LMFDB - Embedded newform 350.2.o.c.257.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,2,Mod(143,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.3
Root			$-0.144868 - 1.25092i$ of defining polynomial
Character	$\chi$	$=$	350.257
Dual form			350.2.o.c.143.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.523277 + 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +2.02179i q^{6} +(-1.83959 + 1.90155i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +(2.01999 + 3.49872i) q^{11} +(0.523277 + 1.95290i) q^{12} +(-0.204875 - 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.97024 + 0.527924i) q^{17} +(-1.05057 - 0.281498i) q^{18} +(-3.10166 + 5.37224i) q^{19} +(-2.75092 - 4.58757i) q^{21} +(2.85669 + 2.85669i) q^{22} +(-1.17456 - 4.38350i) q^{23} +(1.01089 + 1.75092i) q^{24} +(-0.250919 - 0.144868i) q^{26} +(-2.73397 + 2.73397i) q^{27} +(-0.642357 + 2.56659i) q^{28} -7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-7.88965 + 2.11403i) q^{33} +2.03974 q^{34} -1.08763 q^{36} +(4.46814 - 1.19723i) q^{37} +(-1.60554 + 5.99195i) q^{38} +(0.507306 - 0.292893i) q^{39} +2.58745i q^{41} +(-3.84454 - 3.71926i) q^{42} +(4.97801 - 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.0815604 + 0.304388i) q^{47} +(1.42962 + 1.42962i) q^{48} +(-0.231803 - 6.99616i) q^{49} +(-2.06196 + 3.57142i) q^{51} +(-0.279864 - 0.0749894i) q^{52} +(8.00039 + 2.14370i) q^{53} +(-1.93321 + 3.34841i) q^{54} +(0.0438127 + 2.64539i) q^{56} +(-8.86840 - 8.86840i) q^{57} +(-1.85281 - 6.91477i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(5.17076 - 5.17076i) q^{62} +(2.76682 - 0.790700i) q^{63} -1.00000i q^{64} +(-7.07367 + 4.08398i) q^{66} +(0.817530 - 3.05106i) q^{67} +(1.97024 - 0.527924i) q^{68} +9.17514 q^{69} +7.12240 q^{71} +(-1.05057 + 0.281498i) q^{72} +(2.98311 - 11.1331i) q^{73} +(4.00603 - 2.31288i) q^{74} +6.20333i q^{76} +(-10.3690 - 2.59511i) q^{77} +(0.414214 - 0.414214i) q^{78} +(-4.39618 - 2.53813i) q^{79} +(-5.53997 - 9.59552i) q^{81} +(0.669683 + 2.49929i) q^{82} +(3.85372 + 3.85372i) q^{83} +(-4.67615 - 2.59749i) q^{84} +(3.51999 - 6.09680i) q^{86} +(13.9802 + 3.74598i) q^{87} +(3.90231 + 1.04562i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 - 3.20895i) q^{92} +(3.82650 + 14.2807i) q^{93} +(0.157563 + 0.272906i) q^{94} +(1.75092 + 1.01089i) q^{96} +(6.63103 - 6.63103i) q^{97} +(-2.03464 - 6.69778i) q^{98} -4.39398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46}+ \cdots - 40 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.523277	+	1.95290i	−0.302114	+	1.12751i	0.633287	+	0.773917i	$0.281705\pi$
$3$	−0.523277	+	1.95290i	−0.302114	+	1.12751i	−0.935401	+	0.353588i	$0.884961\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			2.02179i			0.825391i
$7$	−1.83959	+	1.90155i	−0.695300	+	0.718719i
$7$	−1.83959	+	1.90155i	−0.695300	+	0.718719i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.941911	−	0.543813i	−0.313970	−	0.181271i
$10$		0			0
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	0.991397	+	0.130886i	$0.0417820\pi$
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	−0.382349	+	0.924018i	$0.624885\pi$
$12$	0.523277	+	1.95290i	0.151057	+	0.563753i
$13$	−0.204875	−	0.204875i	−0.0568221	−	0.0568221i	0.678125	−	0.734947i	$-0.262793\pi$
$13$	−0.204875	−	0.204875i	−0.0568221	−	0.0568221i	−0.734947	+	0.678125i	$0.762793\pi$
$14$	−1.28475	+	2.31288i	−0.343364	+	0.618143i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.97024	+	0.527924i	0.477853	+	0.128040i	0.489703	−	0.871890i	$-0.337105\pi$
$17$	1.97024	+	0.527924i	0.477853	+	0.128040i	−0.0118498	+	0.999930i	$0.503772\pi$
$18$	−1.05057	−	0.281498i	−0.247621	−	0.0663498i
$19$	−3.10166	+	5.37224i	−0.711571	+	1.23248i	0.252697	+	0.967545i	$0.418682\pi$
$19$	−3.10166	+	5.37224i	−0.711571	+	1.23248i	−0.964267	+	0.264931i	$0.914651\pi$
$20$		0			0
$21$	−2.75092	−	4.58757i	−0.600300	−	1.00109i
$22$	2.85669	+	2.85669i	0.609049	+	0.609049i
$23$	−1.17456	−	4.38350i	−0.244912	−	0.914023i	−0.973428	−	0.228994i	$-0.926456\pi$
$23$	−1.17456	−	4.38350i	−0.244912	−	0.914023i	0.728516	−	0.685029i	$-0.240210\pi$
$24$	1.01089	+	1.75092i	0.206348	+	0.357405i
$25$		0			0
$26$	−0.250919	−	0.144868i	−0.0492094	−	0.0284110i
$27$	−2.73397	+	2.73397i	−0.526152	+	0.526152i
$28$	−0.642357	+	2.56659i	−0.121394	+	0.485040i
$29$		−	7.15869i		−	1.32934i	−0.747139	−	0.664668i	$-0.768573\pi$
$29$		−	7.15869i		−	1.32934i	0.747139	−	0.664668i	$-0.231427\pi$
$30$		0			0
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.191627	−	0.981468i	$-0.438624\pi$
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.945790	+	0.324780i	$0.105290\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−7.88965	+	2.11403i	−1.37341	+	0.368005i
$34$	2.03974			0.349813
$35$		0			0
$36$	−1.08763			−0.181271
$37$	4.46814	−	1.19723i	0.734558	−	0.196824i	0.127900	−	0.991787i	$-0.459176\pi$
$37$	4.46814	−	1.19723i	0.734558	−	0.196824i	0.606658	+	0.794963i	$0.292510\pi$
$38$	−1.60554	+	5.99195i	−0.260453	+	0.972023i
$39$	0.507306	−	0.292893i	0.0812340	−	0.0469005i
$40$		0			0
$41$			2.58745i			0.404093i	0.979376	+	0.202046i	$0.0647591\pi$
$41$			2.58745i			0.404093i	−0.979376	+	0.202046i	$0.935241\pi$
$42$	−3.84454	−	3.71926i	−0.593225	−	0.573895i
$43$	4.97801	−	4.97801i	0.759140	−	0.759140i	−0.217026	−	0.976166i	$-0.569636\pi$
$43$	4.97801	−	4.97801i	0.759140	−	0.759140i	0.976166	+	0.217026i	$0.0696356\pi$
$44$	3.49872	+	2.01999i	0.527452	+	0.304524i
$45$		0			0
$46$	−2.26907	−	3.93014i	−0.334556	−	0.579468i
$47$	0.0815604	+	0.304388i	0.0118968	+	0.0443995i	0.971619	−	0.236551i	$-0.0760170\pi$
$47$	0.0815604	+	0.304388i	0.0118968	+	0.0443995i	−0.959722	+	0.280950i	$0.909350\pi$
$48$	1.42962	+	1.42962i	0.206348	+	0.206348i
$49$	−0.231803	−	6.99616i	−0.0331148	−	0.999452i
$50$		0			0
$51$	−2.06196	+	3.57142i	−0.288732	+	0.500099i
$52$	−0.279864	−	0.0749894i	−0.0388102	−	0.0103992i
$53$	8.00039	+	2.14370i	1.09894	+	0.294460i	0.762332	−	0.647186i	$-0.224054\pi$
$53$	8.00039	+	2.14370i	1.09894	+	0.294460i	0.336606	+	0.941646i	$0.390721\pi$
$54$	−1.93321	+	3.34841i	−0.263076	+	0.455661i
$55$		0			0
$56$	0.0438127	+	2.64539i	0.00585472	+	0.353505i
$57$	−8.86840	−	8.86840i	−1.17465	−	1.17465i
$58$	−1.85281	−	6.91477i	−0.243285	−	0.907953i
