.42242 q^{86} -2.11218i q^{87} +(7.91453 - 7.91453i) q^{88} -1.66373 q^{89} +(-6.28973 - 6.28973i) q^{91} +(-0.725212 - 0.725212i) q^{92} +23.4445i q^{93} -6.11645i q^{94} +(-6.82860 - 6.82860i) q^{96} +(8.67432 - 8.67432i) q^{97} -1.16527 q^{98} +(8.13830 - 8.13830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	0.0136316	−	0.999907i	$-0.495661\pi$
$3$	1.75550	−	1.75550i	1.01354	−	1.01354i	0.999907	−	0.0136316i	$-0.00433922\pi$
$4$	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	0.953667	−	0.300865i	$-0.0972753\pi$
$7$	1.72715	+	1.72715i	0.652802	+	0.652802i	−0.300865	+	0.953667i	$0.597275\pi$
$8$		−	3.07658i		−	1.08773i
$9$		−	3.16356i		−	1.05452i
$10$		0			0
$11$	2.57251	+	2.57251i	0.775641	+	0.775641i	0.979086	−	0.203446i	$-0.0652140\pi$
$11$	2.57251	+	2.57251i	0.775641	+	0.775641i	−0.203446	+	0.979086i	$0.565214\pi$
$12$	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	$-0.903081\pi$
$19$		−	2.61358i		−	0.599596i	0.954003	−	0.299798i	$-0.0969193\pi$
$20$		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	0.595858	−	0.803090i	$-0.296812\pi$
$23$	−0.993850	−	0.993850i	−0.207232	−	0.207232i	−0.803090	+	0.595858i	$0.796812\pi$
$24$	−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	−0.649041	−	0.760753i	$-0.724830\pi$
$29$	0.601589	−	0.601589i	0.111712	−	0.111712i	0.760753	+	0.649041i	$0.224830\pi$
$30$		0			0
$31$	−6.67744	+	6.67744i	−1.19930	+	1.19930i	−0.224928	+	0.974376i	$0.572215\pi$
$31$	−6.67744	+	6.67744i	−1.19930	+	1.19930i	−0.974376	+	0.224928i	$0.927785\pi$
$32$		−	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	−0.338320	+	0.941031i	$0.609859\pi$
$37$	−7.78199	+	7.78199i	−1.27935	+	1.27935i	−0.941031	+	0.338320i	$0.890141\pi$
$38$	−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	−0.998487	−	0.0549831i	$-0.982489\pi$
$41$	−6.74550	−	6.74550i	−1.05347	−	1.05347i	−0.0549831	−	0.998487i	$-0.517511\pi$
$42$		−	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
$45$		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	$-0.651340\pi$
$53$		−	12.9453i		−	1.77817i	0.457737	−	0.889087i	$-0.348660\pi$
$54$	−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	$-0.970895\pi$
$59$		−	1.40270i		−	0.182616i	0.995823	−	0.0913081i	$-0.0291048\pi$
$60$		0			0
$61$	0.804485	+	0.804485i	0.103004	+	0.103004i	0.756731	−	0.653727i	$-0.226795\pi$
$61$	0.804485	+	0.804485i	0.103004	+	0.103004i	−0.653727	+	0.756731i	$0.726795\pi$
$62$	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	0.0320251	−	0.999487i	$-0.489804\pi$
$71$	8.69168	−	8.69168i	1.03151	−	1.03151i	0.999487	−	0.0320251i	$-0.0101957\pi$
$72$	−9.73296			−1.14704
$73$	−1.04359	+	1.04359i	−0.122143	+	0.122143i	−0.765536	−	0.643393i	$-0.777526\pi$
$73$	−1.04359	+	1.04359i	−0.122143	+	0.122143i	0.643393	+	0.765536i	$0.277526\pi$
$74$	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	0.967335	−	0.253501i	$-0.0815821\pi$
$79$	6.34470	+	6.34470i	0.713834	+	0.713834i	−0.253501	+	0.967335i	$0.581582\pi$
$80$		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	$0.0442848\pi$
$83$			2.52680i			0.277353i	−0.990338	+	0.138676i	$0.955715\pi$
$84$	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	−0.112867	−	0.993610i	$-0.536003\pi$
$97$	8.67432	−	8.67432i	0.880744	−	0.880744i	0.993610	+	0.112867i	$0.0360032\pi$
$98$	−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	−0.339134	−	0.940738i	$-0.610134\pi$
