LMFDB - Embedded newform 525.2.t.g.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.g.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78651 - 1.03144i) q^{2} +(0.627739 + 1.61429i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.543588 - 3.53142i) q^{6} +(0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 + 2.02671i) q^{9} +O(q^{10})$	\(q+(-1.78651 - 1.03144i) q^{2} +(0.627739 + 1.61429i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.543588 - 3.53142i) q^{6} +(0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 + 2.02671i) q^{9} +(-4.06348 + 2.34605i) q^{11} +(-2.44528 + 3.04666i) q^{12} +0.638688i q^{13} +(-2.74595 + 4.71679i) q^{14} +(1.71189 - 2.96508i) q^{16} +(2.07462 + 3.59334i) q^{17} +(6.04198 - 1.33930i) q^{18} +(-0.776975 - 0.448587i) q^{19} +(4.27698 - 1.64544i) q^{21} +9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(0.850763 - 0.330830i) q^{24} +(0.658769 - 1.14102i) q^{26} +(-4.66019 - 2.29839i) q^{27} +(5.17866 - 2.96508i) q^{28} +2.14740i q^{29} +(-2.02453 + 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(-6.33802 - 5.08695i) q^{33} -8.55938i q^{34} +(-6.45320 - 2.03489i) q^{36} +(-5.69122 + 9.85748i) q^{37} +(0.925382 + 1.60281i) q^{38} +(-1.03103 + 0.400929i) q^{39} -4.10624 q^{41} +(-9.33802 - 1.47185i) q^{42} -3.14924 q^{43} +(-9.16509 - 5.29147i) q^{44} +(7.01829 + 12.1560i) q^{46} +(3.40471 - 5.89714i) q^{47} +(5.86113 + 0.902197i) q^{48} +(-6.99982 - 0.0504365i) q^{49} +(-4.49840 + 5.60472i) q^{51} +(-1.24755 + 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(5.95481 + 8.91281i) q^{54} +(-1.39435 - 0.00502336i) q^{56} +(0.236414 - 1.53586i) q^{57} +(2.21492 - 3.83635i) q^{58} +(-0.254055 - 0.440035i) q^{59} +(4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +(5.34105 + 5.87139i) q^{63} +9.89660 q^{64} +(6.07604 + 15.6252i) q^{66} +(2.41425 + 4.18160i) q^{67} +(-4.67925 + 8.10471i) q^{68} +(1.79301 - 11.6483i) q^{69} -1.22800i q^{71} +(1.06811 + 1.16571i) q^{72} +(-12.5197 + 7.22826i) q^{73} +(20.3348 - 11.7403i) q^{74} -2.02356i q^{76} +(6.16830 + 10.7733i) q^{77} +(2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(0.784903 - 8.96571i) q^{81} +(7.33583 + 4.23534i) q^{82} -2.76359 q^{83} +(8.03735 + 6.49859i) q^{84} +(5.62613 + 3.24825i) q^{86} +(-3.46653 + 1.34801i) q^{87} +(1.23641 + 2.14153i) q^{88} +(-6.90067 + 11.9523i) q^{89} +(1.68980 + 0.00608775i) q^{91} -15.3471i q^{92} +(-3.15776 - 2.53444i) q^{93} +(-12.1651 + 7.02352i) q^{94} +(-10.9642 - 8.79992i) q^{96} -12.9085i q^{97} +(12.4532 + 7.31000i) q^{98} +(4.23321 - 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.78651	−	1.03144i	−1.26325	−	0.729338i	−0.289549	−	0.957163i	$-0.593505\pi$
$2$	−1.78651	−	1.03144i	−1.26325	−	0.729338i	−0.973702	+	0.227825i	$0.926839\pi$
$3$	0.627739	+	1.61429i	0.362425	+	0.932013i
$3$	0.627739	+	1.61429i	0.362425	+	0.932013i
$4$	1.12774	+	1.95330i	0.563869	+	0.976650i
$5$		0			0
$5$		0			0
$6$	0.543588	−	3.53142i	0.221919	−	1.44170i
$7$	0.00953166	−	2.64573i	0.00360263	−	0.999994i
$7$	0.00953166	−	2.64573i	0.00360263	−	0.999994i
$8$		−	0.527019i		−	0.186329i
$9$	−2.21189	+	2.02671i	−0.737296	+	0.675570i
$10$		0			0
$11$	−4.06348	+	2.34605i	−1.22519	+	0.707362i	−0.966019	−	0.258471i	$-0.916781\pi$
$11$	−4.06348	+	2.34605i	−1.22519	+	0.707362i	−0.259167	+	0.965833i	$0.583448\pi$
$12$	−2.44528	+	3.04666i	−0.705890	+	0.879496i
$13$			0.638688i			0.177140i	0.996070	+	0.0885701i	$0.0282297\pi$
$13$			0.638688i			0.177140i	−0.996070	+	0.0885701i	$0.971770\pi$
$14$	−2.74595	+	4.71679i	−0.733885	+	1.26062i
$15$		0			0
$16$	1.71189	−	2.96508i	0.427972	−	0.741270i
$17$	2.07462	+	3.59334i	0.503169	+	0.871514i	0.999993	+	0.00366299i	$0.00116597\pi$
$17$	2.07462	+	3.59334i	0.503169	+	0.871514i	−0.496824	+	0.867851i	$0.665501\pi$
$18$	6.04198	−	1.33930i	1.42411	−	0.315676i
$19$	−0.776975	−	0.448587i	−0.178250	−	0.102913i	0.408220	−	0.912884i	$-0.366150\pi$
$19$	−0.776975	−	0.448587i	−0.178250	−	0.102913i	−0.586470	+	0.809971i	$0.699483\pi$
$20$		0			0
$21$	4.27698	−	1.64544i	0.933313	−	0.359065i
$22$	9.67925			2.06362
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.261960	−	0.965079i	$-0.584369\pi$
$23$	−5.89275	−	3.40218i	−1.22872	−	0.709403i	−0.966763	+	0.255675i	$0.917702\pi$
$24$	0.850763	−	0.330830i	0.173661	−	0.0675304i
$25$		0			0
$26$	0.658769	−	1.14102i	0.129195	−	0.223773i
$27$	−4.66019	−	2.29839i	−0.896854	−	0.442326i
$28$	5.17866	−	2.96508i	0.978675	−	0.560347i
$29$			2.14740i			0.398762i	0.979922	+	0.199381i	$0.0638932\pi$
$29$			2.14740i			0.398762i	−0.979922	+	0.199381i	$0.936107\pi$
$30$		0			0
$31$	−2.02453	+	1.16886i	−0.363615	+	0.209933i	−0.670666	−	0.741760i	$-0.733991\pi$
$31$	−2.02453	+	1.16886i	−0.363615	+	0.209933i	0.307050	+	0.951693i	$0.400658\pi$
$32$	−7.02943	+	4.05844i	−1.24264	+	0.717438i
$33$	−6.33802	−	5.08695i	−1.10331	−	0.885524i
$34$		−	8.55938i		−	1.46792i
$35$		0			0
$36$	−6.45320	−	2.03489i	−1.07553	−	0.339148i
$37$	−5.69122	+	9.85748i	−0.935631	+	1.62056i	−0.162126	+	0.986770i	$0.551835\pi$
$37$	−5.69122	+	9.85748i	−0.935631	+	1.62056i	−0.773505	+	0.633790i	$0.781498\pi$
$38$	0.925382	+	1.60281i	0.150117	+	0.260010i
$39$	−1.03103	+	0.400929i	−0.165097	+	0.0642000i
$40$		0			0
$41$	−4.10624			−0.641287			−0.320643	−	0.947200i	$-0.603899\pi$
$41$	−4.10624			−0.641287			−0.320643	+	0.947200i	$0.603899\pi$
$42$	−9.33802	−	1.47185i	−1.44089	−	0.227111i
$43$	−3.14924			−0.480254			−0.240127	−	0.970741i	$-0.577189\pi$
$43$	−3.14924			−0.480254			−0.240127	+	0.970741i	$0.577189\pi$
$44$	−9.16509	−	5.29147i	−1.38169	−	0.797719i
$45$		0			0
$46$	7.01829	+	12.1560i	1.03479	+	1.79231i
$47$	3.40471	−	5.89714i	0.496629	−	0.860186i	−0.503364	−	0.864075i	$-0.667904\pi$
$47$	3.40471	−	5.89714i	0.496629	−	0.860186i	0.999992	+	0.00388861i	$0.00123779\pi$
$48$	5.86113	+	0.902197i	0.845981	+	0.130221i
$49$	−6.99982	−	0.0504365i	−0.999974	−	0.00720521i
$50$		0			0
$51$	−4.49840	+	5.60472i	−0.629901	+	0.784818i
$52$	−1.24755	+	0.720273i	−0.173004	+	0.0998839i
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	−0.628653	−	0.777686i	$-0.716393\pi$
$53$	−1.96187	+	1.13269i	−0.269484	+	0.155587i	0.359169	+	0.933272i	$0.383060\pi$
$54$	5.95481	+	8.91281i	0.810347	+	1.21288i
$55$		0			0
$56$	−1.39435	−	0.00502336i	−0.186328	−	0.000671275i
$57$	0.236414	−	1.53586i	0.0313138	−	0.203430i
$58$	2.21492	−	3.83635i	0.290833	−	0.503737i
$59$	−0.254055	−	0.440035i	−0.0330751	−	0.0572877i	0.849014	−	0.528370i	$-0.177197\pi$
$59$	−0.254055	−	0.440035i	−0.0330751	−	0.0572877i	−0.882089	+	0.471083i	$0.843863\pi$
$60$		0			0
$61$	4.48946	+	2.59199i	0.574816	+	0.331870i	0.759070	−	0.651008i	$-0.225654\pi$
$61$	4.48946	+	2.59199i	0.574816	+	0.331870i	−0.184255	+	0.982879i	$0.558987\pi$
$62$	4.82244			0.612450
$63$	5.34105	+	5.87139i	0.672909	+	0.739725i
$64$	9.89660			1.23708
$65$		0			0
$66$	6.07604	+	15.6252i	0.747909	+	1.92332i
$67$	2.41425	+	4.18160i	0.294947	+	0.510863i	0.974973	−	0.222325i	$-0.0713647\pi$
$67$	2.41425	+	4.18160i	0.294947	+	0.510863i	−0.680026	+	0.733188i	$0.738031\pi$
$68$	−4.67925	+	8.10471i	−0.567443	+	0.982840i
$69$	1.79301	−	11.6483i	0.215853	−	1.40229i
$70$		0			0
$71$		−	1.22800i		−	0.145737i	−0.997342	−	0.0728686i	$-0.976785\pi$
$71$		−	1.22800i		−	0.145737i	0.997342	−	0.0728686i	$-0.0232154\pi$
$72$	1.06811	+	1.16571i	0.125878	+	0.137380i
$73$	−12.5197	+	7.22826i	−1.46532	+	0.846004i	−0.999249	−	0.0387429i	$-0.987665\pi$
$73$	−12.5197	+	7.22826i	−1.46532	+	0.846004i	−0.466072	+	0.884747i	$0.654331\pi$
$74$	20.3348	−	11.7403i	2.36387	−	1.36478i
$75$		0			0
$76$		−	2.02356i		−	0.232118i
$77$	6.16830	+	10.7733i	0.702943	+	1.22773i
$78$	2.25548	+	0.347183i	0.255382	+	0.0393108i
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	0.489068	+	0.872246i	$0.337337\pi$
$79$	−4.54056	+	7.86448i	−0.510853	+	0.884824i	−0.999921	+	0.0125778i	$0.995996\pi$
$80$		0			0