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	0.892523	−	0.451002i	$-0.148933\pi$
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	−0.836841	+	0.547446i	$0.815600\pi$
$60$		0			0
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	0.0645484	−	0.997915i	$-0.479439\pi$
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	−0.831945	+	0.554858i	$0.812773\pi$
$62$	5.17076	−	5.17076i	0.656688	−	0.656688i
$63$	2.76682	−	0.790700i	0.348587	−	0.0996189i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−7.07367	+	4.08398i	−0.870708	+	0.502704i
$67$	0.817530	−	3.05106i	0.0998772	−	0.372747i	−0.897837	−	0.440329i	$-0.854862\pi$
$67$	0.817530	−	3.05106i	0.0998772	−	0.372747i	0.997714	+	0.0675822i	$0.0215285\pi$
$68$	1.97024	−	0.527924i	0.238926	−	0.0640201i
$69$	9.17514			1.10456
$70$		0			0
$71$	7.12240			0.845273			0.422637	−	0.906299i	$-0.361105\pi$
$71$	7.12240			0.845273			0.422637	+	0.906299i	$0.361105\pi$
$72$	−1.05057	+	0.281498i	−0.123810	+	0.0331749i
$73$	2.98311	−	11.1331i	0.349147	−	1.30303i	−0.538545	−	0.842597i	$-0.681026\pi$
$73$	2.98311	−	11.1331i	0.349147	−	1.30303i	0.887692	−	0.460438i	$-0.152307\pi$
$74$	4.00603	−	2.31288i	0.465691	−	0.268867i
$75$		0			0
$76$			6.20333i			0.711571i
$77$	−10.3690	−	2.59511i	−1.18165	−	0.295740i
$78$	0.414214	−	0.414214i	0.0469005	−	0.0469005i
$79$	−4.39618	−	2.53813i	−0.494609	−	0.285562i	0.231876	−	0.972745i	$-0.425514\pi$
$79$	−4.39618	−	2.53813i	−0.494609	−	0.285562i	−0.726484	+	0.687183i	$0.758847\pi$
$80$		0			0
$81$	−5.53997	−	9.59552i	−0.615553	−	1.06617i
$82$	0.669683	+	2.49929i	0.0739541	+	0.276000i
$83$	3.85372	+	3.85372i	0.423001	+	0.423001i	0.886236	−	0.463235i	$-0.153311\pi$
$83$	3.85372	+	3.85372i	0.423001	+	0.423001i	−0.463235	+	0.886236i	$0.653311\pi$
$84$	−4.67615	−	2.59749i	−0.510210	−	0.283410i
$85$		0			0
$86$	3.51999	−	6.09680i	0.379570	−	0.657434i
$87$	13.9802	+	3.74598i	1.49883	+	0.401611i
$88$	3.90231	+	1.04562i	0.415988	+	0.111464i
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	−0.935883	−	0.352310i	$-0.885396\pi$
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	0.773051	+	0.634343i	$0.218729\pi$
$90$		0			0
$91$	0.766467	−	0.0126942i	0.0803475	−	0.00133071i
$92$	−3.20895	−	3.20895i	−0.334556	−	0.334556i
$93$	3.82650	+	14.2807i	0.396789	+	1.48084i
$94$	0.157563	+	0.272906i	0.0162513	+	0.0281481i
$95$		0			0
$96$	1.75092	+	1.01089i	0.178702	+	0.103174i
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	−0.285191	−	0.958471i	$-0.592057\pi$
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	0.958471	+	0.285191i	$0.0920572\pi$
$98$	−2.03464	−	6.69778i	−0.205530	−	0.676578i
$99$		−	4.39398i		−	0.441611i
$100$		0			0
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	−0.861364	−	0.507989i	$-0.830389\pi$
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	0.00924966	+	0.999957i	$0.497056\pi$
$102$	−1.06735	+	3.98340i	−0.105683	+	0.394416i
$103$	−4.13612	+	1.10827i	−0.407544	+	0.109201i	−0.456766	−	0.889587i	$-0.650992\pi$
$103$	−4.13612	+	1.10827i	−0.407544	+	0.109201i	0.0492221	+	0.998788i	$0.484326\pi$
$104$	−0.289737			−0.0284110
$105$		0			0
$106$	8.28261			0.804479
$107$	−14.3653	+	3.84918i	−1.38875	+	0.372114i	−0.874291	−	0.485402i	$-0.838673\pi$
$107$	−14.3653	+	3.84918i	−1.38875	+	0.372114i	−0.514457	+	0.857516i	$0.672007\pi$
$108$	−1.00070	+	3.73467i	−0.0962926	+	0.359369i
$109$	−11.4586	+	6.61564i	−1.09754	+	0.633664i	−0.935573	−	0.353133i	$-0.885116\pi$
$109$	−11.4586	+	6.61564i	−1.09754	+	0.633664i	−0.161964	+	0.986797i	$0.551783\pi$
$110$		0			0
$111$			9.35230i			0.887681i
$112$	0.726997	+	2.54391i	0.0686947	+	0.240377i
$113$	−9.75336	+	9.75336i	−0.917519	+	0.917519i	−0.996848	−	0.0793296i	$-0.974722\pi$
$113$	−9.75336	+	9.75336i	−0.917519	+	0.917519i	0.0793296	+	0.996848i	$0.474722\pi$
$114$	−10.8615	−	6.27091i	−1.01728	−	0.587324i
$115$		0			0
$116$	−3.57935	−	6.19961i	−0.332334	−	0.575619i
$117$	0.0815604	+	0.304388i	0.00754026	+	0.0281406i
$118$	0.604862	+	0.604862i	0.0556821	+	0.0556821i
$119$	−4.62831	+	2.77535i	−0.424276	+	0.254416i
$120$		0			0
$121$	−2.66069	+	4.60846i	−0.241881	+	0.418951i
$122$	−6.68495	−	1.79123i	−0.605227	−	0.162170i
$123$	−5.05303	−	1.35396i	−0.455617	−	0.122082i
$124$	3.65628	−	6.33287i	0.328344	−	0.568708i
$125$		0			0
$126$	2.46790	−	1.47986i	0.219858	−	0.131837i
$127$	2.19984	+	2.19984i	0.195204	+	0.195204i	0.797940	−	0.602736i	$-0.205923\pi$
$127$	2.19984	+	2.19984i	0.195204	+	0.195204i	−0.602736	+	0.797940i	$0.705923\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	7.11667	+	12.3264i	0.626587	+	1.08528i
$130$		0			0
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	0.197773	−	0.980248i	$-0.436629\pi$
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	−0.750033	+	0.661400i	$0.769963\pi$
$132$	−5.77563	+	5.77563i	−0.502704	+	0.502704i
$133$	−4.50980	−	15.7807i	−0.391049	−	1.36836i
$134$		−	3.15869i		−	0.272870i
$135$		0			0
$136$	1.76647	−	1.01987i	0.151473	−	0.0874531i
$137$	−1.85804	+	6.93431i	−0.158743	+	0.592438i	0.840012	+	0.542567i	$0.182548\pi$
$137$	−1.85804	+	6.93431i	−0.158743	+	0.592438i	−0.998756	+	0.0498710i	$0.984119\pi$
$138$	8.86251	−	2.37470i	0.754427	−	0.202148i
$139$	12.4172			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$139$	12.4172			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$140$		0			0
$141$	−0.637116			−0.0536549
$142$	6.87971	−	1.84341i	0.577332	−	0.154696i
$143$	0.302955	−	1.13064i	0.0253344	−	0.0945492i
$144$	−0.941911	+	0.543813i	−0.0784926	+	0.0453177i
$145$		0			0
$146$		−	11.5259i		−	0.953887i
$147$	13.7841	+	3.20824i	1.13689	+	0.264611i
$148$	3.27091	−	3.27091i	0.268867	−	0.268867i
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.946637	+	0.322302i	$0.104457\pi$
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.752440	+	0.658661i	$0.228877\pi$
$150$		0			0
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	0.929065	−	0.369916i	$-0.120613\pi$
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	−0.784889	+	0.619636i	$0.787280\pi$
$152$	1.60554	+	5.99195i	0.130226	+	0.486012i
$153$	−1.56870	−	1.56870i	−0.126822	−	0.126822i
$154$	−10.6873	+	0.177002i	−0.861207	+	0.0142632i
$155$		0			0
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	5.91389	+	1.58462i	0.471980	+	0.126467i	0.486966	−	0.873421i	$-0.338104\pi$