$107$	6.22304	−	6.22304i	0.601604	−	0.601604i	0.940738	+	0.339134i	$0.110134\pi$
$108$	−0.209524	−	0.209524i	−0.0201615	−	0.0201615i
$109$	10.1218	+	10.1218i	0.969496	+	0.969496i	0.999548	−	0.0300524i	$-0.00956740\pi$
$109$	10.1218	+	10.1218i	0.969496	+	0.969496i	−0.0300524	+	0.999548i	$0.509567\pi$
$110$		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	0.976737	−	0.214440i	$-0.0687925\pi$
$113$	8.10334	+	8.10334i	0.762298	+	0.762298i	−0.214440	+	0.976737i	$0.568792\pi$
$114$	−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	$-0.964398\pi$
$127$		−	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
$130$		0			0
$131$	−1.57140	+	1.57140i	−0.137294	+	0.137294i	−0.772414	−	0.635120i	$-0.780951\pi$
$131$	−1.57140	+	1.57140i	−0.137294	+	0.137294i	0.635120	+	0.772414i	$0.280951\pi$
$132$	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	−0.155093	−	0.987900i	$-0.549568\pi$
$139$	9.81865	−	9.81865i	0.832807	−	0.832807i	0.987900	+	0.155093i	$0.0495676\pi$
$140$		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	$0.0367002\pi$
$151$			2.82731i			0.230083i	−0.993361	+	0.115042i	$0.963300\pi$
$152$	−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	0.957641	−	0.287966i	$-0.0929789\pi$
$163$	8.54984	+	8.54984i	0.669675	+	0.669675i	−0.287966	+	0.957641i	$0.592979\pi$
$164$	−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	−0.849681	−	0.527297i	$-0.823205\pi$
$167$	−4.16611	+	4.16611i	−0.322383	+	0.322383i	0.527297	+	0.849681i	$0.323205\pi$
$168$		−	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	−0.760693	−	0.649112i	$-0.775141\pi$
$173$	−1.46761	+	1.46761i	−0.111580	+	0.111580i	0.649112	+	0.760693i	$0.275141\pi$
$174$	−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	$-0.871161\pi$
$179$		−	10.5373i		−	0.787597i	0.919197	−	0.393799i	$-0.128839\pi$
$180$		0			0
$181$	−2.39758	−	2.39758i	−0.178210	−	0.178210i	0.612365	−	0.790575i	$-0.290218\pi$
$181$	−2.39758	−	2.39758i	−0.178210	−	0.178210i	−0.790575	+	0.612365i	$0.790218\pi$
$182$	−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	0.334032	−	0.942562i	$-0.391591\pi$
$193$	−8.45396	−	8.45396i	−0.608529	−	0.608529i	−0.942562	+	0.334032i	$0.891591\pi$
$194$	−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	0.675652	−	0.737221i	$-0.263862\pi$
$197$	−0.864156	−	0.864156i	−0.0615686	−	0.0615686i	−0.737221	+	0.675652i	$0.763862\pi$
$198$	−9.17248	−	9.17248i	−0.651860	−	0.651860i
$199$	15.3689	−	15.3689i	1.08947	−	1.08947i	0.0938906	−	0.995583i	$-0.470070\pi$
$199$	15.3689	−	15.3689i	1.08947	−	1.08947i	0.995583	−	0.0938906i	$-0.0299304\pi$
$200$		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	0.164425	−	0.986390i	$-0.447423\pi$
$211$	−11.9397	−	11.9397i	−0.821965	−	0.821965i	−0.986390	+	0.164425i	$0.947423\pi$
$212$		−	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	$-0.895687\pi$
$223$		−	9.61320i		−	0.643748i	0.946783	−	0.321874i	$-0.104313\pi$
$224$	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	0.664120	−	0.747626i	$-0.268806\pi$
$227$	−1.25815	−	1.25815i	−0.0835064	−	0.0835064i	−0.747626	+	0.664120i	$0.768806\pi$
$228$	−3.34796	−	3.34796i	−0.221724	−	0.221724i
$229$			16.7429i			1.10640i	0.833048	+	0.553201i	$0.186594\pi$
$229$			16.7429i			1.10640i	−0.833048	+	0.553201i	$0.813406\pi$