$81$	0.784903	−	8.96571i	0.0872114	−	0.996190i
$82$	7.33583	+	4.23534i	0.810107	+	0.467715i
$83$	−2.76359			−0.303343			−0.151671	−	0.988431i	$-0.548466\pi$
$83$	−2.76359			−0.303343			−0.151671	+	0.988431i	$0.548466\pi$
$84$	8.03735	+	6.49859i	0.876947	+	0.709054i
$85$		0			0
$86$	5.62613	+	3.24825i	0.606682	+	0.350268i
$87$	−3.46653	+	1.34801i	−0.371652	+	0.144521i
$88$	1.23641	+	2.14153i	0.131802	+	0.228288i
$89$	−6.90067	+	11.9523i	−0.731470	+	1.26694i	0.224785	+	0.974408i	$0.427832\pi$
$89$	−6.90067	+	11.9523i	−0.731470	+	1.26694i	−0.956255	+	0.292535i	$0.905501\pi$
$90$		0			0
$91$	1.68980	+	0.00608775i	0.177139	+	0.000638170i
$92$		−	15.3471i		−	1.60004i
$93$	−3.15776	−	2.53444i	−0.327444	−	0.262809i
$94$	−12.1651	+	7.02352i	−1.25473	+	0.724421i
$95$		0			0
$96$	−10.9642	−	8.79992i	−1.11902	−	0.898138i
$97$		−	12.9085i		−	1.31066i	−0.755344	−	0.655329i	$-0.772530\pi$
$97$		−	12.9085i		−	1.31066i	0.755344	−	0.655329i	$-0.227470\pi$
$98$	12.4532	+	7.31000i	1.25796	+	0.738422i
$99$	4.23321	−	13.4247i	0.425453	−	1.34923i
$100$		0			0
$101$	−4.51989	−	7.82869i	−0.449746	−	0.778983i	0.548623	−	0.836070i	$-0.315152\pi$
$101$	−4.51989	−	7.82869i	−0.449746	−	0.778983i	−0.998369	+	0.0570865i	$0.981819\pi$
$102$	13.8174	−	5.37305i	1.36812	−	0.532012i
$103$	13.4412	+	7.76030i	1.32440	+	0.764645i	0.984428	−	0.175789i	$-0.0562476\pi$
$103$	13.4412	+	7.76030i	1.32440	+	0.764645i	0.339976	+	0.940434i	$0.389581\pi$
$104$	0.336601			0.0330064
$105$		0			0
$106$	4.67320			0.453901
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	0.707229	−	0.706985i	$-0.249945\pi$
$107$	4.64012	+	2.67897i	0.448577	+	0.258986i	−0.258652	+	0.965971i	$0.583278\pi$
$108$	−0.766021	−	11.6947i	−0.0737104	−	1.12533i
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	0.831650	−	0.555299i	$-0.187396\pi$
$109$	−0.679436	−	1.17682i	−0.0650782	−	0.112719i	−0.896729	+	0.442581i	$0.854063\pi$
$110$		0			0
$111$	−19.4855	−	2.99938i	−1.84948	−	0.284689i
$112$	−7.82849	−	4.55746i	−0.739723	−	0.430640i
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	−2.00650	+	2.49998i	−0.187926	+	0.234145i
$115$		0			0
$116$	−4.19452	+	2.42171i	−0.389451	+	0.224850i
$117$	−1.29443	−	1.41271i	−0.119671	−	0.130605i
$118$			1.04817i			0.0964917i
$119$	9.52681	−	5.45464i	0.873321	−	0.500026i
$120$		0			0
$121$	5.50793	−	9.54001i	0.500721	−	0.867274i
$122$	−5.34696	−	9.26121i	−0.484091	−	0.838471i
$123$	−2.57765	−	6.62868i	−0.232418	−	0.597688i
$124$	−4.56627	−	2.63634i	−0.410063	−	0.236750i
$125$		0			0
$126$	−3.48584	−	15.9982i	−0.310543	−	1.42524i
$127$	16.8492			1.49513			0.747563	−	0.664191i	$-0.231224\pi$
$127$	16.8492			1.49513			0.747563	+	0.664191i	$0.231224\pi$
$128$	−3.62150	−	2.09088i	−0.320099	−	0.184809i
$129$	−1.97690	−	5.08379i	−0.174056	−	0.447603i
$130$		0			0
$131$	6.93473	−	12.0113i	0.605890	−	1.04943i	−0.386020	−	0.922490i	$-0.626150\pi$
$131$	6.93473	−	12.0113i	0.605890	−	1.04943i	0.991910	−	0.126942i	$-0.0405163\pi$
$132$	2.78870	−	18.1168i	0.242725	−	1.57687i
$133$	−1.19425	+	2.05139i	−0.103554	+	0.177878i
$134$		−	9.96060i		−	0.860465i
$135$		0			0
$136$	1.89376	−	1.09336i	0.162389	−	0.0937551i
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	−0.330844	−	0.943685i	$-0.607333\pi$
$137$	3.75708	−	2.16915i	0.320989	−	0.185323i	0.651833	+	0.758362i	$0.274000\pi$
$138$	−15.2178	+	18.9604i	−1.29542	+	1.61402i
$139$			10.9631i			0.929881i	0.885342	+	0.464941i	$0.153924\pi$
$139$			10.9631i			0.929881i	−0.885342	+	0.464941i	$0.846076\pi$
$140$		0			0
$141$	11.6570	+	1.79435i	0.981695	+	0.151111i
$142$	−1.26661	+	2.19384i	−0.106292	+	0.184103i
$143$	−1.49840	−	2.59530i	−0.125302	−	0.217030i
$144$	2.22284	+	10.0279i	0.185237	+	0.835660i
$145$		0			0
$146$	29.8221			2.46809
$147$	−4.31264	−	11.3314i	−0.355700	−	0.934600i
$148$	−25.6728			−2.11029
$149$	7.50546	+	4.33328i	0.614871	+	0.354996i	0.774870	−	0.632121i	$-0.217816\pi$
$149$	7.50546	+	4.33328i	0.614871	+	0.354996i	−0.159998	+	0.987117i	$0.551149\pi$
$150$		0			0
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	−0.998432	−	0.0559778i	$-0.982172\pi$
$151$	−6.73018	−	11.6570i	−0.547694	−	0.948634i	0.450738	−	0.892656i	$-0.351161\pi$
$152$	−0.236414	+	0.409481i	−0.0191757	+	0.0332133i
$153$	−11.8715	−	3.74343i	−0.959753	−	0.302638i
$154$	0.0922593	−	25.6087i	0.00743447	−	2.06361i
$155$		0			0
$156$	−1.94587	−	1.56177i	−0.155794	−	0.125042i
$157$	6.76643	−	3.90660i	0.540020	−	0.311781i	−0.205067	−	0.978748i	$-0.565741\pi$
$157$	6.76643	−	3.90660i	0.540020	−	0.311781i	0.745087	+	0.666967i	$0.232408\pi$
$158$	16.2235	−	9.36664i	1.29067	−	0.745170i
$159$	−3.06003	−	2.45601i	−0.242677	−	0.194774i
$160$		0			0
$161$	−9.05743	+	15.5582i	−0.713825	+	1.22616i
$162$	−10.6498	+	15.2077i	−0.836730	+	1.19483i
$163$	8.33945	−	14.4443i	0.653196	−	1.13137i	−0.329147	−	0.944279i	$-0.606761\pi$
$163$	8.33945	−	14.4443i	0.653196	−	1.13137i	0.982343	−	0.187090i	$-0.0599055\pi$
$164$	−4.63077	−	8.02072i	−0.361602	−	0.626313i
$165$		0			0
$166$	4.93717	+	2.85047i	0.383198	+	0.221240i
$167$	−0.465112			−0.0359915			−0.0179957	−	0.999838i	$-0.505729\pi$
$167$	−0.465112			−0.0359915			−0.0179957	+	0.999838i	$0.505729\pi$
$168$	−0.867179	−	2.25405i	−0.0669043	−	0.173903i
$169$	12.5921			0.968621
$170$		0			0
$171$	2.62774	−	0.582479i	0.200948	−	0.0445432i
$172$	−3.55152	−	6.15141i	−0.270801	−	0.469040i
$173$	−5.59208	+	9.68576i	−0.425158	+	0.736395i	−0.996435	−	0.0843622i	$-0.973115\pi$
$173$	−5.59208	+	9.68576i	−0.425158	+	0.736395i	0.571277	+	0.820757i	$0.306448\pi$
$174$	7.58338	+	1.16730i	0.574894	+	0.0884929i
$175$		0			0
$176$			16.0647i			1.21092i
$177$	0.550867	−	0.686346i	0.0414057	−	0.0515889i
$178$	24.6562	−	14.2353i	1.84806	−	1.06698i
$179$	−0.214505	+	0.123845i	−0.0160329	+	0.00925660i	−0.507995	−	0.861360i	$-0.669613\pi$
$179$	−0.214505	+	0.123845i	−0.0160329	+	0.00925660i	0.491962	+	0.870617i	$0.336280\pi$
$180$		0			0
$181$			14.3385i			1.06578i	0.846186	+	0.532888i	$0.178893\pi$
$181$			14.3385i			1.06578i	−0.846186	+	0.532888i	$0.821107\pi$
$182$	−3.01256	−	1.75380i	−0.223306	−	0.130000i
$183$	−1.36603	+	8.87439i	−0.100980	+	0.656014i
$184$	−1.79301	+	3.10559i	−0.132183	+	0.228947i
$185$		0			0
$186$	3.02723	+	7.78483i	0.221967	+	0.570812i
$187$	−16.8604	−	9.73433i	−1.23295	−	0.711845i
$188$	15.3585			1.12013
$189$	−6.12536	+	12.3077i	−0.445554	+	0.895255i
$190$		0			0
$191$	14.7572	+	8.52006i	1.06779	+	0.616490i	0.927577	−	0.373632i	$-0.121888\pi$
$191$	14.7572	+	8.52006i	1.06779	+	0.616490i	0.140214	+	0.990121i	$0.455221\pi$
$192$	6.21248	+	15.9760i	0.448347	+	1.15297i
$193$	1.41181	+	2.44533i	0.101624	+	0.176019i	0.912354	−	0.409402i	$-0.134263\pi$
$193$	1.41181	+	2.44533i	0.101624	+	0.176019i	−0.810730	+	0.585421i	$0.800929\pi$
$194$	−13.3143	+	23.0611i	−0.955913	+	1.65569i
$195$		0			0
$196$	−7.79545	−	13.7296i	−0.556818	−	0.980688i
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	−21.4094	+	19.6170i	−1.52150	+	1.39412i
$199$	10.5777	−	6.10706i	0.749836	−	0.432918i	−0.0757989	−	0.997123i	$-0.524151\pi$
$199$	10.5777	−	6.10706i	0.749836	−	0.432918i	0.825635	+	0.564205i	$0.190817\pi$
$200$		0			0
$201$	−5.23481	+	6.52225i	−0.369235	+	0.460044i
$202$			18.6480i			1.31207i
$203$	5.68145	+	0.0204683i	0.398760	+	0.00143659i
$204$	−16.0207	−	2.46605i	−1.12168	−	0.172658i
$205$		0			0
$206$	−16.0086	−	27.7277i	−1.11537	−	1.93188i
$207$	19.9293	−	4.41764i	1.38518	−	0.307047i
$208$	1.89376	+	1.09336i	0.131309	+	0.0758111i
$209$	4.20964			0.291187
$210$		0			0
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$	−4.42496	−	2.55475i	−0.303908	−	0.175461i
$213$	1.98236	−	0.770865i	0.135829	−	0.0528188i
$214$	−5.52640	−	9.57200i	−0.377777	−	0.654329i
$215$		0			0
$216$	−1.21130	+	2.45601i	−0.0824183	+	0.167110i
$217$	3.07320	+	5.36750i	0.208622	+	0.364369i
$218$			2.80319i			0.189856i
$219$	−19.5276	−	15.6730i	−1.31956	−	1.05909i