$157$	5.91389	+	1.58462i	0.471980	+	0.126467i	−0.0149859	+	0.999888i	$0.504770\pi$
$158$	−4.90330	−	1.31384i	−0.390086	−	0.104523i
$159$	−8.37284	+	14.5022i	−0.664010	+	1.15010i
$160$		0			0
$161$	10.4962	+	5.83037i	0.827213	+	0.459498i
$162$	−7.83471	−	7.83471i	−0.615553	−	0.615553i
$163$	4.28549	+	15.9937i	0.335666	+	1.25272i	0.903146	+	0.429334i	$0.141252\pi$
$163$	4.28549	+	15.9937i	0.335666	+	1.25272i	−0.567480	+	0.823387i	$0.692082\pi$
$164$	1.29373	+	2.24080i	0.101023	+	0.174977i
$165$		0			0
$166$	4.71983	+	2.72499i	0.366329	+	0.211500i
$167$	10.2873	−	10.2873i	0.796056	−	0.796056i	−0.186415	−	0.982471i	$-0.559687\pi$
$167$	10.2873	−	10.2873i	0.796056	−	0.796056i	0.982471	+	0.186415i	$0.0596869\pi$
$168$	−5.18910	−	1.29871i	−0.400348	−	0.100198i
$169$		−	12.9161i		−	0.993543i
$170$		0			0
$171$	5.84298	−	3.37345i	0.446824	−	0.257974i
$172$	1.82208	−	6.80009i	0.138932	−	0.518502i
$173$	−7.50720	+	2.01155i	−0.570762	+	0.152935i	−0.532646	−	0.846338i	$-0.678802\pi$
$173$	−7.50720	+	2.01155i	−0.570762	+	0.152935i	−0.0381159	+	0.999273i	$0.512136\pi$
$174$	14.4734			1.09722
$175$		0			0
$176$	4.03997			0.304524
$177$	−1.67052	+	0.447613i	−0.125564	+	0.0336447i
$178$	−0.795171	+	2.96762i	−0.0596006	+	0.222432i
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	−0.369676	−	0.929161i	$-0.620531\pi$
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	0.619839	+	0.784729i	$0.287198\pi$
$180$		0			0
$181$		−	6.99107i		−	0.519642i	−0.965657	−	0.259821i	$-0.916336\pi$
$181$		−	6.99107i		−	0.519642i	0.965657	−	0.259821i	$-0.0836636\pi$
$182$	0.737064	−	0.210638i	0.0546348	−	0.0156135i
$183$	9.89407	−	9.89407i	0.731390	−	0.731390i
$184$	−3.93014	−	2.26907i	−0.289734	−	0.167278i
$185$		0			0
$186$	7.39223	+	12.8037i	0.542024	+	0.938814i
$187$	2.13280	+	7.95971i	0.155966	+	0.582071i
$188$	0.222827	+	0.222827i	0.0162513	+	0.0162513i
$189$	−0.169398	−	10.2282i	−0.0123219	−	0.743990i
$190$		0			0
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	−0.935543	−	0.353214i	$-0.885089\pi$
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	0.773664	+	0.633597i	$0.218422\pi$
$192$	1.95290	+	0.523277i	0.140938	+	0.0377643i
$193$	−19.3907	−	5.19573i	−1.39577	−	0.373997i	−0.518949	−	0.854805i	$-0.673676\pi$
$193$	−19.3907	−	5.19573i	−1.39577	−	0.373997i	−0.876825	+	0.480809i	$0.840343\pi$
$194$	4.68885	−	8.12132i	0.336640	−	0.583077i
$195$		0			0
$196$	−3.69883	−	5.94295i	−0.264202	−	0.424497i
$197$	7.84901	+	7.84901i	0.559219	+	0.559219i	0.929085	−	0.369866i	$-0.120596\pi$
$197$	7.84901	+	7.84901i	0.559219	+	0.559219i	−0.369866	+	0.929085i	$0.620596\pi$
$198$	−1.13725	−	4.24426i	−0.0808205	−	0.301626i
$199$	−5.40103	−	9.35485i	−0.382869	−	0.663148i	0.608602	−	0.793475i	$-0.291730\pi$
$199$	−5.40103	−	9.35485i	−0.382869	−	0.663148i	−0.991471	+	0.130327i	$0.958397\pi$
$200$		0			0
$201$	5.53062	+	3.19310i	0.390100	+	0.225224i
$202$	−6.99218	+	6.99218i	−0.491968	+	0.491968i
$203$	13.6126	+	13.1691i	0.955419	+	0.924288i
$204$			4.12392i			0.288732i
$205$		0			0
$206$	−3.70835	+	2.14101i	−0.258373	+	0.149172i
$207$	−1.27748	+	4.76761i	−0.0887908	+	0.331372i
$208$	−0.279864	+	0.0749894i	−0.0194051	+	0.00519958i
$209$	−25.0613			−1.73353
$210$		0			0
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	8.00039	−	2.14370i	0.549469	−	0.147230i
$213$	−3.72699	+	13.9093i	−0.255369	+	0.953050i
$214$	−12.8796	+	7.43604i	−0.880431	+	0.508317i
$215$		0			0
$216$			3.86642i			0.263076i
$217$	−4.69728	+	18.7683i	−0.318872	+	1.27408i
$218$	−9.35593	+	9.35593i	−0.633664	+	0.633664i
$219$	20.1809	+	11.6514i	1.36370	+	0.787330i
$220$		0			0
$221$	−0.295494	−	0.511811i	−0.0198771	−	0.0344281i
$222$	2.42055	+	9.03363i	0.162457	+	0.606298i
$223$	−9.35230	−	9.35230i	−0.626277	−	0.626277i	0.320853	−	0.947129i	$-0.396031\pi$
$223$	−9.35230	−	9.35230i	−0.626277	−	0.626277i	−0.947129	+	0.320853i	$0.896031\pi$
$224$	1.36064	+	2.26907i	0.0909114	+	0.151608i
$225$		0			0
$226$	−6.89667	+	11.9454i	−0.458759	+	0.794595i
$227$	−15.6420	−	4.19127i	−1.03820	−	0.278184i	−0.300832	−	0.953677i	$-0.597264\pi$
$227$	−15.6420	−	4.19127i	−1.03820	−	0.278184i	−0.737367	+	0.675493i	$0.763931\pi$
$228$	−12.1145	−	3.24606i	−0.802300	−	0.214976i
$229$	5.88820	−	10.1987i	0.389103	−	0.673947i	−0.603226	−	0.797570i	$-0.706118\pi$
$229$	5.88820	−	10.1987i	0.389103	−	0.673947i	0.992329	+	0.123624i	$0.0394515\pi$
$230$		0			0
$231$	10.4938	−	18.8915i	0.690442	−	1.24297i
$232$	−5.06196	−	5.06196i	−0.332334	−	0.332334i
$233$	1.48154	+	5.52920i	0.0970591	+	0.362230i	0.997324	−	0.0731138i	$-0.0232936\pi$
$233$	1.48154	+	5.52920i	0.0970591	+	0.362230i	−0.900264	+	0.435343i	$0.856627\pi$
$234$	0.157563	+	0.272906i	0.0103002	+	0.0178405i
$235$		0			0
$236$	0.740802	+	0.427702i	0.0482221	+	0.0278410i
$237$	7.25713	−	7.25713i	0.471402	−	0.471402i
$238$	−3.75229	+	3.87867i	−0.243225	+	0.251417i
$239$			8.33794i			0.539337i	0.962953	+	0.269668i	$0.0869141\pi$
$239$			8.33794i			0.539337i	−0.962953	+	0.269668i	$0.913086\pi$
$240$		0			0
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	−0.415031	−	0.909807i	$-0.636229\pi$
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	0.580401	+	0.814331i	$0.302896\pi$
$242$	−1.37728	+	5.14006i	−0.0885347	+	0.330416i
$243$	10.4340	−	2.79578i	0.669340	−	0.179349i
$244$	−6.92077			−0.443057
$245$		0			0
$246$	−5.23128			−0.333535
$247$	1.73609	−	0.465184i	0.110465	−	0.0295989i
$248$	1.89263	−	7.06340i	0.120182	−	0.448526i
$249$	−9.54248	+	5.50936i	−0.604730	+	0.349141i
$250$		0			0
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$	2.00079	−	2.06818i	0.126038	−	0.130283i
$253$	12.9641	−	12.9641i	0.815043	−	0.815043i
$254$	2.69424	+	1.55552i	0.169052	+	0.0976020i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50754	+	5.62621i	0.0940377	+	0.350954i	0.996872	−	0.0790355i	$-0.0251841\pi$
$257$	1.50754	+	5.62621i	0.0940377	+	0.350954i	−0.902834	+	0.429989i	$0.858517\pi$
$258$	10.0645	+	10.0645i	0.626587	+	0.626587i
$259$	−5.94295	+	10.6988i	−0.369277	+	0.664793i
$260$		0			0
$261$	−3.89299	+	6.74285i	−0.240970	+	0.417372i
$262$	−7.05006	−	1.88906i	−0.435554	−	0.116706i
$263$	1.67793	+	0.449601i	0.103466	+	0.0277236i	0.310180	−	0.950678i	$-0.399611\pi$
$263$	1.67793	+	0.449601i	0.103466	+	0.0277236i	−0.206715	+	0.978401i	$0.566277\pi$