$230$		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	−0.941951	−	0.335751i	$-0.891010\pi$
$233$	−9.25323	+	9.25323i	−0.606199	+	0.606199i	0.335751	+	0.941951i	$0.391010\pi$
$234$	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	−0.981098	−	0.193511i	$-0.938012\pi$
$241$	−12.2266	+	12.2266i	−0.787587	+	0.787587i	0.193511	+	0.981098i	$0.438012\pi$
$242$	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	$-0.974357\pi$
$257$		−	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
$260$		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	$0.0955218\pi$
$263$			9.58787i			0.591213i	−0.955310	+	0.295607i	$0.904478\pi$
$264$		−	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	−0.843159	−	0.537664i	$-0.819307\pi$
$269$	−5.01049	+	5.01049i	−0.305495	+	0.305495i	0.537664	+	0.843159i	$0.319307\pi$
$270$		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	−0.796485	−	0.604658i	$-0.793310\pi$
$277$	−3.19263	+	3.19263i	−0.191827	+	0.191827i	0.604658	+	0.796485i	$0.293310\pi$
$278$	−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	$0.0327347\pi$
$281$			3.44172i			0.205316i	−0.994717	+	0.102658i	$0.967265\pi$
$282$	−10.7374	−	10.7374i	−0.639405	−	0.639405i
$283$	−16.6458	−	16.6458i	−0.989493	−	0.989493i	0.0104528	−	0.999945i	$-0.496673\pi$
$283$	−16.6458	−	16.6458i	−0.989493	−	0.989493i	−0.999945	+	0.0104528i	$0.996673\pi$
$284$	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	−0.862127	−	0.506693i	$-0.830868\pi$
$311$	−6.26814	+	6.26814i	−0.355434	+	0.355434i	0.506693	+	0.862127i	$0.330868\pi$
$312$	19.6685	+	19.6685i	1.11351	+	1.11351i
$313$	12.1015	+	12.1015i	0.684016	+	0.684016i	0.960903	−	0.276887i	$-0.0893026\pi$
$313$	12.1015	+	12.1015i	0.684016	+	0.684016i	−0.276887	+	0.960903i	$0.589303\pi$
$314$			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	0.471723	−	0.881747i	$-0.343632\pi$
$317$	−7.30027	−	7.30027i	−0.410024	−	0.410024i	−0.881747	+	0.471723i	$0.843632\pi$
$318$	−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	$0.0577667\pi$
$331$			6.56727i			0.360970i	−0.983578	+	0.180485i	$0.942233\pi$
$332$			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	0.178379	−	0.983962i	$-0.442915\pi$
$337$	21.3377	−	21.3377i	1.16234	−	1.16234i	0.983962	−	0.178379i	$-0.0570852\pi$
$338$		−	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	0.560746	−	0.827988i	$-0.310514\pi$
$347$	−4.97815	−	4.97815i	−0.267241	−	0.267241i	−0.827988	+	0.560746i	$0.810514\pi$
$348$		−	1.54126i		−	0.0826200i
$349$			35.4396i			1.89704i	0.316723	+	0.948518i	$0.397417\pi$
$349$			35.4396i			1.89704i	−0.316723	+	0.948518i	$0.602583\pi$
$350$		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	$-0.820210\pi$
$359$		−	20.2839i		−	1.07054i	0.844681	−	0.535271i	$-0.179790\pi$
$360$		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	0.901781	−	0.432193i	$-0.142260\pi$
$367$	8.99600	+	8.99600i	0.469587	+	0.469587i	−0.432193	+	0.901781i	$0.642260\pi$
$368$	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	−0.438253	−	0.898852i	$-0.644402\pi$
$379$	8.96691	−	8.96691i	0.460599	−	0.460599i	0.898852	+	0.438253i	$0.144402\pi$
$380$		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	$0.146203\pi$
$383$			17.3523i			0.886661i	−0.896358	+	0.443331i	$0.853797\pi$
$384$	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	$0.164137\pi$
$389$			19.4510i			0.986205i	−0.869971	+	0.493103i	$0.835863\pi$