$220$		0			0
$221$	−2.29503	+	1.32503i	−0.154380	+	0.0891314i
$222$	31.7173	+	25.4565i	2.12872	+	1.70853i
$223$		−	0.392378i		−	0.0262755i	−0.999914	−	0.0131378i	$-0.995818\pi$
$223$		−	0.392378i		−	0.0262755i	0.999914	−	0.0131378i	$-0.00418200\pi$
$224$	10.6706	+	18.6367i	0.712956	+	1.24522i
$225$		0			0
$226$	−12.3143	+	21.3290i	−0.819137	+	1.41879i
$227$	−11.7125	−	20.2867i	−0.777388	−	1.34648i	−0.933442	−	0.358728i	$-0.883211\pi$
$227$	−11.7125	−	20.2867i	−0.777388	−	1.34648i	0.156054	−	0.987749i	$-0.450123\pi$
$228$	3.26661	−	1.27026i	0.216337	−	0.0841253i
$229$	6.69286	+	3.86412i	0.442276	+	0.255348i	0.704563	−	0.709642i	$-0.251143\pi$
$229$	6.69286	+	3.86412i	0.442276	+	0.255348i	−0.262286	+	0.964990i	$0.584477\pi$
$230$		0			0
$231$	−13.5191	+	16.7202i	−0.889493	+	1.10011i
$232$	1.13172			0.0743011
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	0.379780	−	0.925077i	$-0.376000\pi$
$233$	−3.53323	−	2.03991i	−0.231469	−	0.133639i	−0.611250	+	0.791438i	$0.709333\pi$
$234$	0.855394	+	3.85894i	0.0559188	+	0.252267i
$235$		0			0
$236$	0.573014	−	0.992490i	0.0373001	−	0.0646056i
$237$	−15.5459	−	2.39296i	−1.00981	−	0.155440i
$238$	−22.6458	−	0.0815851i	−1.46791	−	0.00528837i
$239$		−	5.76281i		−	0.372765i	−0.982477	−	0.186383i	$-0.940324\pi$
$239$		−	5.76281i		−	0.372765i	0.982477	−	0.186383i	$-0.0596764\pi$
$240$		0			0
$241$	−17.6840	+	10.2098i	−1.13912	+	0.657674i	−0.946214	−	0.323542i	$-0.895126\pi$
$241$	−17.6840	+	10.2098i	−1.13912	+	0.657674i	−0.192911	+	0.981216i	$0.561793\pi$
$242$	−19.6799	+	11.3622i	−1.26507	+	0.730390i
$243$	14.9660	−	4.36106i	0.960069	−	0.279762i
$244$			11.6923i			0.748525i
$245$		0			0
$246$	−2.23210	+	14.5009i	−0.142314	+	0.924542i
$247$	0.286507	−	0.496245i	0.0182300	−	0.0315753i
$248$	0.616011	+	1.06696i	0.0391167	+	0.0677522i
$249$	−1.73481	−	4.46124i	−0.109939	−	0.282720i
$250$		0			0
$251$	4.42544			0.279331			0.139666	−	0.990199i	$-0.455397\pi$
$251$	4.42544			0.279331			0.139666	+	0.990199i	$0.455397\pi$
$252$	−5.44528	+	17.0541i	−0.343020	+	1.07431i
$253$	31.9268			2.00722
$254$	−30.1012	−	17.3790i	−1.88872	−	1.09045i
$255$		0			0
$256$	−5.58338	−	9.67069i	−0.348961	−	0.604418i
$257$	−12.7539	+	22.0904i	−0.795565	+	1.37796i	0.126915	+	0.991914i	$0.459492\pi$
$257$	−12.7539	+	22.0904i	−0.795565	+	1.37796i	−0.922480	+	0.386045i	$0.873841\pi$
$258$	−1.71189	+	11.1213i	−0.106578	+	0.692381i
$259$	26.0260	+	15.1514i	1.61718	+	0.941463i
$260$		0			0
$261$	−4.35215	−	4.74981i	−0.269392	−	0.294006i
$262$	−24.7779	+	14.3055i	−1.53078	+	0.883798i
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	−0.509528	−	0.860454i	$-0.670180\pi$
$263$	−0.310020	+	0.178990i	−0.0191166	+	0.0110370i	0.490411	+	0.871491i	$0.336847\pi$
$264$	−2.68092	+	3.34026i	−0.164999	+	0.205579i
$265$		0			0
$266$	4.24942	−	2.43304i	0.260549	−	0.149179i
$267$	−23.6264	−	3.63678i	−1.44591	−	0.222568i
$268$	−5.44528	+	9.43149i	−0.332623	+	0.576120i
$269$	4.26905	+	7.39421i	0.260288	+	0.450833i	0.966319	−	0.257349i	$-0.0828490\pi$
$269$	4.26905	+	7.39421i	0.260288	+	0.450833i	−0.706030	+	0.708182i	$0.749516\pi$
$270$		0			0
$271$	−7.30474	−	4.21739i	−0.443731	−	0.256188i	0.261448	−	0.965218i	$-0.415800\pi$
$271$	−7.30474	−	4.21739i	−0.443731	−	0.256188i	−0.705179	+	0.709029i	$0.749133\pi$
$272$	14.2061			0.861369
$273$	1.05092	+	2.73165i	0.0636048	+	0.165327i
$274$	−8.94940			−0.540653
$275$		0			0
$276$	24.7747	−	9.63395i	1.49126	−	0.579896i
$277$	5.05294	+	8.75195i	0.303602	+	0.525853i	0.976949	−	0.213473i	$-0.0684775\pi$
$277$	5.05294	+	8.75195i	0.303602	+	0.525853i	−0.673347	+	0.739326i	$0.735144\pi$
$278$	11.3078	−	19.5857i	0.678198	−	1.17467i
$279$	2.10909	−	6.68851i	0.126268	−	0.400431i
$280$		0			0
$281$		−	15.1554i		−	0.904094i	−0.891994	−	0.452047i	$-0.850694\pi$
$281$		−	15.1554i		−	0.904094i	0.891994	−	0.452047i	$-0.149306\pi$
$282$	−18.9745	−	15.2291i	−1.12992	−	0.906880i
$283$	−20.7322	+	11.9697i	−1.23240	+	0.711527i	−0.967530	−	0.252757i	$-0.918663\pi$
$283$	−20.7322	+	11.9697i	−1.23240	+	0.711527i	−0.264871	+	0.964284i	$0.585329\pi$
$284$	2.39866	−	1.38487i	0.142334	−	0.0821768i
$285$		0			0
$286$			6.18202i			0.365551i
$287$	−0.0391393	+	10.8640i	−0.00231032	+	0.641283i
$288$	7.32303	−	23.2234i	0.431514	−	1.36845i
$289$	−0.108084	+	0.187206i	−0.00635786	+	0.0110121i
$290$		0			0
$291$	20.8381	−	8.10315i	1.22155	−	0.475015i
$292$	−28.2379	−	16.3032i	−1.65250	−	0.954071i
$293$	21.2223			1.23982			0.619909	−	0.784673i	$-0.287169\pi$
$293$	21.2223			1.23982			0.619909	+	0.784673i	$0.287169\pi$
$294$	−3.98313	+	24.6919i	−0.232301	+	1.44006i
$295$		0			0
$296$	5.19508	+	2.99938i	0.301958	+	0.174335i
$297$	24.3288	−	1.59357i	1.41170	−	0.0924681i
$298$	−8.93904	−	15.4829i	−0.517825	−	0.896899i
$299$	2.17293	−	3.76363i	0.125664	−	0.217656i
$300$		0			0
$301$	−0.0300174	+	8.33204i	−0.00173018	+	0.480251i
$302$			27.7671i			1.59782i
$303$	9.80049	−	12.2108i	0.563023	−	0.701492i
$304$	−2.66019	+	1.53586i	−0.152572	+	0.0880877i
$305$		0			0
$306$	17.3474	+	18.9324i	0.991683	+	1.08229i
$307$			24.2817i			1.38583i	0.721019	+	0.692916i	$0.243674\pi$
$307$			24.2817i			1.38583i	−0.721019	+	0.692916i	$0.756326\pi$
$308$	−14.0872	+	24.1980i	−0.802691	+	1.37881i
$309$	−4.08982	+	26.5695i	−0.232662	+	1.51149i
$310$		0			0
$311$	3.55858	+	6.16364i	0.201789	+	0.349508i	0.949105	−	0.314960i	$-0.101991\pi$
$311$	3.55858	+	6.16364i	0.201789	+	0.349508i	−0.747316	+	0.664469i	$0.768658\pi$
$312$	0.211297	+	0.543372i	0.0119623	+	0.0307624i
$313$	−3.07200	−	1.77362i	−0.173640	−	0.100251i	0.410661	−	0.911788i	$-0.365298\pi$
$313$	−3.07200	−	1.77362i	−0.173640	−	0.100251i	−0.584301	+	0.811537i	$0.698631\pi$
$314$	−16.1177			−0.909575
$315$		0			0
$316$	−20.4823			−1.15222
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.915599	−	0.402093i	$-0.131717\pi$
$317$	18.2527	+	10.5382i	1.02517	+	0.591885i	0.109576	+	0.993978i	$0.465051\pi$
$318$	2.93355	+	7.54392i	0.164505	+	0.423042i
$319$	−5.03791	−	8.72592i	−0.282069	−	0.488558i
$320$		0			0
$321$	−1.41187	+	9.17220i	−0.0788028	+	0.511942i
$322$	32.2285	−	18.4527i	1.79603	−	1.02833i
$323$		−	3.72259i		−	0.207130i
$324$	18.3979	−	8.57782i	1.02210	−	0.476546i
$325$		0			0
$326$	−29.7970	+	17.2033i	−1.65030	+	0.952802i
$327$	1.47322	−	1.83554i	0.0814693	−	0.101506i
$328$			2.16407i			0.119491i
$329$	−15.5698	−	9.06418i	−0.858391	−	0.499724i
$330$		0			0
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	−0.587581	−	0.809165i	$-0.699920\pi$
$331$	7.40412	−	12.8243i	0.406967	−	0.704888i	0.994548	+	0.104277i	$0.0332529\pi$
$332$	−3.11660	−	5.39811i	−0.171046	−	0.296260i
$333$	−7.38990	−	33.3381i	−0.404964	−	1.82692i
$334$	0.830926	+	0.479736i	0.0454663	+	0.0262500i
$335$		0			0
$336$	2.44284	−	15.4984i	0.133268	−	0.845506i
$337$	−20.5062			−1.11704			−0.558522	−	0.829490i	$-0.688631\pi$
$337$	−20.5062			−1.11704			−0.558522	+	0.829490i	$0.688631\pi$
$338$	−22.4958	−	12.9880i	−1.22361	−	0.706453i
$339$	19.2730	−	7.49455i	1.04677	−	0.407048i
$340$		0			0
$341$	5.48442	−	9.49929i	0.296998	−	0.514415i
$342$	−5.29527	−	1.66975i	−0.286335	−	0.0902899i
$343$	−0.200161	+	18.5192i	−0.0108077	+	0.999942i
$344$			1.65971i			0.0894854i
$345$		0			0
$346$	19.9806	−	11.5358i	1.07416	−	0.620168i
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	−0.820617	−	0.571479i	$-0.806370\pi$
$347$	−13.7103	+	7.91567i	−0.736010	+	0.424935i	0.0846070	+	0.996414i	$0.473037\pi$
$348$	−6.54241	−	5.25099i	−0.350710	−	0.281482i
$349$			8.96019i			0.479628i	0.970819	+	0.239814i	$0.0770865\pi$
$349$			8.96019i			0.479628i	−0.970819	+	0.239814i	$0.922914\pi$
$350$		0			0
$351$	1.46796	−	2.97641i	0.0783538	−	0.158869i
$352$	19.0426	−	32.9828i	1.01498	−	1.75799i
$353$	−6.72876	−	11.6545i	−0.358136	−	0.620309i	0.629514	−	0.776989i	$-0.283254\pi$
$353$	−6.72876	−	11.6545i	−0.358136	−	0.620309i	−0.987649	+	0.156680i	$0.949921\pi$