$264$	−4.08398	+	7.07367i	−0.251352	+	0.435354i
$265$		0			0
$266$	−8.44048	−	14.0758i	−0.517519	−	0.863041i
$267$	−4.39223	−	4.39223i	−0.268800	−	0.268800i
$268$	−0.817530	−	3.05106i	−0.0499386	−	0.186373i
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	0.802577	−	0.596549i	$-0.203462\pi$
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	−0.917915	+	0.396777i	$0.870128\pi$
$270$		0			0
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.177032	−	0.984205i	$-0.556649\pi$
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.940862	+	0.338789i	$0.889983\pi$
$272$	1.44231	−	1.44231i	0.0874531	−	0.0874531i
$273$	−0.376284	+	1.50347i	−0.0227737	+	0.0909943i
$274$			7.17893i			0.433695i
$275$		0			0
$276$	7.94591	−	4.58757i	0.478287	−	0.276139i
$277$	1.26567	−	4.72353i	0.0760465	−	0.283810i	−0.917422	−	0.397916i	$-0.869734\pi$
$277$	1.26567	−	4.72353i	0.0760465	−	0.283810i	0.993469	+	0.114106i	$0.0364004\pi$
$278$	11.9941	−	3.21380i	0.719356	−	0.192751i
$279$	−7.95333			−0.476153
$280$		0			0
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$	−0.615407	+	0.164898i	−0.0366470	+	0.00981952i
$283$	2.92041	−	10.8991i	0.173601	−	0.647886i	−0.823185	−	0.567773i	$-0.807805\pi$
$283$	2.92041	−	10.8991i	0.173601	−	0.647886i	0.996786	−	0.0801133i	$-0.0255282\pi$
$284$	6.16818	−	3.56120i	0.366014	−	0.211318i
$285$		0			0
$286$		−	1.17053i		−	0.0692148i
$287$	−4.92018	−	4.75986i	−0.290429	−	0.280966i
$288$	−0.769067	+	0.769067i	−0.0453177	+	0.0453177i
$289$	−11.1193	−	6.41973i	−0.654076	−	0.377631i
$290$		0			0
$291$	9.47985	+	16.4196i	0.555719	+	0.962533i
$292$	−2.98311	−	11.1331i	−0.174573	−	0.651517i
$293$	7.23407	+	7.23407i	0.422619	+	0.422619i	0.886105	−	0.463485i	$-0.153401\pi$
$293$	7.23407	+	7.23407i	0.422619	+	0.422619i	−0.463485	+	0.886105i	$0.653401\pi$
$294$	14.1448	−	0.468657i	0.824939	−	0.0273326i
$295$		0			0
$296$	2.31288	−	4.00603i	0.134433	−	0.232846i
$297$	−15.0880	−	4.04281i	−0.875493	−	0.234588i
$298$	23.1323	+	6.19829i	1.34002	+	0.359057i
$299$	−0.657432	+	1.13871i	−0.0380203	+	0.0658531i
$300$		0			0
$301$	0.308440	+	18.6235i	0.0177782	+	1.07344i
$302$	2.50552	+	2.50552i	0.144176	+	0.144176i
$303$	−5.17439	−	19.3111i	−0.297261	−	1.10939i
$304$	3.10166	+	5.37224i	0.177893	+	0.308119i
$305$		0			0
$306$	−1.92125	−	1.10924i	−0.109831	−	0.0634108i
$307$	1.07859	−	1.07859i	0.0615584	−	0.0615584i	−0.675657	−	0.737216i	$-0.736140\pi$
$307$	1.07859	−	1.07859i	0.0615584	−	0.0615584i	0.737216	+	0.675657i	$0.236140\pi$
$308$	−10.2773	+	2.93705i	−0.585605	+	0.167354i
$309$		−	8.65735i		−	0.492500i
$310$		0			0
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	−0.717420	−	0.696641i	$-0.754677\pi$
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	0.244599	+	0.969624i	$0.421344\pi$
$312$	0.151613	−	0.565826i	0.00858338	−	0.0320336i
$313$	−2.92361	+	0.783378i	−0.165252	+	0.0442791i	−0.340496	−	0.940246i	$-0.610595\pi$
$313$	−2.92361	+	0.783378i	−0.165252	+	0.0442791i	0.175244	+	0.984525i	$0.443928\pi$
$314$	6.12251			0.345513
$315$		0			0
$316$	−5.07627			−0.285562
$317$	1.88227	−	0.504353i	0.105719	−	0.0283273i	−0.205572	−	0.978642i	$-0.565905\pi$
$317$	1.88227	−	0.504353i	0.105719	−	0.0283273i	0.311291	+	0.950315i	$0.399239\pi$
$318$	−4.33410	+	16.1751i	−0.243044	+	0.907054i
$319$	25.0463	−	14.4605i	1.40232	−	0.809631i
$320$		0			0
$321$		−	30.0682i		−	1.67824i
$322$	11.6475	+	2.91510i	0.649091	+	0.162452i
$323$	−8.94715	+	8.94715i	−0.497833	+	0.497833i
$324$	−9.59552	−	5.53997i	−0.533084	−	0.307776i
$325$		0			0
$326$	8.27894	+	14.3395i	0.458528	+	0.794194i
$327$	−6.92363	−	25.8393i	−0.382878	−	1.42892i
$328$	1.82961	+	1.82961i	0.101023	+	0.101023i
$329$	−0.728847	−	0.404858i	−0.0401826	−	0.0223205i
$330$		0			0
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	−0.129365	−	0.991597i	$-0.541294\pi$
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	0.923431	−	0.383765i	$-0.125373\pi$
$332$	5.26428	+	1.41056i	0.288915	+	0.0774145i
$333$	−4.85966	−	1.30214i	−0.266308	−	0.0713570i
$334$	7.27423	−	12.5993i	0.398028	−	0.689405i
$335$		0			0
$336$	−5.34841	+	0.0885800i	−0.291780	+	0.00483244i
$337$	0.823226	+	0.823226i	0.0448440	+	0.0448440i	0.729173	−	0.684329i	$-0.239905\pi$
$337$	0.823226	+	0.823226i	0.0448440	+	0.0448440i	−0.684329	+	0.729173i	$0.739905\pi$
$338$	−3.34292	−	12.4759i	−0.181831	−	0.678602i
$339$	−13.9436	−	24.1510i	−0.757312	−	1.31170i
$340$		0			0
$341$	25.5846	+	14.7713i	1.38548	+	0.799910i
$342$	4.77078	−	4.77078i	0.257974	−	0.257974i
$343$	13.7300	+	12.4293i	0.741350	+	0.671119i
$344$		−	7.03997i		−	0.379570i
$345$		0			0
$346$	−6.73077	+	3.88601i	−0.361849	+	0.208913i
$347$	4.32336	−	16.1350i	0.232090	−	0.866172i	−0.747349	−	0.664432i	$-0.768674\pi$
$347$	4.32336	−	16.1350i	0.232090	−	0.866172i	0.979439	−	0.201740i	$-0.0646597\pi$
$348$	13.9802	−	3.74598i	0.749417	−	0.200806i
$349$	36.7146			1.96529			0.982644	−	0.185503i	$-0.0593916\pi$
$349$	36.7146			1.96529			0.982644	+	0.185503i	$0.0593916\pi$
$350$		0			0
$351$	1.12024			0.0597942
$352$	3.90231	−	1.04562i	0.207994	−	0.0557318i
$353$	3.69356	−	13.7845i	0.196588	−	0.733677i	−0.795262	−	0.606266i	$-0.792667\pi$
$353$	3.69356	−	13.7845i	0.196588	−	0.733677i	0.991850	−	0.127411i	$-0.0406667\pi$
$354$	−1.49774	+	0.864723i	−0.0796042	+	0.0459595i
$355$		0			0
$356$			3.07230i			0.162832i
$357$	−2.99808	−	10.4909i	−0.158675	−	0.555236i
$358$	2.73277	−	2.73277i	0.144431	−	0.144431i
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.269435	−	0.963019i	$-0.586837\pi$
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.968716	+	0.248172i	$0.920170\pi$
$360$		0			0
$361$	−9.74064	−	16.8713i	−0.512665	−	0.887962i
$362$	−1.80942	−	6.75285i	−0.0951011	−	0.354922i
$363$	−7.60756	−	7.60756i	−0.399293	−	0.399293i
$364$	0.657432	−	0.394227i	0.0344588	−	0.0206631i
$365$		0			0
$366$	6.99616	−	12.1177i	0.365695	−	0.633403i
$367$	−21.8990	−	5.86782i	−1.14312	−	0.306298i	−0.362914	−	0.931823i	$-0.618218\pi$
$367$	−21.8990	−	5.86782i	−1.14312	−	0.306298i	−0.780204	+	0.625525i	$0.784885\pi$
$368$	−4.38350	−	1.17456i	−0.228506	−	0.0612279i
$369$	1.40709	−	2.43715i	0.0732502	−	0.126873i
$370$		0			0
$371$	−18.7938	+	11.2696i	−0.975726	+	0.585090i
$372$	10.4542	+	10.4542i	0.542024	+	0.542024i