$390$		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	0.786505	−	0.617584i	$-0.211888\pi$
$397$	3.36574	+	3.36574i	0.168922	+	0.168922i	−0.617584	+	0.786505i	$0.711888\pi$
$398$	−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	0.990704	−	0.136032i	$-0.0434350\pi$
$401$	17.1148	+	17.1148i	0.854672	+	0.854672i	−0.136032	+	0.990704i	$0.543435\pi$
$402$	−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	0.736567	−	0.676365i	$-0.236446\pi$
$419$	1.23229	+	1.23229i	0.0602015	+	0.0602015i	−0.676365	+	0.736567i	$0.736446\pi$
$420$		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	0.999364	+	0.0356645i	$0.0113548\pi$
$431$	21.4877	+	21.4877i	1.03503	+	1.03503i	0.0356645	+	0.999364i	$0.488645\pi$
$432$	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
$435$		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	−0.773919	−	0.633285i	$-0.781706\pi$
$439$	−2.94661	+	2.94661i	−0.140634	+	0.140634i	0.633285	+	0.773919i	$0.281706\pi$
$440$		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	0.374892	−	0.927068i	$-0.377680\pi$
$449$	−11.7004	−	11.7004i	−0.552176	−	0.552176i	−0.927068	+	0.374892i	$0.877680\pi$
$450$		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	$0.0106356\pi$
$457$			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
$460$		0			0
$461$			11.1662i			0.520062i	0.965600	+	0.260031i	$0.0837327\pi$
$461$			11.1662i			0.520062i	−0.965600	+	0.260031i	$0.916267\pi$
$462$	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	$-0.918552\pi$
$467$		−	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
$470$		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	−0.928079	−	0.372384i	$-0.878540\pi$
$479$	−12.1620	+	12.1620i	−0.555695	+	0.555695i	0.372384	+	0.928079i	$0.378540\pi$
$480$		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	0.987256	−	0.159143i	$-0.0508730\pi$
$487$	18.2749	+	18.2749i	0.828113	+	0.828113i	−0.159143	+	0.987256i	$0.550873\pi$
$488$	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	$0.0890523\pi$
$491$			12.2373i			0.552261i	−0.961120	+	0.276131i	$0.910948\pi$
$492$	−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	0.801325	−	0.598229i	$-0.204129\pi$
$499$	4.53684	+	4.53684i	0.203097	+	0.203097i	−0.598229	+	0.801325i	$0.704129\pi$
$500$		0			0
$501$			14.6272i			0.653496i
$502$		−	20.5248i		−	0.916065i
$503$	−15.0825	−	15.0825i	−0.672497	−	0.672497i	0.285794	−	0.958291i	$-0.407743\pi$
$503$	−15.0825	−	15.0825i	−0.672497	−	0.672497i	−0.958291	+	0.285794i	$0.907743\pi$
$504$	−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	0.215738	−	0.976451i	$-0.430784\pi$
$521$	−17.3636	−	17.3636i	−0.760714	−	0.760714i	−0.976451	+	0.215738i	$0.930784\pi$
$522$	−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	−0.267816	−	0.963470i	$-0.586302\pi$
$541$	16.1805	−	16.1805i	0.695654	−	0.695654i	0.963470	+	0.267816i	$0.0863020\pi$
$542$			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	−0.901812	−	0.432130i	$-0.857762\pi$
$547$	−10.9849	+	10.9849i	−0.469682	+	0.469682i	0.432130	+	0.901812i	$0.357762\pi$
$548$	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	$-0.791711\pi$
$563$		−	28.8837i		−	1.21730i	0.793437	−	0.608652i	$-0.208289\pi$
$564$	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	$-0.874765\pi$
$569$		−	18.2893i		−	0.766729i	0.923597	−	0.383365i	$-0.125235\pi$