$354$	−1.69205	+	0.657976i	−0.0899316	+	0.0349710i
$355$		0			0
$356$	−31.1286			−1.64981
$357$	14.7857	+	11.9550i	0.782544	+	0.632725i
$358$	0.510954			0.0270048
$359$	−4.85824	−	2.80491i	−0.256408	−	0.148037i	0.366287	−	0.930502i	$-0.380629\pi$
$359$	−4.85824	−	2.80491i	−0.256408	−	0.148037i	−0.622695	+	0.782465i	$0.713962\pi$
$360$		0			0
$361$	−9.09754	−	15.7574i	−0.478818	−	0.829337i
$362$	14.7894	−	25.6159i	0.777311	−	1.34634i
$363$	18.8579	+	2.90278i	0.989784	+	0.152356i
$364$	1.89376	+	3.30755i	0.0992600	+	0.173363i
$365$		0			0
$366$	11.5938	−	14.4452i	0.606019	−	0.755062i
$367$	1.71154	−	0.988156i	0.0893415	−	0.0515813i	−0.454664	−	0.890663i	$-0.650241\pi$
$367$	1.71154	−	0.988156i	0.0893415	−	0.0515813i	0.544005	+	0.839082i	$0.316907\pi$
$368$	−20.1755	+	11.6483i	−1.05172	+	0.607210i
$369$	9.08255	−	8.32215i	0.472818	−	0.433234i
$370$		0			0
$371$	2.97809	+	5.20139i	0.154615	+	0.270043i
$372$	1.38940	−	9.02623i	0.0720370	−	0.467988i
$373$	−11.5467	+	19.9995i	−0.597866	+	1.03553i	0.395270	+	0.918565i	$0.370651\pi$
$373$	−11.5467	+	19.9995i	−0.597866	+	1.03553i	−0.993136	+	0.116969i	$0.962682\pi$
$374$	20.0808	+	34.7809i	1.03835	+	1.79848i
$375$		0			0
$376$	−3.10790	−	1.79435i	−0.160278	−	0.0925364i
$377$	−1.37152			−0.0706368
$378$	23.6377	−	15.6699i	1.21579	−	0.805972i
$379$	−17.0645			−0.876547			−0.438273	−	0.898842i	$-0.644410\pi$
$379$	−17.0645			−0.876547			−0.438273	+	0.898842i	$0.644410\pi$
$380$		0			0
$381$	10.5769	+	27.1996i	0.541871	+	1.39348i
$382$	−17.5759	−	30.4423i	−0.899259	−	1.55756i
$383$	−13.3056	+	23.0460i	−0.679886	+	1.17760i	0.295129	+	0.955457i	$0.404637\pi$
$383$	−13.3056	+	23.0460i	−0.679886	+	1.17760i	−0.975015	+	0.222139i	$0.928696\pi$
$384$	1.10193	−	7.15869i	0.0562327	−	0.365316i
$385$		0			0
$386$		−	5.82479i		−	0.296474i
$387$	6.96576	−	6.38259i	0.354090	−	0.324445i
$388$	25.2141	−	14.5574i	1.28005	−	0.739040i
$389$	8.20951	−	4.73976i	0.416239	−	0.240316i	−0.277228	−	0.960804i	$-0.589416\pi$
$389$	8.20951	−	4.73976i	0.416239	−	0.240316i	0.693467	+	0.720489i	$0.256082\pi$
$390$		0			0
$391$		−	28.2329i		−	1.42780i
$392$	−0.0265810	+	3.68904i	−0.00134254	+	0.186324i
$393$	23.7430	+	3.65473i	1.19767	+	0.184357i
$394$	9.89848	−	17.1447i	0.498678	−	0.863736i
$395$		0			0
$396$	30.9964	−	6.87083i	1.55763	−	0.345272i
$397$	−10.7042	−	6.18009i	−0.537230	−	0.310170i	0.206726	−	0.978399i	$-0.433719\pi$
$397$	−10.7042	−	6.18009i	−0.537230	−	0.310170i	−0.743956	+	0.668229i	$0.767053\pi$
$398$	−25.1963			−1.26297
$399$	−4.06123	−	0.640127i	−0.203316	−	0.0320464i
$400$		0			0
$401$	7.11494	+	4.10781i	0.355303	+	0.205134i	0.667019	−	0.745041i	$-0.267570\pi$
$401$	7.11494	+	4.10781i	0.355303	+	0.205134i	−0.311715	+	0.950176i	$0.600904\pi$
$402$	16.0793	−	6.25265i	0.801964	−	0.311854i
$403$	−0.746537	−	1.29304i	−0.0371877	−	0.0644109i
$404$	10.1945	−	17.6574i	0.507196	−	0.878490i
$405$		0			0
$406$	−10.1288	−	5.89664i	−0.502686	−	0.292646i
$407$		−	53.4076i		−	2.64732i
$408$	2.95379	+	2.37074i	0.146235	+	0.117369i
$409$	−17.9575	+	10.3678i	−0.887942	+	0.512653i	−0.873269	−	0.487239i	$-0.838004\pi$
$409$	−17.9575	+	10.3678i	−0.887942	+	0.512653i	−0.0146731	+	0.999892i	$0.504671\pi$
$410$		0			0
$411$	5.86011	+	4.70337i	0.289058	+	0.232000i
$412$			35.0064i			1.72464i
$413$	−1.16664	+	0.667967i	−0.0574065	+	0.0328685i
$414$	−40.1604	−	12.6638i	−1.97378	−	0.622390i
$415$		0			0
$416$	−2.59208	−	4.48961i	−0.127087	−	0.220121i
$417$	−17.6977	+	6.88198i	−0.866661	+	0.337012i
$418$	−7.52054	−	4.34199i	−0.367842	−	0.212374i
$419$	6.93924			0.339004			0.169502	−	0.985530i	$-0.445784\pi$
$419$	6.93924			0.339004			0.169502	+	0.985530i	$0.445784\pi$
$420$		0			0
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$	−10.0779	−	5.81849i	−0.490585	−	0.283240i
$423$	4.42093	+	19.9442i	0.214953	+	0.969719i
$424$	0.596948	+	1.03394i	0.0289904	+	0.0502128i
$425$		0			0
$426$	−4.33660	−	0.667529i	−0.210109	−	0.0323419i
$427$	6.90050	−	11.8532i	0.333939	−	0.573617i
$428$			12.0847i			0.584137i
$429$	3.24897	−	4.04802i	0.156862	−	0.195440i
$430$		0			0
$431$	−26.9043	+	15.5332i	−1.29594	+	0.748209i	−0.979699	−	0.200472i	$-0.935752\pi$
$431$	−26.9043	+	15.5332i	−1.29594	+	0.748209i	−0.316236	+	0.948681i	$0.602419\pi$
$432$	−14.7926	+	9.88323i	−0.711712	+	0.475507i
$433$		−	22.3083i		−	1.07207i	−0.844196	−	0.536034i	$-0.819922\pi$
$433$		−	22.3083i		−	1.07207i	0.844196	−	0.536034i	$-0.180078\pi$
$434$	0.0459658	−	12.7589i	0.00220643	−	0.612446i
$435$		0			0
$436$	1.53245	−	2.65429i	0.0733912	−	0.127117i
$437$	3.05235	+	5.28682i	0.146014	+	0.252903i
$438$	18.7205	+	48.1416i	0.894498	+	2.30029i
$439$	−22.4126	−	12.9399i	−1.06970	−	0.617590i	−0.141598	−	0.989924i	$-0.545224\pi$
$439$	−22.4126	−	12.9399i	−1.06970	−	0.617590i	−0.928099	+	0.372334i	$0.878557\pi$
$440$		0			0
$441$	15.5850	−	14.0750i	0.742145	−	0.670240i
$442$	5.46677			0.260028
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.975756	−	0.218862i	$-0.0702343\pi$
$443$	26.8166	+	15.4826i	1.27409	+	0.735599i	0.298338	+	0.954460i	$0.403568\pi$
$444$	−16.1158	−	41.4435i	−0.764823	−	1.96682i
$445$		0			0
$446$	−0.404714	+	0.700985i	−0.0191638	+	0.0331926i
$447$	−2.28372	+	14.8362i	−0.108016	+	0.701728i
$448$	0.0943310	−	26.1838i	0.00445672	−	1.23707i
$449$			24.2032i			1.14222i	0.820874	+	0.571110i	$0.193487\pi$
$449$			24.2032i			1.14222i	−0.820874	+	0.571110i	$0.806513\pi$
$450$		0			0
$451$	16.6856	−	9.63346i	0.785696	−	0.453622i
$452$	23.3204	−	13.4640i	1.09690	−	0.633295i
$453$	14.5930	−	18.1820i	0.685641	−	0.854267i
$454$			48.3231i			2.26792i
$455$		0			0
$456$	−0.809428	−	0.124594i	−0.0379049	−	0.00583467i
$457$	−1.20726	+	2.09103i	−0.0564731	+	0.0978143i	−0.892880	−	0.450295i	$-0.851319\pi$
$457$	−1.20726	+	2.09103i	−0.0564731	+	0.0978143i	0.836407	+	0.548109i	$0.184652\pi$
$458$	−7.97122	−	13.8066i	−0.372471	−	0.645138i
$459$	−1.40919	−	21.5140i	−0.0657755	−	1.00419i
$460$		0			0
$461$	7.45376			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$461$	7.45376			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$462$	41.3979	−	15.9267i	1.92601	−	0.740975i
$463$	−13.8862			−0.645345			−0.322672	−	0.946511i	$-0.604581\pi$
$463$	−13.8862			−0.645345			−0.322672	+	0.946511i	$0.604581\pi$
$464$	6.36721	+	3.67611i	0.295590	+	0.170659i
$465$		0			0
$466$	4.20809	+	7.28862i	0.194936	+	0.337639i
$467$	10.0692	−	17.4404i	0.465948	−	0.807045i	−0.533296	−	0.845929i	$-0.679047\pi$
$467$	10.0692	−	17.4404i	0.465948	−	0.807045i	0.999244	+	0.0388836i	$0.0123802\pi$
$468$	1.29966	−	4.12158i	0.0600767	−	0.190520i
$469$	11.0864	−	6.34759i	0.511923	−	0.293105i
$470$		0			0
$471$	10.5540	+	8.47068i	0.486300	+	0.390309i
$472$	−0.231907	+	0.133892i	−0.0106744	+	0.00616286i
$473$	12.7969	−	7.38828i	0.588401	−	0.339713i
$474$	25.3046	+	20.3097i	1.16228	+	0.932855i
$475$		0			0
$476$	21.3983	+	12.4573i	0.980789	+	0.570980i
$477$	2.04382	−	6.48153i	0.0935799	−	0.296769i
$478$	−5.94399	+	10.2953i	−0.271872	+	0.470896i
$479$	−16.6189	−	28.7847i	−0.759335	−	1.31521i	−0.943190	−	0.332253i	$-0.892191\pi$
$479$	−16.6189	−	28.7847i	−0.759335	−	1.31521i	0.183855	−	0.982953i	$-0.441142\pi$
$480$		0			0
$481$	−6.29586	−	3.63491i	−0.287066	−	0.165738i
$482$	42.1234			1.91867
$483$	−30.8012	−	4.85486i	−1.40150	−	0.220904i
$484$	24.8460			1.12936
$485$		0			0
$486$	−31.2350	−	7.64548i	−1.41685	−	0.346806i
$487$	−16.1039	−	27.8927i	−0.729736	−	1.26394i	−0.956995	−	0.290105i	$-0.906310\pi$
$487$	−16.1039	−	27.8927i	−0.729736	−	1.26394i	0.227259	−	0.973834i	$-0.427024\pi$
$488$	1.36603	−	2.36603i	0.0618371	−	0.107105i
$489$	28.5524	+	4.39504i	1.29118	+	0.198751i
$490$		0			0
$491$		−	22.5003i		−	1.01542i	−0.861527	−	0.507712i	$-0.830491\pi$
$491$		−	22.5003i		−	1.01542i	0.861527	−	0.507712i	$-0.169509\pi$
$492$	10.0409	−	12.5103i	0.452678	−	0.564009i
$493$	−7.71635	+	4.45504i	−0.347527	+	0.200645i