$373$	3.32215	+	12.3984i	0.172014	+	0.641966i	0.997041	+	0.0768720i	$0.0244933\pi$
$373$	3.32215	+	12.3984i	0.172014	+	0.641966i	−0.825027	+	0.565094i	$0.808840\pi$
$374$	4.12025	+	7.13648i	0.213053	+	0.369019i
$375$		0			0
$376$	0.272906	+	0.157563i	0.0140741	+	0.00812567i
$377$	−1.46664	+	1.46664i	−0.0755356	+	0.0755356i
$378$	−2.81087	−	9.83581i	−0.144576	−	0.505900i
$379$			14.4739i			0.743476i	0.928338	+	0.371738i	$0.121238\pi$
$379$			14.4739i			0.743476i	−0.928338	+	0.371738i	$0.878762\pi$
$380$		0			0
$381$	−5.44718	+	3.14493i	−0.279068	+	0.161120i
$382$	−1.15807	+	4.32196i	−0.0592518	+	0.221131i
$383$	−1.69189	+	0.453341i	−0.0864517	+	0.0231647i	−0.301786	−	0.953376i	$-0.597583\pi$
$383$	−1.69189	+	0.453341i	−0.0864517	+	0.0231647i	0.215334	+	0.976540i	$0.430916\pi$
$384$	2.02179			0.103174
$385$		0			0
$386$	−20.0747			−1.02178
$387$	−7.39595	+	1.98174i	−0.375957	+	0.100737i
$388$	2.42713	−	9.05816i	0.123219	−	0.459858i
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	−0.559839	−	0.828601i	$-0.689137\pi$
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	0.437670	+	0.899135i	$0.355804\pi$
$390$		0			0
$391$		−	9.25661i		−	0.468127i
$392$	−5.11094	−	4.78312i	−0.258142	−	0.241584i
$393$	10.4344	−	10.4344i	0.526348	−	0.526348i
$394$	9.61304	+	5.55009i	0.484298	+	0.279610i
$395$		0			0
$396$	−2.19699	−	3.80530i	−0.110403	−	0.191223i
$397$	−10.2668	−	38.3163i	−0.515277	−	1.92304i	−0.349791	−	0.936828i	$-0.613747\pi$
$397$	−10.2668	−	38.3163i	−0.515277	−	1.92304i	−0.165486	−	0.986212i	$-0.552919\pi$
$398$	−7.63821	−	7.63821i	−0.382869	−	0.382869i
$399$	33.1780	−	0.549491i	1.66098	−	0.0275089i
$400$		0			0
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	6.16860	+	1.65287i	0.307662	+	0.0824378i
$403$	−2.04653	−	0.548365i	−0.101945	−	0.0273160i
$404$	−4.94422	+	8.56364i	−0.245984	+	0.426057i
$405$		0			0
$406$	16.5572	+	9.19714i	0.821720	+	0.456446i
$407$	13.2144	+	13.2144i	0.655012	+	0.655012i
$408$	1.06735	+	3.98340i	0.0528417	+	0.197208i
$409$	−7.65280	−	13.2550i	−0.378407	−	0.655419i	0.612424	−	0.790529i	$-0.290195\pi$
$409$	−7.65280	−	13.2550i	−0.378407	−	0.655419i	−0.990831	+	0.135110i	$0.956861\pi$
$410$		0			0
$411$	−12.5697	−	7.25713i	−0.620019	−	0.357968i
$412$	−3.02785	+	3.02785i	−0.149172	+	0.149172i
$413$	−2.19547	−	0.549475i	−0.108032	−	0.0270379i
$414$			4.93579i			0.242581i
$415$		0			0
$416$	−0.250919	+	0.144868i	−0.0123023	+	0.00710276i
$417$	−6.49762	+	24.2495i	−0.318190	+	1.18750i
$418$	−24.2073	+	6.48634i	−1.18402	+	0.317257i
$419$	−27.7027			−1.35337			−0.676684	−	0.736274i	$-0.736584\pi$
$419$	−27.7027			−1.35337			−0.676684	+	0.736274i	$0.736584\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	7.30776	−	1.95811i	0.355736	−	0.0953192i
$423$	0.0887072	−	0.331060i	0.00431309	−	0.0160967i
$424$	7.17295	−	4.14131i	0.348349	−	0.201120i
$425$		0			0
$426$			14.4000i			0.697681i
$427$	17.6058	−	5.03138i	0.852005	−	0.243485i
$428$	−10.5161	+	10.5161i	−0.508317	+	0.508317i
$429$	2.04950	+	1.18328i	0.0989509	+	0.0571293i
$430$		0			0
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	−0.995929	−	0.0901384i	$-0.971269\pi$
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	0.419902	−	0.907569i	$-0.362064\pi$
$432$	1.00070	+	3.73467i	0.0481463	+	0.179684i
$433$	13.2515	+	13.2515i	0.636829	+	0.636829i	0.949772	−	0.312943i	$-0.101315\pi$
$433$	13.2515	+	13.2515i	0.636829	+	0.636829i	−0.312943	+	0.949772i	$0.601315\pi$
$434$	0.320383	+	19.3446i	0.0153789	+	0.928569i
$435$		0			0
$436$	−6.61564	+	11.4586i	−0.316832	+	0.548769i
$437$	27.1923	+	7.28615i	1.30078	+	0.348544i
$438$	22.5088	+	6.03122i	1.07551	+	0.288183i
$439$	−7.05383	+	12.2176i	−0.336661	+	0.583114i	−0.983802	−	0.179256i	$-0.942631\pi$
$439$	−7.05383	+	12.2176i	−0.336661	+	0.583114i	0.647141	+	0.762370i	$0.275964\pi$
$440$		0			0
$441$	−3.58626	+	6.71582i	−0.170774	+	0.319801i
$442$	−0.417892	−	0.417892i	−0.0198771	−	0.0198771i
$443$	−5.45161	−	20.3457i	−0.259014	−	0.966652i	−0.965813	−	0.259238i	$-0.916528\pi$
$443$	−5.45161	−	20.3457i	−0.259014	−	0.966652i	0.706800	−	0.707414i	$-0.250138\pi$
$444$	4.67615	+	8.09933i	0.221920	+	0.384377i
$445$		0			0
$446$	−11.4542	−	6.61308i	−0.542371	−	0.313138i
$447$	−34.2370	+	34.2370i	−1.61936	+	1.61936i
$448$	1.90155	+	1.83959i	0.0898399	+	0.0869125i
$449$			31.3247i			1.47831i	0.673538	+	0.739153i	$0.264774\pi$
$449$			31.3247i			1.47831i	−0.673538	+	0.739153i	$0.735226\pi$
$450$		0			0
$451$	−9.05278	+	5.22662i	−0.426279	+	0.246112i
$452$	−3.56998	+	13.3233i	−0.167918	+	0.626677i
$453$	−6.91977	+	1.85415i	−0.325119	+	0.0871154i
$454$	−16.1938			−0.760014
$455$		0			0
$456$	−12.5418			−0.587324
$457$	−2.76404	+	0.740622i	−0.129296	+	0.0346448i	−0.322887	−	0.946438i	$-0.604653\pi$
$457$	−2.76404	+	0.740622i	−0.129296	+	0.0346448i	0.193591	+	0.981082i	$0.437987\pi$
$458$	3.04796	−	11.3751i	0.142422	−	0.531525i
$459$	−6.82989	+	3.94324i	−0.318792	+	0.184055i
$460$		0			0
$461$		−	3.02674i		−	0.140969i	−0.997513	−	0.0704846i	$-0.977545\pi$
$461$		−	3.02674i		−	0.140969i	0.997513	−	0.0704846i	$-0.0224546\pi$
$462$	5.24675	−	20.9638i	0.244101	−	0.975325i
$463$	−19.2889	+	19.2889i	−0.896431	+	0.896431i	−0.995118	−	0.0986876i	$-0.968536\pi$
$463$	−19.2889	+	19.2889i	−0.896431	+	0.896431i	0.0986876	+	0.995118i	$0.468536\pi$
$464$	−6.19961	−	3.57935i	−0.287810	−	0.166167i
$465$		0			0
$466$	2.86212	+	4.95734i	0.132585	+	0.229644i
$467$	6.50385	+	24.2727i	0.300962	+	1.12321i	0.936366	+	0.351026i	$0.114167\pi$
$467$	6.50385	+	24.2727i	0.300962	+	1.12321i	−0.635403	+	0.772180i	$0.719166\pi$
$468$	0.222827	+	0.222827i	0.0103002	+	0.0103002i
$469$	4.29784	+	7.16729i	0.198456	+	0.330955i
$470$		0			0
$471$	−6.18921	+	10.7200i	−0.285184	+	0.493953i
$472$	0.826257	+	0.221395i	0.0380316	+	0.0101905i
$473$	27.4722	+	7.36115i	1.26317	+	0.338466i
$474$	5.13157	−	8.88814i	0.235701	−	0.408246i
$475$		0			0
$476$	−2.62056	+	4.71767i	−0.120113	+	0.216234i
$477$	−6.36989	−	6.36989i	−0.291657	−	0.291657i
$478$	2.15802	+	8.05384i	0.0987055	+	0.368374i
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	0.755704	−	0.654913i	$-0.227295\pi$
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	−0.945024	+	0.327002i	$0.893961\pi$
$480$		0			0
$481$	−1.16069	−	0.670127i	−0.0529231	−	0.0305551i