$570$		0			0
$571$	−7.35702	−	7.35702i	−0.307882	−	0.307882i	0.536206	−	0.844087i	$-0.319857\pi$
$571$	−7.35702	−	7.35702i	−0.307882	−	0.307882i	−0.844087	+	0.536206i	$0.819857\pi$
$572$	−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	$0.0176230\pi$
$587$			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
$590$		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	$0.101826\pi$
$593$			15.3155i			0.628934i	−0.949268	+	0.314467i	$0.898174\pi$
$594$	−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	0.994173	−	0.107792i	$-0.0343782\pi$
$601$	21.7299	+	21.7299i	0.886381	+	0.886381i	−0.107792	+	0.994173i	$0.534378\pi$
$602$	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	−0.463818	−	0.885930i	$-0.653521\pi$
$607$	10.3997	−	10.3997i	0.422112	−	0.422112i	0.885930	+	0.463818i	$0.153521\pi$
$608$	−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	−0.835509	−	0.549476i	$-0.814827\pi$
$617$	−7.10492	+	7.10492i	−0.286033	+	0.286033i	0.549476	+	0.835509i	$0.314827\pi$
$618$	15.9952	+	15.9952i	0.643421	+	0.643421i
$619$	−24.3145	−	24.3145i	−0.977281	−	0.977281i	0.0224668	−	0.999748i	$-0.492848\pi$
$619$	−24.3145	−	24.3145i	−0.977281	−	0.977281i	−0.999748	+	0.0224668i	$0.992848\pi$
$620$		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	$0.0525125\pi$
$631$			8.25061i			0.328451i	−0.986423	+	0.164226i	$0.947487\pi$
$632$	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	−0.424434	−	0.905459i	$-0.639527\pi$
$641$	12.1786	−	12.1786i	0.481024	−	0.481024i	0.905459	+	0.424434i	$0.139527\pi$
$642$	−24.6256			−0.971895
$643$	8.88071	−	8.88071i	0.350221	−	0.350221i	−0.509971	−	0.860192i	$-0.670344\pi$
$643$	8.88071	−	8.88071i	0.350221	−	0.350221i	0.860192	+	0.509971i	$0.170344\pi$
$644$		−	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	0.559290	−	0.828972i	$-0.311074\pi$
$653$	−6.89142	−	6.89142i	−0.269682	−	0.269682i	−0.828972	+	0.559290i	$0.811074\pi$
$654$		−	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	$-0.931146\pi$
$661$		−	11.0362i		−	0.429258i	0.976696	−	0.214629i	$-0.0688542\pi$
$662$	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	0.179395	−	0.983777i	$-0.442586\pi$
$673$	−20.8675	−	20.8675i	−0.804382	−	0.804382i	−0.983777	+	0.179395i	$0.942586\pi$
$674$	−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	−0.714648	−	0.699485i	$-0.753413\pi$
$677$	−0.394531	+	0.394531i	−0.0151631	+	0.0151631i	0.699485	+	0.714648i	$0.253413\pi$
$678$		−	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	−0.0214974	−	0.999769i	$-0.506843\pi$
$683$	25.5664	−	25.5664i	0.978272	−	0.978272i	0.999769	+	0.0214974i	$0.00684335\pi$
$684$	−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	0.997262	+	0.0739501i	$0.0235606\pi$
$691$	28.1588	+	28.1588i	1.07121	+	1.07121i	0.0739501	+	0.997262i	$0.476439\pi$
$692$	−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	−0.824166	−	0.566348i	$-0.808356\pi$
$709$	−6.86493	+	6.86493i	−0.257818	+	0.257818i	0.566348	+	0.824166i	$0.308356\pi$
$710$		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	−0.377329	−	0.926079i	$-0.623157\pi$
$719$	14.7143	−	14.7143i	0.548750	−	0.548750i	0.926079	+	0.377329i	$0.123157\pi$
$720$		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	$-0.923301\pi$
$733$		−	12.9215i		−	0.477265i	0.971110	−	0.238633i	$-0.0766992\pi$