$494$	−1.02369	+	0.591030i	−0.0460582	+	0.0265917i
$495$		0			0
$496$			8.00383i			0.359383i
$497$	−3.24897	−	0.0117049i	−0.145736	−	0.000525037i
$498$	−1.50225	+	9.75939i	−0.0673176	+	0.437329i
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	−0.928837	−	0.370489i	$-0.879190\pi$
$499$	−3.20702	+	5.55472i	−0.143566	+	0.248663i	0.785271	+	0.619152i	$0.212524\pi$
$500$		0			0
$501$	−0.291969	−	0.750828i	−0.0130442	−	0.0335445i
$502$	−7.90608	−	4.56458i	−0.352866	−	0.203727i
$503$	−38.0103			−1.69479			−0.847397	−	0.530960i	$-0.821831\pi$
$503$	−38.0103			−1.69479			−0.847397	+	0.530960i	$0.821831\pi$
$504$	3.09433	−	2.81483i	0.137832	−	0.125383i
$505$		0			0
$506$	−57.0374	−	32.9306i	−2.53562	−	1.46394i
$507$	7.90453	+	20.3273i	0.351053	+	0.902768i
$508$	19.0015	+	32.9116i	0.843056	+	1.46022i
$509$	−6.34981	+	10.9982i	−0.281450	+	0.487486i	−0.971742	−	0.236045i	$-0.924149\pi$
$509$	−6.34981	+	10.9982i	−0.281450	+	0.487486i	0.690292	+	0.723531i	$0.257482\pi$
$510$		0			0
$511$	19.0047	+	33.1927i	0.840719	+	1.46836i
$512$			31.3992i			1.38766i
$513$	2.58982	+	3.87630i	0.114344	+	0.171143i
$514$	45.5698	−	26.3097i	2.01000	−	1.16047i
$515$		0			0
$516$	7.70075	−	9.59466i	0.339007	−	0.422382i
$517$			31.9506i			1.40518i
$518$	−30.8679	−	53.9124i	−1.35626	−	2.36878i
$519$	−19.1460	−	2.94713i	−0.840417	−	0.129365i
$520$		0			0
$521$	18.0970	+	31.3449i	0.792843	+	1.37324i	0.924200	+	0.381909i	$0.124733\pi$
$521$	18.0970	+	31.3449i	0.792843	+	1.37324i	−0.131357	+	0.991335i	$0.541933\pi$
$522$	2.87601	+	12.9746i	0.125880	+	0.567881i
$523$	4.27382	+	2.46749i	0.186881	+	0.107896i	0.590522	−	0.807022i	$-0.298922\pi$
$523$	4.27382	+	2.46749i	0.186881	+	0.107896i	−0.403640	+	0.914918i	$0.632255\pi$
$524$	31.2823			1.36657
$525$		0			0
$526$	0.738470			0.0321988
$527$	−8.40023	−	4.84988i	−0.365920	−	0.211264i
$528$	−25.9332	+	10.0844i	−1.12860	+	0.438869i
$529$	11.6496	+	20.1778i	0.506506	+	0.877295i
$530$		0			0
$531$	1.45376	+	0.458415i	0.0630880	+	0.0198935i
$532$	−5.35379	−	0.0192878i	−0.232116	−	0.000836234i
$533$		−	2.62261i		−	0.113598i
$534$	38.4576	+	30.8663i	1.66422	+	1.33572i
$535$		0			0
$536$	2.20378	−	1.27235i	0.0951888	−	0.0549573i
$537$	−0.334575	−	0.268533i	−0.0144380	−	0.0115880i
$538$		−	17.6131i		−	0.759354i
$539$	28.5620	−	16.2170i	1.23025	−	0.698515i
$540$		0			0
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	−0.987638	−	0.156750i	$-0.949898\pi$
$541$	−8.32849	+	14.4254i	−0.358070	+	0.620195i	0.629569	+	0.776945i	$0.283232\pi$
$542$	8.69998	+	15.0688i	0.373696	+	0.647261i
$543$	−23.1466	+	9.00086i	−0.993317	+	0.386264i
$544$	−29.1668	−	16.8394i	−1.25051	−	0.721985i
$545$		0			0
$546$	0.940053	−	5.96408i	0.0402306	−	0.255239i
$547$	−21.2868			−0.910159			−0.455079	−	0.890451i	$-0.650389\pi$
$547$	−21.2868			−0.910159			−0.455079	+	0.890451i	$0.650389\pi$
$548$	8.47401	+	4.89247i	0.361992	+	0.208996i
$549$	−15.1834	+	3.36563i	−0.648011	+	0.143642i
$550$		0			0
$551$	0.963296	−	1.66848i	0.0410378	−	0.0710795i
$552$	−6.13887	−	0.944951i	−0.261288	−	0.0402198i
$553$	20.7641	+	12.0881i	0.882977	+	0.514037i
$554$		−	20.8472i		−	0.885713i
$555$		0			0
$556$	−21.4143	+	12.3636i	−0.908169	+	0.524331i
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	−0.105401	−	0.994430i	$-0.533613\pi$
$557$	16.5937	−	9.58040i	0.703099	−	0.405935i	0.808501	+	0.588495i	$0.200279\pi$
$558$	−10.6667	+	9.77368i	−0.451557	+	0.413753i
$559$		−	2.01138i		−	0.0850723i
$560$		0			0
$561$	5.13017	−	33.3282i	0.216596	−	1.40712i
$562$	−15.6319	+	27.0752i	−0.659390	+	1.14210i
$563$	13.6243	+	23.5981i	0.574198	+	0.994540i	0.996128	+	0.0879116i	$0.0280193\pi$
$563$	13.6243	+	23.5981i	0.574198	+	0.994540i	−0.421930	+	0.906628i	$0.638647\pi$
$564$	9.64113	+	24.7931i	0.405965	+	1.04398i
$565$		0			0
$566$	49.3843			2.07578
$567$	−23.7134	−	2.16210i	−0.995869	−	0.0907998i
$568$	−0.647181			−0.0271551
$569$	22.7124	+	13.1130i	0.952153	+	0.549726i	0.893749	−	0.448567i	$-0.148066\pi$
$569$	22.7124	+	13.1130i	0.952153	+	0.549726i	0.0584038	+	0.998293i	$0.481399\pi$
$570$		0			0
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	0.997287	+	0.0736170i	$0.0234542\pi$
$571$	13.4388	+	23.2767i	0.562397	+	0.974101i	−0.434889	+	0.900484i	$0.643212\pi$
$572$	3.37960	−	5.85363i	0.141308	−	0.244753i
$573$	−4.49023	+	29.1708i	−0.187582	+	1.21863i
$574$	11.2755	−	19.3683i	0.470631	−	0.808416i
$575$		0			0
$576$	−21.8902	+	20.0575i	−0.912091	+	0.835731i
$577$	8.93069	−	5.15614i	0.371790	−	0.214653i	−0.302450	−	0.953165i	$-0.597805\pi$
$577$	8.93069	−	5.15614i	0.371790	−	0.214653i	0.674240	+	0.738512i	$0.264471\pi$
$578$	0.386185	−	0.222964i	0.0160632	−	0.00927407i
$579$	−3.06123	+	3.81410i	−0.127220	+	0.158509i
$580$		0			0
$581$	−0.0263416	+	7.31171i	−0.00109283	+	0.303341i
$582$	−45.5853	−	7.01690i	−1.88957	−	0.290860i
$583$	5.31469	−	9.20532i	0.220112	−	0.381245i
$584$	3.80943	+	6.59812i	0.157635	+	0.273032i
$585$		0			0
$586$	−37.9138	−	21.8895i	−1.56620	−	0.904248i
$587$	−22.1492			−0.914197			−0.457098	−	0.889416i	$-0.651111\pi$
$587$	−22.1492			−0.914197			−0.457098	+	0.889416i	$0.651111\pi$
$588$	17.2701	−	21.2028i	0.712209	−	0.874387i
$589$	2.09734			0.0864195
$590$		0			0
$591$	−15.4920	+	6.02425i	−0.637255	+	0.247805i
$592$	19.4855	+	33.7498i	0.800848	+	1.38711i
$593$	−1.45861	+	2.52638i	−0.0598978	+	0.103746i	−0.894419	−	0.447229i	$-0.852411\pi$
$593$	−1.45861	+	2.52638i	−0.0598978	+	0.103746i	0.834522	+	0.550975i	$0.185744\pi$
$594$	−45.1072	−	22.2467i	−1.85077	−	0.912795i
$595$		0			0
$596$			19.5472i			0.800686i
$597$	16.4986	+	13.2419i	0.675244	+	0.541956i
$598$	−7.76391	+	4.48250i	−0.317490	+	0.183303i
$599$	−31.4551	+	18.1606i	−1.28522	+	0.742023i	−0.977798	−	0.209550i	$-0.932800\pi$
$599$	−31.4551	+	18.1606i	−1.28522	+	0.742023i	−0.307424	+	0.951573i	$0.599467\pi$
$600$		0			0
$601$		−	7.15198i		−	0.291735i	−0.989304	−	0.145868i	$-0.953403\pi$
$601$		−	7.15198i		−	0.291735i	0.989304	−	0.145868i	$-0.0465974\pi$
$602$	8.64763	−	14.8543i	0.352451	−	0.605416i
$603$	−13.8149	−	4.35625i	−0.562587	−	0.177400i
$604$	15.1798	−	26.2921i	0.617656	−	1.06981i
$605$		0			0
$606$	−30.1034	+	11.7061i	−1.22287	+	0.475527i
$607$	37.8248	+	21.8382i	1.53526	+	0.886384i	0.999106	+	0.0422651i	$0.0134574\pi$
$607$	37.8248	+	21.8382i	1.53526	+	0.886384i	0.536156	+	0.844119i	$0.319876\pi$
$608$	7.28226			0.295334
$609$	3.53342	+	9.18438i	0.143182	+	0.372170i
$610$		0			0
$611$	3.76643	+	2.17455i	0.152373	+	0.0879729i
$612$	−6.07589	−	27.4102i	−0.245603	−	1.10799i
$613$	−7.27926	−	12.6080i	−0.294007	−	0.509234i	0.680747	−	0.732519i	$-0.261655\pi$
$613$	−7.27926	−	12.6080i	−0.294007	−	0.509234i	−0.974753	+	0.223285i	$0.928322\pi$
$614$	25.0452	−	43.3795i	1.01074	−	1.75065i
$615$		0			0
$616$	5.67771	−	3.25081i	0.228761	−	0.130979i
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	34.7114	−	43.2483i	1.39630	−	1.73970i
$619$	−33.0429	+	19.0773i	−1.32810	+	0.766782i	−0.985006	−	0.172518i	$-0.944810\pi$
$619$	−33.0429	+	19.0773i	−1.32810	+	0.766782i	−0.343098	+	0.939299i	$0.611476\pi$
$620$		0			0
$621$	19.6418	+	29.3987i	0.788197	+	1.17973i
$622$		−	14.6819i		−	0.588689i
$623$	31.5569	+	18.3713i	1.26430	+	0.736030i
$624$	−0.576223	+	3.74343i	−0.0230674	+	0.149857i
$625$		0			0
$626$	3.65877	+	6.33717i	0.146234	+	0.253284i
$627$	2.64255	+	6.79559i	0.105533	+	0.271390i
$628$	15.2615	+	8.81125i	0.609001	+	0.351607i
$629$	−47.2285			−1.88312
$630$		0			0
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$	4.14473	+	2.39296i	0.164869	+	0.0951869i
$633$	3.54115	+	9.10644i	0.140748	+	0.361948i
$634$	−21.7391	−	37.6532i	−0.863369	−	1.49540i
$635$		0			0
$636$	1.34640	−	8.74690i	0.0533883	−	0.346837i
$637$	0.0322132	−	4.47070i	0.00127633	−	0.177136i
$638$			20.7852i			0.822895i
$639$	2.48881	+	2.71621i	0.0984557	+	0.107452i
$640$		0			0
$641$	20.0037	−	11.5491i	0.790099	−	0.456164i	−0.0498985	−	0.998754i	$-0.515890\pi$