$482$	2.09613	−	2.09613i	0.0954763	−	0.0954763i
$483$	−16.8785	+	17.4470i	−0.767999	+	0.793867i
$484$			5.32139i			0.241881i
$485$		0			0
$486$	9.35485	−	5.40103i	0.424345	−	0.244996i
$487$	−2.76375	+	10.3144i	−0.125237	+	0.467392i	−0.999848	−	0.0174340i	$-0.994450\pi$
$487$	−2.76375	+	10.3144i	−0.125237	+	0.467392i	0.874611	+	0.484826i	$0.161117\pi$
$488$	−6.68495	+	1.79123i	−0.302613	+	0.0810850i
$489$	−33.4765			−1.51386
$490$		0			0
$491$	25.7259			1.16100			0.580498	−	0.814262i	$-0.302858\pi$
$491$	25.7259			1.16100			0.580498	+	0.814262i	$0.302858\pi$
$492$	−5.05303	+	1.35396i	−0.227808	+	0.0610411i
$493$	3.77924	−	14.1043i	0.170209	−	0.635227i
$494$	1.55654	−	0.898666i	0.0700319	−	0.0404329i
$495$		0			0
$496$		−	7.31256i		−	0.328344i
$497$	−13.1023	+	13.5436i	−0.587719	+	0.607514i
$498$	−7.79141	+	7.79141i	−0.349141	+	0.349141i
$499$	−12.6429	−	7.29940i	−0.565975	−	0.326766i	0.189565	−	0.981868i	$-0.439292\pi$
$499$	−12.6429	−	7.29940i	−0.565975	−	0.326766i	−0.755540	+	0.655102i	$0.772626\pi$
$500$		0			0
$501$	14.7069	+	25.4732i	0.657058	+	1.13806i
$502$	4.18770	+	15.6287i	0.186906	+	0.697543i
$503$	−13.9891	−	13.9891i	−0.623744	−	0.623744i	0.322743	−	0.946487i	$-0.395395\pi$
$503$	−13.9891	−	13.9891i	−0.623744	−	0.623744i	−0.946487	+	0.322743i	$0.895395\pi$
$504$	1.39733	−	2.51555i	0.0622419	−	0.112051i
$505$		0			0
$506$	9.16697	−	15.8777i	0.407522	−	0.705848i
$507$	25.2237	+	6.75868i	1.12022	+	0.300163i
$508$	3.00504	+	0.805197i	0.133327	+	0.0357248i
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	−0.832621	−	0.553843i	$-0.813161\pi$
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	0.895953	+	0.444149i	$0.146494\pi$
$510$		0			0
$511$	15.6825	+	26.1530i	0.693754	+	1.15694i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−6.20768	−	23.1674i	−0.274076	−	1.02287i
$514$	2.91234	+	5.04433i	0.128458	+	0.222496i
$515$		0			0
$516$	12.3264	+	7.11667i	0.542641	+	0.313294i
$517$	−0.900216	+	0.900216i	−0.0395914	+	0.0395914i
$518$	−2.97139	+	11.8724i	−0.130555	+	0.521644i
$519$		−	15.7134i		−	0.689741i
$520$		0			0
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.153595	−	0.988134i	$-0.450915\pi$
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.932547	+	0.361049i	$0.117581\pi$
$522$	−2.01516	+	7.52068i	−0.0882011	+	0.329171i
$523$	−30.5069	+	8.17429i	−1.33397	+	0.357437i	−0.854195	−	0.519954i	$-0.825949\pi$
$523$	−30.5069	+	8.17429i	−1.33397	+	0.357437i	−0.479777	+	0.877390i	$0.659283\pi$
$524$	−7.29876			−0.318848
$525$		0			0
$526$	1.73712			0.0757422
$527$	14.4075	−	3.86048i	0.627600	−	0.168165i
$528$	−2.11403	+	7.88965i	−0.0920012	+	0.343353i
$529$	2.08308	−	1.20267i	0.0905687	−	0.0522899i
$530$		0			0
$531$		−	0.930359i		−	0.0403742i
$532$	−11.7960	−	11.4116i	−0.511419	−	0.494755i
$533$	0.530105	−	0.530105i	0.0229614	−	0.0229614i
$534$	−5.37936	−	3.10577i	−0.232788	−	0.134400i
$535$		0			0
$536$	−1.57935	−	2.73551i	−0.0682174	−	0.118156i
$537$	2.02232	+	7.54741i	0.0872696	+	0.325695i
$538$	−2.67525	−	2.67525i	−0.115338	−	0.115338i
$539$	24.0094	−	14.9432i	1.03416	−	0.643648i
$540$		0			0
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	0.127262	+	0.991869i	$0.459381\pi$
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	−0.922615	+	0.385722i	$0.873952\pi$
$542$	−20.5257	−	5.49985i	−0.881655	−	0.236239i
$543$	13.6528	+	3.65827i	0.585899	+	0.156991i
$544$	1.01987	−	1.76647i	0.0437266	−	0.0757366i
$545$		0			0
$546$	0.0256649	+	1.54963i	0.00109836	+	0.0663182i
$547$	20.0765	+	20.0765i	0.858409	+	0.858409i	0.991151	−	0.132742i	$-0.0423781\pi$
$547$	20.0765	+	20.0765i	0.858409	+	0.858409i	−0.132742	+	0.991151i	$0.542378\pi$
$548$	1.85804	+	6.93431i	0.0793717	+	0.296219i
$549$	3.76360	+	6.51875i	0.160627	+	0.278213i
$550$		0			0
$551$	38.4582	+	22.2039i	1.63838	+	0.945916i
$552$	6.48781	−	6.48781i	0.276139	−	0.276139i
$553$	12.9136	−	3.69043i	0.549141	−	0.156933i
$554$		−	4.89016i		−	0.207763i
$555$		0			0
$556$	10.7536	−	6.20859i	0.456054	−	0.263303i
$557$	6.65499	−	24.8367i	0.281981	−	1.05237i	−0.669037	−	0.743229i	$-0.733293\pi$
$557$	6.65499	−	24.8367i	0.281981	−	1.05237i	0.951017	−	0.309137i	$-0.100040\pi$
$558$	−7.68233	+	2.05847i	−0.325219	+	0.0871421i
$559$	−2.03974			−0.0862718
$560$		0			0
$561$	−16.6605			−0.703408
$562$	−28.4732	+	7.62937i	−1.20107	+	0.321825i
$563$	−1.38907	+	5.18407i	−0.0585422	+	0.218482i	−0.989000	−	0.147917i	$-0.952743\pi$
$563$	−1.38907	+	5.18407i	−0.0585422	+	0.218482i	0.930458	+	0.366400i	$0.119410\pi$
$564$	−0.551759	+	0.318558i	−0.0232332	+	0.0134137i
$565$		0			0
$566$		−	11.2836i		−	0.474286i
$567$	28.4377	+	7.11728i	1.19427	+	0.298898i
$568$	5.03630	−	5.03630i	0.211318	−	0.211318i
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.885483	−	0.464672i	$-0.153828\pi$
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.0403234	+	0.999187i	$0.487161\pi$
$570$		0			0
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	0.650263	−	0.759709i	$-0.274659\pi$
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	−0.983059	+	0.183290i	$0.941325\pi$
$572$	−0.302955	−	1.13064i	−0.0126672	−	0.0472746i
$573$	−6.39672	−	6.39672i	−0.267227	−	0.267227i
$574$	−5.98447	−	3.32424i	−0.249787	−	0.138751i
$575$		0			0
$576$	−0.543813	+	0.941911i	−0.0226589	+	0.0392463i
$577$	22.2641	+	5.96565i	0.926867	+	0.248353i	0.690518	−	0.723315i	$-0.257383\pi$
$577$	22.2641	+	5.96565i	0.926867	+	0.248353i	0.236349	+	0.971668i	$0.424049\pi$
$578$	−12.4020	−	3.32310i	−0.515854	−	0.138223i
$579$	20.2934	−	35.1493i	0.843366	−	1.46075i
$580$		0			0
$581$	−14.4173	+	0.238779i	−0.598132	+	0.00990621i
$582$	13.4065	+	13.4065i	0.555719	+	0.555719i
$583$	8.66048	+	32.3214i	0.358681	+	1.33861i
$584$	−5.76293	−	9.98169i	−0.238472	−	0.413045i
$585$		0			0
$586$	8.85989	+	5.11526i	0.365999	+	0.211310i
$587$	−28.2277	+	28.2277i	−1.16508	+	1.16508i	−0.181734	+	0.983348i	$0.558171\pi$
$587$	−28.2277	+	28.2277i	−1.16508	+	1.16508i	−0.983348	+	0.181734i	$0.941829\pi$
$588$	13.5415	−	4.11362i	0.558441	−	0.169643i
$589$			45.3622i			1.86912i
$590$		0			0
$591$	−19.4355	+	11.2211i	−0.799471	+	0.461575i
$592$	1.19723	−	4.46814i	0.0492060	−	0.183639i
$593$	34.2220	−	9.16977i	1.40533	−	0.376557i	0.525075	−	0.851056i	$-0.324037\pi$