$734$	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	$0.246229\pi$
$739$			37.9866i			1.39736i	−0.715434	+	0.698680i	$0.753771\pi$
$740$		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	−0.847816	−	0.530290i	$-0.822083\pi$
$743$	−8.65513	+	8.65513i	−0.317526	+	0.317526i	0.530290	+	0.847816i	$0.322083\pi$
$744$	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	−0.865281	−	0.501287i	$-0.832860\pi$
$751$	−9.97504	+	9.97504i	−0.363995	+	0.363995i	0.501287	+	0.865281i	$0.332860\pi$
$752$	−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	$-0.995476\pi$
$757$		−	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
$760$		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	$-0.760517\pi$
$773$		−	37.9989i		−	1.36672i	0.730080	−	0.683362i	$-0.239483\pi$
$774$		−	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	−0.103068	−	0.994674i	$-0.532866\pi$
$787$	25.0127	−	25.0127i	0.891606	−	0.891606i	0.994674	+	0.103068i	$0.0328659\pi$
$788$	−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	$0.157315\pi$
$797$			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
$800$		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	−0.893379	−	0.449303i	$-0.851672\pi$
$809$	−38.1898	−	38.1898i	−1.34268	−	1.34268i	−0.449303	−	0.893379i	$-0.648328\pi$
$810$		0			0
$811$	−37.3327	+	37.3327i	−1.31093	+	1.31093i	−0.390200	+	0.920730i	$0.627594\pi$
$811$	−37.3327	+	37.3327i	−1.31093	+	1.31093i	−0.920730	+	0.390200i	$0.872406\pi$
$812$	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	−0.838609	−	0.544734i	$-0.816631\pi$
$821$	−8.42042	+	8.42042i	−0.293875	+	0.293875i	0.544734	+	0.838609i	$0.316631\pi$
$822$	−43.8520	−	43.8520i	−1.52951	−	1.52951i
$823$	27.9601	+	27.9601i	0.974627	+	0.974627i	0.999686	−	0.0250590i	$-0.00797737\pi$
$823$	27.9601	+	27.9601i	0.974627	+	0.974627i	−0.0250590	+	0.999686i	$0.507977\pi$
$824$			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	0.895588	−	0.444884i	$-0.146755\pi$
$827$	12.9612	+	12.9612i	0.450704	+	0.450704i	−0.444884	+	0.895588i	$0.646755\pi$
$828$	−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	0.409339	−	0.912382i	$-0.365759\pi$
$839$	−14.5709	−	14.5709i	−0.503043	−	0.503043i	−0.912382	+	0.409339i	$0.865759\pi$
$840$		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	−0.799817	−	0.600243i	$-0.795070\pi$
$853$	−5.82880	+	5.82880i	−0.199574	+	0.199574i	0.600243	+	0.799817i	$0.295070\pi$
$854$	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	0.287944	−	0.957647i	$-0.407028\pi$
$857$	−19.6053	−	19.6053i	−0.669703	−	0.669703i	−0.957647	+	0.287944i	$0.907028\pi$
$858$			37.0717i			1.26561i
$859$			7.00671i			0.239066i	0.992830	+	0.119533i	$0.0381397\pi$
$859$			7.00671i			0.239066i	−0.992830	+	0.119533i	$0.961860\pi$
$860$		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	0.963732	+	0.266872i	$0.0859900\pi$
$877$	36.4433	+	36.4433i	1.23060	+	1.23060i	0.266872	+	0.963732i	$0.414010\pi$
$878$	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	−0.119102	+	0.992882i	$0.538002\pi$
$881$	−33.0055	+	33.0055i	−1.11198	+	1.11198i	−0.992882	+	0.119102i	$0.961998\pi$
$882$			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	−0.894438	−	0.447192i	$-0.852424\pi$
$887$	−13.3201	+	13.3201i	−0.447246	+	0.447246i	0.447192	+	0.894438i	$0.352424\pi$
$888$	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	0.319658	−	0.947533i	$-0.396432\pi$