$641$	20.0037	−	11.5491i	0.790099	−	0.456164i	0.839997	+	0.542590i	$0.182556\pi$
$642$	11.9829	−	14.9299i	0.472927	−	0.589238i
$643$		−	22.7592i		−	0.897536i	−0.893648	−	0.448768i	$-0.851863\pi$
$643$		−	22.7592i		−	0.897536i	0.893648	−	0.448768i	$-0.148137\pi$
$644$	−40.6043	−	0.146283i	−1.60003	−	0.00576436i
$645$		0			0
$646$	−3.83963	+	6.65043i	−0.151068	+	0.261658i
$647$	−1.21349	−	2.10183i	−0.0477073	−	0.0826315i	0.841186	−	0.540746i	$-0.181858\pi$
$647$	−1.21349	−	2.10183i	−0.0477073	−	0.0826315i	−0.888893	+	0.458115i	$0.848525\pi$
$648$	−4.72510	−	0.413659i	−0.185619	−	0.0162500i
$649$	2.06469	+	1.19205i	0.0810463	+	0.0467921i
$650$		0			0
$651$	−6.73555	+	8.33043i	−0.263987	+	0.326495i
$652$	37.6189			1.47327
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.989742	−	0.142865i	$-0.0456315\pi$
$653$	34.7760	+	20.0779i	1.36089	+	0.785709i	0.371146	+	0.928574i	$0.378965\pi$
$654$	−4.52517	+	1.75967i	−0.176948	+	0.0688086i
$655$		0			0
$656$	−7.02943	+	12.1753i	−0.274453	+	0.475366i
$657$	13.0426	−	41.3619i	0.508842	−	1.61368i
$658$	18.4664	+	32.2525i	0.719896	+	1.25734i
$659$			0.627454i			0.0244421i	0.999925	+	0.0122211i	$0.00389018\pi$
$659$			0.627454i			0.0244421i	−0.999925	+	0.0122211i	$0.996110\pi$
$660$		0			0
$661$	−28.5745	+	16.4975i	−1.11142	+	0.641678i	−0.939197	−	0.343380i	$-0.888428\pi$
$661$	−28.5745	+	16.4975i	−1.11142	+	0.641678i	−0.172222	+	0.985058i	$0.555095\pi$
$662$	−26.4550	+	15.2738i	−1.02820	+	0.593634i
$663$	−3.57967	−	2.87307i	−0.139023	−	0.111581i
$664$			1.45646i			0.0565217i
$665$		0			0
$666$	−21.1842	+	67.1810i	−0.820869	+	2.60321i
$667$	7.30584	−	12.6541i	0.282883	−	0.489968i
$668$	−0.524525	−	0.908504i	−0.0202945	−	0.0351511i
$669$	0.633413	−	0.246310i	0.0244891	−	0.00952291i
$670$		0			0
$671$	−24.3238			−0.939009
$672$	−23.3868	+	28.9244i	−0.902164	+	1.11578i
$673$	−1.14437			−0.0441121			−0.0220560	−	0.999757i	$-0.507021\pi$
$673$	−1.14437			−0.0441121			−0.0220560	+	0.999757i	$0.507021\pi$
$674$	36.6345	+	21.1509i	1.41111	+	0.814703i
$675$		0			0
$676$	14.2006	+	24.5961i	0.546176	+	0.946004i
$677$	−7.98910	+	13.8375i	−0.307046	+	0.531820i	−0.977715	−	0.209938i	$-0.932674\pi$
$677$	−7.98910	+	13.8375i	−0.307046	+	0.531820i	0.670669	+	0.741757i	$0.266007\pi$
$678$	−42.1615	−	6.48988i	−1.61920	−	0.249242i
$679$	−34.1524	−	0.123039i	−1.31065	−	0.00472181i
$680$		0			0
$681$	25.3963	−	31.6422i	0.973188	−	1.21253i
$682$	−19.5959	+	11.3137i	−0.750366	+	0.433224i
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	−0.462008	−	0.886876i	$-0.652871\pi$
$683$	1.96122	−	1.13231i	0.0750442	−	0.0433268i	0.537053	+	0.843549i	$0.319538\pi$
$684$	4.10116	+	4.47588i	0.156812	+	0.171140i
$685$		0			0
$686$	19.4590	−	32.8782i	0.742949	−	1.25530i
$687$	−2.03646	+	13.2299i	−0.0776960	+	0.504752i
$688$	−5.39114	+	9.33773i	−0.205535	+	0.355998i
$689$	−0.723434	−	1.25303i	−0.0275607	−	0.0477365i
$690$		0			0
$691$	−2.40044	−	1.38589i	−0.0913169	−	0.0527218i	0.453646	−	0.891182i	$-0.350123\pi$
$691$	−2.40044	−	1.38589i	−0.0913169	−	0.0527218i	−0.544963	+	0.838460i	$0.683456\pi$
$692$	−25.2256			−0.958934
$693$	−35.4778	−	11.3279i	−1.34769	−	0.430311i
$694$	32.6582			1.23969
$695$		0			0
$696$	0.710424	+	1.82693i	0.0269286	+	0.0692496i
$697$	−8.51888	−	14.7551i	−0.322676	−	0.558891i
$698$	9.24191	−	16.0075i	0.349811	−	0.605891i
$699$	1.07507	−	6.98419i	0.0406629	−	0.264166i
$700$		0			0
$701$		−	23.1184i		−	0.873169i	−0.899663	−	0.436585i	$-0.856188\pi$
$701$		−	23.1184i		−	0.873169i	0.899663	−	0.436585i	$-0.143812\pi$
$702$	−5.69250	+	3.80326i	−0.214850	+	0.143545i
$703$	8.84388	−	5.10602i	0.333553	−	0.192577i
$704$	−40.2147	+	23.2180i	−1.51565	+	0.875060i
$705$		0			0
$706$			27.7612i			1.04481i
$707$	−20.7557	+	11.8838i	−0.780599	+	0.446937i
$708$	1.96187	+	0.301989i	0.0737317	+	0.0113495i
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	−0.299517	−	0.954091i	$-0.596826\pi$
$709$	18.0134	−	31.2002i	0.676508	−	1.17175i	0.976026	−	0.217656i	$-0.0698410\pi$
$710$		0			0
$711$	−5.89580	−	26.5978i	−0.221110	−	0.997494i
$712$	6.29910	+	3.63678i	0.236069	+	0.136294i
$713$	15.9067			0.595710
$714$	−14.0840	−	36.6083i	−0.527079	−	1.37003i
$715$		0			0
$716$	−0.483812	−	0.279329i	−0.0180809	−	0.0104390i
$717$	9.30287	−	3.61754i	0.347422	−	0.135099i
$718$	5.78619	+	10.0220i	0.215939	+	0.374017i
$719$	8.57099	−	14.8454i	0.319644	−	0.553640i	−0.660770	−	0.750589i	$-0.729770\pi$
$719$	8.57099	−	14.8454i	0.319644	−	0.553640i	0.980414	+	0.196949i	$0.0631034\pi$
$720$		0			0
$721$	20.6598	−	35.4880i	0.769412	−	1.32164i
$722$			37.5343i			1.39688i
$723$	−27.5826	−	22.1380i	−1.02581	−	0.823322i
$724$	−28.0075	+	16.1701i	−1.04089	+	0.600958i
$725$		0			0
$726$	−30.6958	−	24.6367i	−1.13923	−	0.914352i
$727$		−	16.6832i		−	0.618747i	−0.950941	−	0.309374i	$-0.899881\pi$
$727$		−	16.6832i		−	0.618747i	0.950941	−	0.309374i	$-0.100119\pi$
$728$	0.00320836	−	0.890556i	0.000118910	−	0.0330062i
$729$	16.4348	+	21.4219i	0.608695	+	0.793404i
$730$		0			0
$731$	−6.53347	−	11.3163i	−0.241649	−	0.418548i
$732$	−18.8749	+	7.33973i	−0.697635	+	0.271284i
$733$	−32.9814	−	19.0418i	−1.21820	−	0.703326i	−0.253664	−	0.967292i	$-0.581636\pi$
$733$	−32.9814	−	19.0418i	−1.21820	−	0.703326i	−0.964532	+	0.263967i	$0.914969\pi$
$734$	−4.07690			−0.150481
$735$		0			0
$736$	55.2302			2.03581
$737$	−19.6205	−	11.3279i	−0.722730	−	0.417268i
$738$	−24.8098	+	5.49948i	−0.913263	+	0.202439i
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	0.995182	−	0.0980422i	$-0.0312580\pi$
$739$	11.2186	+	19.4312i	0.412684	+	0.714790i	−0.582498	+	0.812832i	$0.697925\pi$
$740$		0			0
$741$	0.980937	+	0.150995i	0.0360356	+	0.00554693i
$742$	0.0445433	−	12.3640i	0.00163524	−	0.453898i
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	−1.33570	+	1.66420i	−0.0489690	+	0.0610124i
$745$		0			0
$746$	41.2565	−	23.8195i	1.51051	−	0.872093i
$747$	6.11275	−	5.60098i	0.223654	−	0.204929i
$748$		−	43.9111i		−	1.60555i
$749$	7.13207	−	12.2510i	0.260600	−	0.447641i
$750$		0			0
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	−0.748069	−	0.663620i	$-0.769019\pi$
$751$	5.49944	−	9.52531i	0.200677	−	0.347583i	0.948747	+	0.316037i	$0.102352\pi$
$752$	−11.6570	−	20.1905i	−0.425086	−	0.736271i
$753$	2.77802	+	7.14396i	0.101237	+	0.260340i
$754$	2.45023	+	1.41464i	0.0892320	+	0.0515181i
$755$		0			0
$756$	−30.9485	+	1.91522i	−1.12559	+	0.0696558i
$757$	27.8216			1.01119			0.505597	−	0.862770i	$-0.331272\pi$
$757$	27.8216			1.01119			0.505597	+	0.862770i	$0.331272\pi$
$758$	30.4859	+	17.6011i	1.10730	+	0.639299i
$759$	20.0417	+	51.5392i	0.727466	+	1.87075i
$760$		0			0
$761$	−6.54766	+	11.3409i	−0.237352	+	0.411106i	−0.959954	−	0.280159i	$-0.909613\pi$
$761$	−6.54766	+	11.3409i	−0.237352	+	0.411106i	0.722601	+	0.691265i	$0.242946\pi$
$762$	9.15904	−	59.5017i	0.331797	−	2.15552i
$763$	−3.12002	+	1.78639i	−0.112952	+	0.0646717i
$764$			38.4336i			1.39048i
$765$		0			0
$766$	47.5412	−	27.4479i	1.71773	−	0.991734i
$767$	0.281045	−	0.162262i	0.0101480	−	0.00585893i
$768$	12.1064	−	15.0839i	0.436853	−	0.544293i
$769$			7.74247i			0.279201i	0.990208	+	0.139600i	$0.0445818\pi$
$769$			7.74247i			0.279201i	−0.990208	+	0.139600i	$0.955418\pi$
$770$		0			0
$771$	−43.6664	−	6.72153i	−1.57261	−	0.242070i
$772$	−3.18431	+	5.51538i	−0.114606	+	0.198503i
$773$	−19.1733	−	33.2091i	−0.689614	−	1.19445i	−0.971963	−	0.235135i	$-0.924447\pi$
$773$	−19.1733	−	33.2091i	−0.689614	−	1.19445i	0.282349	−	0.959312i	$-0.408887\pi$
$774$	−19.0276	+	4.21777i	−0.683934	+	0.151605i
$775$		0			0
$776$	−6.80301			−0.244214
$777$	−8.12129	+	51.5248i	−0.291350	+	1.84844i
$778$	−19.5551			−0.701086
$779$	3.19045	+	1.84201i	0.114310	+	0.0659967i
$780$		0			0
$781$	2.88096	+	4.98997i	0.103089	+	0.178555i
$782$	−29.1205	+	50.4383i	−1.04135	+	1.80367i
$783$	4.93557	−	10.0073i	0.176383	−	0.357632i