$593$	34.2220	−	9.16977i	1.40533	−	0.376557i	0.880256	+	0.474499i	$0.157371\pi$
$594$	−15.6202			−0.640905
$595$		0			0
$596$	23.9483			0.980963
$597$	21.0953	−	5.65247i	0.863373	−	0.231340i
$598$	−0.340312	+	1.27006i	−0.0139164	+	0.0519367i
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	−0.172775	−	0.984961i	$-0.555273\pi$
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	0.766614	+	0.642108i	$0.221940\pi$
$600$		0			0
$601$		−	1.73528i		−	0.0707833i	−0.999374	−	0.0353917i	$-0.988732\pi$
$601$		−	1.73528i		−	0.0707833i	0.999374	−	0.0353917i	$-0.0112679\pi$
$602$	5.11804	+	17.9091i	0.208596	+	0.729919i
$603$	−2.42925	+	2.42925i	−0.0989266	+	0.0989266i
$604$	3.06862	+	1.77167i	0.124860	+	0.0720881i
$605$		0			0
$606$	−9.99616	−	17.3139i	−0.406066	−	0.703327i
$607$	−10.2070	−	38.0930i	−0.414288	−	1.54615i	−0.786257	−	0.617900i	$-0.787984\pi$
$607$	−10.2070	−	38.0930i	−0.414288	−	1.54615i	0.371968	−	0.928245i	$-0.378683\pi$
$608$	4.38642	+	4.38642i	0.177893	+	0.177893i
$609$	−32.8410	+	19.6930i	−1.33079	+	0.798000i
$610$		0			0
$611$	0.0456517	−	0.0790711i	0.00184687	−	0.00319887i
$612$	−2.14288	−	0.574183i	−0.0866208	−	0.0232100i
$613$	0.330293	+	0.0885018i	0.0133404	+	0.00357455i	0.265483	−	0.964116i	$-0.414469\pi$
$613$	0.330293	+	0.0885018i	0.0133404	+	0.00357455i	−0.252143	+	0.967690i	$0.581135\pi$
$614$	0.762678	−	1.32100i	0.0307792	−	0.0533111i
$615$		0			0
$616$	−9.16697	+	5.49694i	−0.369348	+	0.221478i
$617$	−11.1876	−	11.1876i	−0.450397	−	0.450397i	0.445089	−	0.895486i	$-0.353172\pi$
$617$	−11.1876	−	11.1876i	−0.450397	−	0.450397i	−0.895486	+	0.445089i	$0.853172\pi$
$618$	−2.24069	−	8.36236i	−0.0901337	−	0.336383i
$619$	18.2682	+	31.6414i	0.734260	+	1.27178i	0.955047	+	0.296454i	$0.0958042\pi$
$619$	18.2682	+	31.6414i	0.734260	+	1.27178i	−0.220787	+	0.975322i	$0.570862\pi$
$620$		0			0
$621$	15.1956	+	8.77316i	0.609777	+	0.352055i
$622$	−6.80819	+	6.80819i	−0.272984	+	0.272984i
$623$	−2.23356	−	7.81566i	−0.0894855	−	0.313128i
$624$		−	0.585786i		−	0.0234502i
$625$		0			0
$626$	−2.62123	+	1.51337i	−0.104766	+	0.0604864i
$627$	13.1140	−	48.9421i	0.523723	−	1.95456i
$628$	5.91389	−	1.58462i	0.235990	−	0.0632333i
$629$	9.43535			0.376212
$630$		0			0
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	−4.90330	+	1.31384i	−0.195043	+	0.0522616i
$633$	−3.95888	+	14.7747i	−0.157351	+	0.587243i
$634$	1.68760	−	0.974335i	0.0670231	−	0.0386958i
$635$		0			0
$636$			16.7457i			0.664010i
$637$	−1.38585	+	1.48083i	−0.0549093	+	0.0586726i
$638$	20.4502	−	20.4502i	0.809631	−	0.809631i
$639$	−6.70867	−	3.87325i	−0.265391	−	0.153223i
$640$		0			0
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	0.972129	−	0.234445i	$-0.0753272\pi$
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	−0.689100	+	0.724666i	$0.741994\pi$
$642$	−7.78222	−	29.0436i	−0.307140	−	1.14626i
$643$	−7.65201	−	7.65201i	−0.301766	−	0.301766i	0.539939	−	0.841704i	$-0.318447\pi$
$643$	−7.65201	−	7.65201i	−0.301766	−	0.301766i	−0.841704	+	0.539939i	$0.818447\pi$
$644$	12.0051	−	0.198828i	0.473068	−	0.00783492i
$645$		0			0
$646$	−6.32659	+	10.9580i	−0.248916	+	0.431136i
$647$	−31.2468	−	8.37254i	−1.22844	−	0.329159i	−0.414466	−	0.910065i	$-0.636032\pi$
$647$	−31.2468	−	8.37254i	−1.22844	−	0.329159i	−0.813971	+	0.580906i	$0.802698\pi$
$648$	−10.7024	−	2.86770i	−0.420430	−	0.112654i
$649$	−1.72791	+	2.99282i	−0.0678262	+	0.117478i
$650$		0			0
$651$	−34.1947	−	18.9943i	−1.34019	−	0.744447i
$652$	11.7082	+	11.7082i	0.458528	+	0.458528i
$653$	0.132578	+	0.494788i	0.00518818	+	0.0193625i	0.968471	−	0.249125i	$-0.0801429\pi$
$653$	0.132578	+	0.494788i	0.00518818	+	0.0193625i	−0.963283	+	0.268487i	$0.913476\pi$
$654$	−13.3754	−	23.1669i	−0.523020	−	0.905898i
$655$		0			0
$656$	2.24080	+	1.29373i	0.0874886	+	0.0505116i
$657$	−8.86417	+	8.86417i	−0.345824	+	0.345824i
$658$	−0.808797	−	0.202423i	−0.0315302	−	0.00789127i
$659$			19.5542i			0.761723i	0.924632	+	0.380862i	$0.124373\pi$
$659$			19.5542i			0.761723i	−0.924632	+	0.380862i	$0.875627\pi$
$660$		0			0
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.339388	−	0.940647i	$-0.389780\pi$
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.984318	+	0.176405i	$0.0564468\pi$
$662$	7.47819	−	27.9090i	0.290648	−	1.08471i
$663$	1.15414	−	0.309250i	0.0448230	−	0.0120103i
$664$	5.44998			0.211500
$665$		0			0
$666$	−5.03109			−0.194951
$667$	−31.3801	+	8.40828i	−1.21504	+	0.325570i
$668$	3.76542	−	14.0527i	0.145688	−	0.543716i
$669$	23.1579	−	13.3702i	0.895337	−	0.516923i
$670$		0			0
$671$		−	27.9597i		−	1.07937i
$672$	−5.14324	+	1.46983i	−0.198405	+	0.0567000i
$673$	−18.4813	+	18.4813i	−0.712401	+	0.712401i	−0.967037	−	0.254636i	$-0.918044\pi$
$673$	−18.4813	+	18.4813i	−0.712401	+	0.712401i	0.254636	+	0.967037i	$0.418044\pi$
$674$	1.00824	+	0.582108i	0.0388360	+	0.0224220i
$675$		0			0
$676$	−6.45803	−	11.1856i	−0.248386	−	0.430217i
$677$	10.6631	+	39.7951i	0.409815	+	1.52945i	0.794999	+	0.606611i	$0.207472\pi$
$677$	10.6631	+	39.7951i	0.409815	+	1.52945i	−0.385183	+	0.922840i	$0.625862\pi$
$678$	−19.7192	−	19.7192i	−0.757312	−	0.757312i
$679$	0.410862	+	24.8076i	0.0157674	+	0.952030i
$680$		0			0
$681$	16.3702	−	28.3541i	0.627309	−	1.08653i
$682$	28.5359	+	7.64618i	1.09270	+	0.292787i
$683$	−8.81689	−	2.36248i	−0.337369	−	0.0903978i	0.0861573	−	0.996282i	$-0.472541\pi$
$683$	−8.81689	−	2.36248i	−0.337369	−	0.0903978i	−0.423526	+	0.905884i	$0.639208\pi$
$684$	3.37345	−	5.84298i	0.128987	−	0.223412i
$685$		0			0
$686$	16.4791	+	8.45219i	0.629175	+	0.322706i
$687$	16.8358	+	16.8358i	0.642325	+	0.642325i
$688$	−1.82208	−	6.80009i	−0.0694661	−	0.259251i
$689$	−1.19989	−	2.07827i	−0.0457121	−	0.0791758i
$690$		0			0
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.991940	−	0.126712i	$-0.959558\pi$
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.605706	−	0.795689i	$-0.707109\pi$
$692$	−5.49565	+	5.49565i	−0.208913	+	0.208913i
$693$	8.35538	+	8.08313i	0.317395	+	0.307053i
$694$		−	16.7042i		−	0.634082i
$695$		0			0
$696$	12.5343	−	7.23668i	0.475111	−	0.274306i
$697$	−1.36598	+	5.09790i	−0.0517401	+	0.193097i
$698$	35.4636	−	9.50244i	1.34232	−	0.359673i
$699$	−11.5732			−0.437739
$700$		0			0
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$	1.08207	−	0.289940i	0.0408402	−	0.0109431i