$907$	−18.9094	−	18.9094i	−0.627876	−	0.627876i	−0.947533	+	0.319658i	$0.896432\pi$
$908$	−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	0.818193	−	0.574943i	$-0.194976\pi$
$911$	7.34196	+	7.34196i	0.243250	+	0.243250i	−0.574943	+	0.818193i	$0.694976\pi$
$912$	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	0.758102	−	0.652136i	$-0.226127\pi$
$929$	3.22981	+	3.22981i	0.105966	+	0.105966i	−0.652136	+	0.758102i	$0.726127\pi$
$930$		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	$-0.984871\pi$
$937$		−	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
$940$		0			0
$941$	−10.8860	−	10.8860i	−0.354872	−	0.354872i	0.507046	−	0.861919i	$-0.330737\pi$
$941$	−10.8860	−	10.8860i	−0.354872	−	0.354872i	−0.861919	+	0.507046i	$0.830737\pi$
$942$	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	−0.926787	−	0.375587i	$-0.877441\pi$
$947$	−16.9623	+	16.9623i	−0.551200	+	0.551200i	0.375587	+	0.926787i	$0.377441\pi$
$948$	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	$0.00661890\pi$
$967$			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
$970$		0			0
$971$		−	39.3251i		−	1.26200i	−0.775781	−	0.631002i	$-0.782644\pi$
$971$		−	39.3251i		−	1.26200i	0.775781	−	0.631002i	$-0.217356\pi$
$972$	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	$0.325714\pi$
$977$			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			0
$981$	32.0211	−	32.0211i	1.02235	−	1.02235i
$982$	13.7924			0.440132
$983$	36.1157	−	36.1157i	1.15191	−	1.15191i	0.165742	−	0.986169i	$-0.446998\pi$
$983$	36.1157	−	36.1157i	1.15191	−	1.15191i	0.986169	−	0.165742i	$-0.0530020\pi$
$984$			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	−0.578110	−	0.815959i	$-0.696210\pi$
$991$	7.48752	−	7.48752i	0.237849	−	0.237849i	0.815959	+	0.578110i	$0.196210\pi$
$992$	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	0.744631	−	0.667476i	$-0.232625\pi$
$997$	2.43619	+	2.43619i	0.0771550	+	0.0771550i	−0.667476	+	0.744631i	$0.732625\pi$
$998$	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.276.3		12
5.2	odd	4		425.2.j.c.174.4		12
5.3	odd	4		425.2.j.b.174.3		12
5.4	even	2		85.2.e.a.21.4	✓	12
15.14	odd	2		765.2.k.b.361.3		12
17.8	even	8		7225.2.a.bb.1.3		6
17.9	even	8		7225.2.a.z.1.3		6
17.13	even	4	inner	425.2.e.f.251.4		12
20.19	odd	2		1360.2.bt.d.1041.6		12
85.9	even	8		1445.2.a.o.1.4		6
85.13	odd	4		425.2.j.c.149.4		12
85.19	even	8		1445.2.d.g.866.6		12
85.47	odd	4		425.2.j.b.149.3		12
85.49	even	8		1445.2.d.g.866.5		12
85.59	even	8		1445.2.a.n.1.4		6
85.64	even	4		85.2.e.a.81.3	yes	12
255.149	odd	4		765.2.k.b.676.4		12
340.319	odd	4		1360.2.bt.d.81.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	5.4	even	2
85.2.e.a.81.3	yes	12	85.64	even	4
425.2.e.f.251.4		12	17.13	even	4	inner
425.2.e.f.276.3		12	1.1	even	1	trivial
425.2.j.b.149.3		12	85.47	odd	4
425.2.j.b.174.3		12	5.3	odd	4
425.2.j.c.149.4		12	85.13	odd	4
425.2.j.c.174.4		12	5.2	odd	4
765.2.k.b.361.3		12	15.14	odd	2
765.2.k.b.676.4		12	255.149	odd	4
1360.2.bt.d.81.6		12	340.319	odd	4
1360.2.bt.d.1041.6		12	20.19	odd	2
1445.2.a.n.1.4		6	85.59	even	8
1445.2.a.o.1.4		6	85.9	even	8
1445.2.d.g.866.5		12	85.49	even	8
1445.2.d.g.866.6		12	85.19	even	8
7225.2.a.z.1.3		6	17.9	even	8
7225.2.a.bb.1.3		6	17.8	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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