$784$	−12.1325	+	20.6687i	−0.433302	+	0.738167i
$785$		0			0
$786$	−38.6474	−	31.0187i	−1.37851	−	1.10640i
$787$	21.6178	−	12.4811i	0.770592	−	0.444901i	−0.0624938	−	0.998045i	$-0.519905\pi$
$787$	21.6178	−	12.4811i	0.770592	−	0.444901i	0.833086	+	0.553144i	$0.186572\pi$
$788$	−18.7453	+	10.8226i	−0.667775	+	0.385540i
$789$	−0.483554	−	0.388104i	−0.0172150	−	0.0138169i
$790$		0			0
$791$	−31.5873	−	0.113798i	−1.12312	−	0.00404619i
$792$	−7.07507	−	2.23098i	−0.251402	−	0.0792744i
$793$	−1.65547	+	2.86736i	−0.0587875	+	0.101823i
$794$	12.7488	+	22.0816i	0.452438	+	0.783645i
$795$		0			0
$796$	23.8578	+	13.7743i	0.845619	+	0.488218i
$797$	−5.81191			−0.205868			−0.102934	−	0.994688i	$-0.532823\pi$
$797$	−5.81191			−0.205868			−0.102934	+	0.994688i	$0.532823\pi$
$798$	6.59516	+	5.33251i	0.233466	+	0.188769i
$799$	28.2539			0.999552
$800$		0			0
$801$	−8.96035	−	40.4229i	−0.316598	−	1.42827i
$802$	−8.47393	−	14.6773i	−0.299225	−	0.518273i
$803$	33.9158	−	58.7438i	1.19686	−	2.07302i
$804$	−18.6434	−	2.86976i	−0.657502	−	0.101209i
$805$		0			0
$806$			3.08003i			0.108490i
$807$	−9.25658	+	11.5331i	−0.325847	+	0.405985i
$808$	−4.12586	+	2.38207i	−0.145147	+	0.0838009i
$809$	1.51563	−	0.875048i	0.0532866	−	0.0307650i	−0.473120	−	0.880998i	$-0.656872\pi$
$809$	1.51563	−	0.875048i	0.0532866	−	0.0307650i	0.526407	+	0.850233i	$0.323539\pi$
$810$		0			0
$811$		−	28.4479i		−	0.998940i	−0.866331	−	0.499470i	$-0.833528\pi$
$811$		−	28.4479i		−	0.998940i	0.866331	−	0.499470i	$-0.166472\pi$
$812$	6.36721	+	11.1207i	0.223445	+	0.390259i
$813$	2.22265	−	14.4394i	0.0779516	−	0.506412i
$814$	−55.0868	+	95.4131i	−1.93079	+	3.34423i
$815$		0			0
$816$	8.91769	+	22.9328i	0.312182	+	0.802807i
$817$	2.44688	+	1.41271i	0.0856055	+	0.0494244i
$818$	42.7750			1.49559
$819$	−3.74998	+	3.41126i	−0.131035	+	0.119199i
$820$		0			0
$821$	25.9378	+	14.9752i	0.905236	+	0.522638i	0.878895	−	0.477015i	$-0.158281\pi$
$821$	25.9378	+	14.9752i	0.905236	+	0.522638i	0.0263407	+	0.999653i	$0.491615\pi$
$822$	−5.61789	−	14.4470i	−0.195946	−	0.503896i
$823$	8.06283	+	13.9652i	0.281053	+	0.486798i	0.971644	−	0.236447i	$-0.0759831\pi$
$823$	8.06283	+	13.9652i	0.281053	+	0.486798i	−0.690592	+	0.723245i	$0.742650\pi$
$824$	4.08982	−	7.08378i	0.142476	−	0.246775i
$825$		0			0
$826$	2.77318	+	0.00999078i	0.0964911	+	0.000347624i
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	31.1041	+	33.9460i	1.08094	+	1.17971i
$829$	18.0763	−	10.4363i	0.627815	−	0.362469i	−0.152091	−	0.988367i	$-0.548601\pi$
$829$	18.0763	−	10.4363i	0.627815	−	0.362469i	0.779905	+	0.625898i	$0.215267\pi$
$830$		0			0
$831$	−10.9563	+	13.6509i	−0.380069	+	0.473543i
$832$			6.32084i			0.219136i
$833$	−14.3407	−	25.2574i	−0.496876	−	0.875117i
$834$	38.7155	+	5.95943i	1.34061	+	0.206358i
$835$		0			0
$836$	4.74737	+	8.22268i	0.164191	+	0.284387i
$837$	12.1212	−	0.793953i	0.418969	−	0.0274430i
$838$	−12.3970	−	7.15741i	−0.428247	−	0.247249i
$839$	−14.2504			−0.491977			−0.245989	−	0.969273i	$-0.579113\pi$
$839$	−14.2504			−0.491977			−0.245989	+	0.969273i	$0.579113\pi$
$840$		0			0
$841$	24.3887			0.840989
$842$	27.1839	+	15.6946i	0.936819	+	0.540873i
$843$	24.4652	−	9.51361i	0.842627	−	0.327666i
$844$	6.36172	+	11.0188i	0.218979	+	0.379283i
$845$		0			0
$846$	12.6732	−	40.1903i	0.435714	−	1.38177i
$847$	−25.1878	−	14.6634i	−0.865464	−	0.503842i
$848$			7.75614i			0.266347i
$849$	−32.3371	−	25.9540i	−1.10981	−	0.890738i
$850$		0			0
$851$	67.0739	−	38.7251i	2.29926	−	1.32748i
$852$	3.74131	+	3.00281i	0.128175	+	0.102875i
$853$			49.6034i			1.69839i	0.528081	+	0.849194i	$0.322912\pi$
$853$			49.6034i			1.69839i	−0.528081	+	0.849194i	$0.677088\pi$
$854$	−24.5537	+	14.0584i	−0.840209	+	0.481067i
$855$		0			0
$856$	1.41187	−	2.44543i	0.0482567	−	0.0835830i
$857$	−2.62252	−	4.54233i	−0.0895834	−	0.155163i	0.817752	−	0.575571i	$-0.195220\pi$
$857$	−2.62252	−	4.54233i	−0.0895834	−	0.155163i	−0.907335	+	0.420408i	$0.861887\pi$
$858$	−9.97960	+	3.88069i	−0.340698	+	0.132485i
$859$	−10.1722	−	5.87292i	−0.347071	−	0.200382i	0.316323	−	0.948651i	$-0.397552\pi$
$859$	−10.1722	−	5.87292i	−0.347071	−	0.200382i	−0.663394	+	0.748270i	$0.730885\pi$
$860$		0			0
$861$	−17.5623	+	6.75658i	−0.598521	+	0.230264i
$862$	64.0863			2.18279
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.116211	−	0.993225i	$-0.537075\pi$
$863$	−30.3896	−	17.5454i	−1.03447	−	0.597254i	−0.918263	+	0.395971i	$0.870408\pi$
$864$	42.0864	−	2.75671i	1.43181	−	0.0937853i
$865$		0			0
$866$	−23.0097	+	39.8539i	−0.781901	+	1.35429i
$867$	−0.370054	−	0.0569621i	−0.0125677	−	0.00193454i
$868$	−7.01857	+	12.0560i	−0.238226	+	0.409208i
$869$		−	42.6096i		−	1.44543i
$870$		0			0
$871$	−2.67074	+	1.54195i	−0.0904944	+	0.0522470i
$872$	−0.620205	+	0.358076i	−0.0210028	+	0.0121260i
$873$	26.1617	+	28.5521i	0.885440	+	0.966343i
$874$		−	12.5933i		−	0.425973i
$875$		0			0
$876$	8.59208	−	55.8184i	0.290299	−	1.88593i
$877$	−8.42662	+	14.5953i	−0.284547	+	0.492850i	−0.972499	−	0.232906i	$-0.925176\pi$
$877$	−8.42662	+	14.5953i	−0.284547	+	0.492850i	0.687952	+	0.725756i	$0.258510\pi$
$878$	26.6936	+	46.2346i	0.900864	+	1.56034i
$879$	13.3220	+	34.2590i	0.449341	+	1.15553i
$880$		0			0
$881$	−51.9437			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$881$	−51.9437			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$882$	−42.3603	+	9.07011i	−1.42635	+	0.305406i
$883$	−14.9096			−0.501748			−0.250874	−	0.968020i	$-0.580718\pi$
$883$	−14.9096			−0.501748			−0.250874	+	0.968020i	$0.580718\pi$
$884$	−5.17638	−	2.98858i	−0.174100	−	0.100517i
$885$		0			0
$886$	−31.9387	−	55.3194i	−1.07300	−	1.85849i
$887$	6.59427	−	11.4216i	0.221414	−	0.383500i	−0.733824	−	0.679340i	$-0.762266\pi$
$887$	6.59427	−	11.4216i	0.221414	−	0.383500i	0.955238	+	0.295840i	$0.0955994\pi$
$888$	−1.58073	+	10.2692i	−0.0530458	+	0.344612i
$889$	0.160601	−	44.5785i	0.00538638	−	1.49512i
$890$		0			0
$891$	17.8446	+	38.2734i	0.597816	+	1.28221i
$892$	0.766431	−	0.442499i	0.0256620	−	0.0148160i
$893$	−5.29076	+	3.05462i	−0.177048	+	0.102219i
$894$	19.3825	−	24.1494i	0.648249	−	0.807678i
$895$		0			0
$896$	−5.56642	+	9.56161i	−0.185961	+	0.319431i
$897$	7.43963	+	1.14518i	0.248402	+	0.0382363i
$898$	24.9642	−	43.2392i	0.833065	−	1.44291i
$899$	−2.51001	−	4.34747i	−0.0837135	−	0.144996i
$900$		0			0
$901$	−8.14028	−	4.69979i	−0.271192	−	0.156573i
$902$	−39.7453			−1.32338
$903$	−13.4692	+	5.18189i	−0.448227	+	0.172442i
$904$	−6.29206			−0.209271
$905$		0			0
$906$	−44.8243	+	17.4305i	−1.48919	+	0.579089i
$907$	23.4709	+	40.6527i	0.779337	+	1.34985i	0.932324	+	0.361623i	$0.117777\pi$
$907$	23.4709	+	40.6527i	0.779337	+	1.34985i	−0.152987	+	0.988228i	$0.548889\pi$
$908$	26.4174	−	45.7562i	0.876691	−	1.51847i
$909$	25.8640	+	8.15567i	0.857854	+	0.270507i
$910$		0			0
$911$			45.2977i			1.50078i	0.660996	+	0.750389i	$0.270134\pi$
$911$			45.2977i			1.50078i	−0.660996	+	0.750389i	$0.729866\pi$
$912$	−4.14924	−	3.33021i	−0.137395	−	0.110274i
$913$	11.2298	−	6.48352i	0.371652	−	0.214573i
$914$	4.31355	−	2.49043i	0.142680	−	0.0823761i
$915$		0			0
$916$			17.4309i			0.575932i
$917$	−31.7126	−	18.4619i	−1.04724	−	0.609667i
$918$	−19.6728	+	39.8884i	−0.649300	+	1.31651i
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	0.251795	+	0.967781i	$0.418979\pi$
$919$	−21.5911	+	37.3969i	−0.712225	+	1.23361i	−0.964020	+	0.265830i	$0.914354\pi$
$920$		0			0
$921$	−39.1978	+	15.2426i	−1.29161	+	0.502260i
$922$	−13.3162	−	7.68811i	−0.438546	−	0.253195i
$923$	0.784311			0.0258159
$924$	−47.9057	−	7.55085i	−1.57598	−	0.248405i
$925$		0			0
$926$	24.8077	+	14.3227i	0.815232	+	0.470675i
$927$	−45.4584	+	10.0765i	−1.49305	+	0.330957i
$928$	−8.71510	−	15.0950i	−0.286087	−	0.495517i
$929$	−4.50570	+	7.80410i	−0.147827	+	0.256044i	−0.930424	−	0.366484i	$-0.880561\pi$
$929$	−4.50570	+	7.80410i	−0.147827	+	0.256044i	0.782597	+	0.622529i	$0.213895\pi$
$930$		0			0
$931$	5.41606	+	3.17922i	0.177504	+	0.104195i
$932$		−	9.20194i		−	0.301419i
$933$	−7.71607	+	9.61375i	−0.252613	+	0.314740i
$934$	−35.9774	+	20.7716i	−1.17722	+	0.679667i
$935$		0			0
$936$	−0.744523	+	0.682191i	−0.0243355	+	0.0222981i
$937$			21.9677i			0.717654i	0.933404	+	0.358827i	$0.116823\pi$
$937$			21.9677i			0.717654i	−0.933404	+	0.358827i	$0.883177\pi$
$938$	−26.3531	−	0.0949410i	−0.860459	−	0.00309993i
$939$	0.934731	−	6.07248i	0.0305038	−	0.198168i
$940$		0			0
$941$	0.823861	+	1.42697i	0.0268571	+	0.0465178i	0.879142	−	0.476561i	$-0.158117\pi$
$941$	0.823861	+	1.42697i	0.0268571	+	0.0465178i	−0.852284	+	0.523079i	$0.824783\pi$
$942$	−10.1177	−	26.0187i	−0.329653	−	0.847735i
$943$	24.1970	+	13.9702i	0.787964	+	0.454931i
$944$	−1.73965			−0.0566209
$945$		0			0
$946$	−30.4823			−0.991064
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	0.832516	−	0.554002i	$-0.186900\pi$
$947$	23.6645	+	13.6627i	0.768994	+	0.443979i	−0.0635217	+	0.997980i	$0.520233\pi$
$948$	−12.8575	−	33.0644i	−0.417592	−	1.07388i
$949$	−4.61660	−	7.99619i	−0.149861	−	0.259567i
$950$		0			0
$951$	−5.55384	+	36.0805i	−0.180095	+	1.16999i
$952$	−2.87470	−	5.02081i	−0.0931695	−	0.162725i
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	−10.3366	+	9.47122i	−0.334660	+	0.306642i
$955$		0			0
$956$	11.2565	−	6.49894i	0.364061	−	0.210191i
$957$	10.9237	−	13.6103i	0.353113	−	0.439958i
$958$			68.5654i			2.21525i
$959$	−5.70319	−	9.96091i	−0.184166	−	0.321655i
$960$		0			0
$961$	−12.7675	+	22.1140i	−0.411856	+	0.713355i
$962$	7.49840	+	12.9876i	0.241758	+	0.418737i
$963$	−15.6929	+	3.47857i	−0.505697	+	0.112096i
$964$	−39.8858	−	23.0281i	−1.28464	−	0.741684i
$965$		0			0
$966$	50.0191	+	40.4429i	1.60934	+	1.30123i
$967$	34.5930			1.11244			0.556218	−	0.831036i	$-0.312252\pi$
$967$	34.5930			1.11244			0.556218	+	0.831036i	$0.312252\pi$
$968$	−5.02776	−	2.90278i	−0.161598	−	0.0932989i
$969$	6.00935	−	2.33681i	0.193048	−	0.0750692i
$970$		0			0
$971$	2.12246	−	3.67621i	0.0681129	−	0.117975i	−0.829958	−	0.557826i	$-0.811636\pi$
$971$	2.12246	−	3.67621i	0.0681129	−	0.117975i	0.898071	+	0.439851i	$0.144969\pi$
$972$	25.3962	+	24.3150i	0.814583	+	0.779903i
$973$	29.0056	+	0.104497i	0.929875	+	0.00335002i
$974$			66.4407i			2.12890i
$975$		0			0
$976$	15.3709	−	8.87439i	0.492010	−	0.284062i
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.147308	−	0.989091i	$-0.452939\pi$
$977$	33.6806	−	19.4455i	1.07754	−	0.622118i	0.930232	+	0.366973i	$0.119606\pi$
$978$	−46.4758	−	37.3019i	−1.48613	−	1.19278i
$979$		−	64.7574i		−	2.06966i
$980$		0			0
$981$	3.88790	+	1.22597i	0.124131	+	0.0391422i
$982$	−23.2077	+	40.1970i	−0.740588	+	1.28274i
$983$	13.1884	+	22.8429i	0.420644	+	0.728577i	0.996003	−	0.0893246i	$-0.0284709\pi$
$983$	13.1884	+	22.8429i	0.420644	+	0.728577i	−0.575359	+	0.817901i	$0.695138\pi$
$984$	−3.49344	+	1.35847i	−0.111367	+	0.0433064i
$985$		0			0
$986$	18.3804			0.585352
$987$	4.85848	−	30.8242i	0.154647	−	0.981144i
$988$	1.29242			0.0411174
$989$	18.5577	+	10.7143i	0.590099	+	0.340694i
$990$		0			0
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	0.954640	−	0.297762i	$-0.0962403\pi$
$991$	6.90833	+	11.9656i	0.219450	+	0.380099i	−0.735190	+	0.677861i	$0.762907\pi$
$992$	9.48750	−	16.4328i	0.301228	−	0.521743i
$993$	25.3501	+	3.90211i	0.804460	+	0.123830i
$994$	5.79224	+	3.37203i	0.183719	+	0.106954i
$995$		0			0
$996$	6.75773	−	8.41972i	0.214127	−	0.266789i
$997$	−53.1001	+	30.6574i	−1.68170	+	0.970929i	−0.721165	+	0.692763i	$0.756393\pi$
$997$	−53.1001	+	30.6574i	−1.68170	+	0.970929i	−0.960533	+	0.278166i	$0.910274\pi$
$998$	11.4587	−	6.61570i	0.362720	−	0.209416i
$999$	49.1786	−	32.8571i	1.55594	−	1.03955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.g.26.1		8
3.2	odd	2		525.2.t.f.26.4		8
5.2	odd	4		525.2.q.f.299.7		16
5.3	odd	4		525.2.q.f.299.2		16
5.4	even	2		105.2.s.c.26.4	✓	8
7.3	odd	6		525.2.t.f.101.4		8
15.2	even	4		525.2.q.e.299.2		16
15.8	even	4		525.2.q.e.299.7		16
15.14	odd	2		105.2.s.d.26.1	yes	8
21.17	even	6	inner	525.2.t.g.101.1		8
35.3	even	12		525.2.q.e.374.2		16
35.4	even	6		735.2.s.l.521.1		8
35.9	even	6		735.2.b.d.146.2		8
35.17	even	12		525.2.q.e.374.7		16
35.19	odd	6		735.2.b.c.146.2		8
35.24	odd	6		105.2.s.d.101.1	yes	8
35.34	odd	2		735.2.s.k.656.4		8
105.17	odd	12		525.2.q.f.374.2		16
105.38	odd	12		525.2.q.f.374.7		16
105.44	odd	6		735.2.b.c.146.7		8
105.59	even	6		105.2.s.c.101.4	yes	8
105.74	odd	6		735.2.s.k.521.4		8
105.89	even	6		735.2.b.d.146.7		8
105.104	even	2		735.2.s.l.656.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	5.4	even	2
105.2.s.c.101.4	yes	8	105.59	even	6
105.2.s.d.26.1	yes	8	15.14	odd	2
105.2.s.d.101.1	yes	8	35.24	odd	6
525.2.q.e.299.2		16	15.2	even	4
525.2.q.e.299.7		16	15.8	even	4
525.2.q.e.374.2		16	35.3	even	12
525.2.q.e.374.7		16	35.17	even	12
525.2.q.f.299.2		16	5.3	odd	4
525.2.q.f.299.7		16	5.2	odd	4
525.2.q.f.374.2		16	105.17	odd	12
525.2.q.f.374.7		16	105.38	odd	12
525.2.t.f.26.4		8	3.2	odd	2
525.2.t.f.101.4		8	7.3	odd	6
525.2.t.g.26.1		8	1.1	even	1	trivial
525.2.t.g.101.1		8	21.17	even	6	inner
735.2.b.c.146.2		8	35.19	odd	6
735.2.b.c.146.7		8	105.44	odd	6
735.2.b.d.146.2		8	35.9	even	6
735.2.b.d.146.7		8	105.89	even	6
735.2.s.k.521.4		8	105.74	odd	6
735.2.s.k.656.4		8	35.34	odd	2
735.2.s.l.521.1		8	35.4	even	6
735.2.s.l.656.1		8	105.104	even	2

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78651 - 1.03144i) q^{2} +(0.627739 + 1.61429i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.543588 - 3.53142i) q^{6} +(0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 + 2.02671i) q^{9} +O(q^{10})\)	\(q+(-1.78651 - 1.03144i) q^{2} +(0.627739 + 1.61429i) q^{3} +(1.12774 + 1.95330i) q^{4} +(0.543588 - 3.53142i) q^{6} +(0.00953166 - 2.64573i) q^{7} -0.527019i q^{8} +(-2.21189 + 2.02671i) q^{9} +(-4.06348 + 2.34605i) q^{11} +(-2.44528 + 3.04666i) q^{12} +0.638688i q^{13} +(-2.74595 + 4.71679i) q^{14} +(1.71189 - 2.96508i) q^{16} +(2.07462 + 3.59334i) q^{17} +(6.04198 - 1.33930i) q^{18} +(-0.776975 - 0.448587i) q^{19} +(4.27698 - 1.64544i) q^{21} +9.67925 q^{22} +(-5.89275 - 3.40218i) q^{23} +(0.850763 - 0.330830i) q^{24} +(0.658769 - 1.14102i) q^{26} +(-4.66019 - 2.29839i) q^{27} +(5.17866 - 2.96508i) q^{28} +2.14740i q^{29} +(-2.02453 + 1.16886i) q^{31} +(-7.02943 + 4.05844i) q^{32} +(-6.33802 - 5.08695i) q^{33} -8.55938i q^{34} +(-6.45320 - 2.03489i) q^{36} +(-5.69122 + 9.85748i) q^{37} +(0.925382 + 1.60281i) q^{38} +(-1.03103 + 0.400929i) q^{39} -4.10624 q^{41} +(-9.33802 - 1.47185i) q^{42} -3.14924 q^{43} +(-9.16509 - 5.29147i) q^{44} +(7.01829 + 12.1560i) q^{46} +(3.40471 - 5.89714i) q^{47} +(5.86113 + 0.902197i) q^{48} +(-6.99982 - 0.0504365i) q^{49} +(-4.49840 + 5.60472i) q^{51} +(-1.24755 + 0.720273i) q^{52} +(-1.96187 + 1.13269i) q^{53} +(5.95481 + 8.91281i) q^{54} +(-1.39435 - 0.00502336i) q^{56} +(0.236414 - 1.53586i) q^{57} +(2.21492 - 3.83635i) q^{58} +(-0.254055 - 0.440035i) q^{59} +(4.48946 + 2.59199i) q^{61} +4.82244 q^{62} +(5.34105 + 5.87139i) q^{63} +9.89660 q^{64} +(6.07604 + 15.6252i) q^{66} +(2.41425 + 4.18160i) q^{67} +(-4.67925 + 8.10471i) q^{68} +(1.79301 - 11.6483i) q^{69} -1.22800i q^{71} +(1.06811 + 1.16571i) q^{72} +(-12.5197 + 7.22826i) q^{73} +(20.3348 - 11.7403i) q^{74} -2.02356i q^{76} +(6.16830 + 10.7733i) q^{77} +(2.25548 + 0.347183i) q^{78} +(-4.54056 + 7.86448i) q^{79} +(0.784903 - 8.96571i) q^{81} +(7.33583 + 4.23534i) q^{82} -2.76359 q^{83} +(8.03735 + 6.49859i) q^{84} +(5.62613 + 3.24825i) q^{86} +(-3.46653 + 1.34801i) q^{87} +(1.23641 + 2.14153i) q^{88} +(-6.90067 + 11.9523i) q^{89} +(1.68980 + 0.00608775i) q^{91} -15.3471i q^{92} +(-3.15776 - 2.53444i) q^{93} +(-12.1651 + 7.02352i) q^{94} +(-10.9642 - 8.79992i) q^{96} -12.9085i q^{97} +(12.4532 + 7.31000i) q^{98} +(4.23321 - 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more