$703$	−7.42684	+	27.7173i	−0.280109	+	1.04538i
$704$	3.49872	−	2.01999i	0.131863	−	0.0761311i
$705$		0			0
$706$		−	14.2708i		−	0.537089i
$707$	6.35191	−	25.3796i	0.238888	−	0.954496i
$708$	−1.22290	+	1.22290i	−0.0459595	+	0.0459595i
$709$	−12.7354	−	7.35277i	−0.478287	−	0.276139i	0.241416	−	0.970422i	$-0.422388\pi$
$709$	−12.7354	−	7.35277i	−0.478287	−	0.276139i	−0.719702	+	0.694283i	$0.755722\pi$
$710$		0			0
$711$	2.76054	+	4.78140i	0.103528	+	0.179316i
$712$	0.795171	+	2.96762i	0.0298003	+	0.111216i
$713$	−23.4656	−	23.4656i	−0.878795	−	0.878795i
$714$	−5.61116	−	9.35745i	−0.209992	−	0.350194i
$715$		0			0
$716$	1.93236	−	3.34695i	0.0722157	−	0.125081i
$717$	−16.2831	−	4.36306i	−0.608105	−	0.162941i
$718$	−26.1658	−	7.01110i	−0.976499	−	0.261652i
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	−0.559831	−	0.828607i	$-0.689134\pi$
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	0.997510	+	0.0705247i	$0.0224674\pi$
$720$		0			0
$721$	5.50134	−	9.90382i	0.204881	−	0.368837i
$722$	−13.7753	−	13.7753i	−0.512665	−	0.512665i
$723$	1.55119	+	5.78913i	0.0576895	+	0.215300i
$724$	−3.49553	−	6.05444i	−0.129911	−	0.225012i
$725$		0			0
$726$	−9.31732	−	5.37936i	−0.345798	−	0.199647i
$727$	14.1380	−	14.1380i	0.524349	−	0.524349i	−0.394533	−	0.918882i	$-0.629093\pi$
$727$	14.1380	−	14.1380i	0.524349	−	0.524349i	0.918882	+	0.394533i	$0.129093\pi$
$728$	0.532998	−	0.550950i	0.0197542	−	0.0204196i
$729$		−	11.4004i		−	0.422236i
$730$		0			0
$731$	12.4359	−	7.17986i	0.459958	−	0.265557i
$732$	3.62148	−	13.5155i	0.133854	−	0.499549i
$733$	26.7908	−	7.17859i	0.989543	−	0.265147i	0.272484	−	0.962160i	$-0.412155\pi$
$733$	26.7908	−	7.17859i	0.989543	−	0.265147i	0.717058	+	0.697013i	$0.245488\pi$
$734$	−22.6715			−0.836821
$735$		0			0
$736$	−4.53813			−0.167278
$737$	12.3262	−	3.30280i	0.454042	−	0.121660i
$738$	0.728364	−	2.71829i	0.0268114	−	0.100062i
$739$	−11.7451	+	6.78102i	−0.432050	+	0.249444i	−0.700219	−	0.713928i	$-0.746915\pi$
$739$	−11.7451	+	6.78102i	−0.432050	+	0.249444i	0.268170	+	0.963372i	$0.413581\pi$
$740$		0			0
$741$			3.63383i			0.133492i
$742$	−15.2366	+	15.7498i	−0.559354	+	0.578194i
$743$	−13.5961	+	13.5961i	−0.498791	+	0.498791i	−0.911062	−	0.412270i	$-0.864736\pi$
$743$	−13.5961	+	13.5961i	−0.498791	+	0.498791i	0.412270	+	0.911062i	$0.364736\pi$
$744$	12.8037	+	7.39223i	0.469407	+	0.271012i
$745$		0			0
$746$	6.41789	+	11.1161i	0.234976	+	0.406990i
$747$	−1.53416	−	5.72557i	−0.0561320	−	0.209488i
$748$	5.82691	+	5.82691i	0.213053	+	0.213053i
$749$	19.1069	−	34.3973i	0.698152	−	1.25685i
$750$		0			0
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	0.125182	+	0.992134i	$0.460049\pi$
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	−0.921804	+	0.387656i	$0.873285\pi$
$752$	0.304388	+	0.0815604i	0.0110999	+	0.00297420i
$753$	−31.5979	−	8.46663i	−1.15149	−	0.308541i
$754$	−1.03707	+	1.79626i	−0.0377678	+	0.0654158i
$755$		0			0
$756$	−5.26079	−	8.77316i	−0.191333	−	0.319077i
$757$	−7.88896	−	7.88896i	−0.286729	−	0.286729i	0.549056	−	0.835785i	$-0.314987\pi$
$757$	−7.88896	−	7.88896i	−0.286729	−	0.286729i	−0.835785	+	0.549056i	$0.814987\pi$
$758$	3.74613	+	13.9807i	0.136065	+	0.507803i
$759$	18.5337	+	32.1013i	0.672730	+	1.16520i
$760$		0			0
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	0.468700	−	0.883357i	$-0.344722\pi$
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	−0.530660	+	0.847585i	$0.678056\pi$
$762$	−4.44761	+	4.44761i	−0.161120	+	0.161120i
$763$	8.49921	−	33.9593i	0.307692	−	1.22941i
$764$			4.47442i			0.161879i
$765$		0			0
$766$	−1.51691	+	0.875788i	−0.0548082	+	0.0316435i
$767$	0.0641463	−	0.239397i	0.00231619	−	0.00864413i
$768$	1.95290	−	0.523277i	0.0704691	−	0.0188821i
$769$	−17.4914			−0.630756			−0.315378	−	0.948966i	$-0.602131\pi$
$769$	−17.4914			−0.630756			−0.315378	+	0.948966i	$0.602131\pi$
$770$		0			0
$771$	−11.7763			−0.424112
$772$	−19.3907	+	5.19573i	−0.697887	+	0.186998i
$773$	−11.5736	+	43.1933i	−0.416274	+	1.55355i	0.365997	+	0.930616i	$0.380728\pi$
$773$	−11.5736	+	43.1933i	−0.416274	+	1.55355i	−0.782271	+	0.622939i	$0.785939\pi$
$774$	−6.63103	+	3.82843i	−0.238347	+	0.137610i
$775$		0			0
$776$		−	9.37769i		−	0.336640i
$777$	−17.7839	−	17.2044i	−0.637994	−	0.617205i
$778$	−1.96738	+	1.96738i	−0.0705341	+	0.0705341i
$779$	−13.9004	−	8.02542i	−0.498035	−	0.287540i
$780$		0			0
$781$	14.3871	+	24.9193i	0.514813	+	0.891682i
$782$	−2.39579	−	8.94120i	−0.0856732	−	0.319737i
$783$	19.5716	+	19.5716i	0.699433	+	0.699433i
$784$	−6.17475	−	3.29733i	−0.220527	−	0.117762i
$785$		0			0
$786$	7.37827	−	12.7795i	0.263174	−	0.455831i
$787$	−25.0643	−	6.71595i	−0.893445	−	0.239398i	−0.217246	−	0.976117i	$-0.569707\pi$
$787$	−25.0643	−	6.71595i	−0.893445	−	0.239398i	−0.676199	+	0.736719i	$0.736374\pi$
$788$	10.7220	+	2.87294i	0.381954	+	0.102344i
$789$	−1.75605	+	3.04156i	−0.0625170	+	0.108283i
$790$		0			0
$791$	−0.604323	−	36.4887i	−0.0214873	−	1.29739i
$792$	−3.10701	−	3.10701i	−0.110403	−	0.110403i
$793$	0.518984	+	1.93688i	0.0184297	+	0.0687805i
$794$	−19.8340	−	34.3535i	−0.703881	−	1.21916i
$795$		0			0
$796$	−9.35485	−	5.40103i	−0.331574	−	0.191434i
$797$	37.3374	−	37.3374i	1.32256	−	1.32256i	0.410861	−	0.911698i	$-0.365228\pi$
$797$	37.3374	−	37.3374i	1.32256	−	1.32256i	0.911698	−	0.410861i	$-0.134772\pi$
$798$	31.9052	−	9.11786i	1.12943	−	0.322769i
$799$			0.642773i			0.0227397i
$800$		0			0
$801$	2.89384	−	1.67076i	0.102249	−	0.0590333i
$802$	5.16876	−	19.2901i	0.182515	−	0.681156i
$803$	44.9776	−	12.0517i	1.58722	−	0.425295i
$804$	6.38621			0.225224
$805$		0			0
$806$	−2.11872			−0.0746287
$807$	7.38854	−	1.97975i	0.260089	−	0.0696906i
$808$	−2.55932	+	9.55150i	−0.0900364	+	0.336021i
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	−0.724036	−	0.689762i	$-0.757715\pi$
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	0.235333	+	0.971915i	$0.424382\pi$
$810$		0			0
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$	18.3734	+	4.59844i	0.644781	+	0.161374i
$813$	30.3791	−	30.3791i	1.06544	−	1.06544i
$814$	16.1842	+	9.34397i	0.567257	+	0.327506i
$815$		0			0
$816$	2.06196	+	3.57142i	0.0721831	+	0.125025i
$817$	11.3030	+	42.1832i	0.395440	+	1.47580i
$818$	−10.8227	−	10.8227i	−0.378407	−	0.378407i
$819$	−0.728847	−	0.404858i	−0.0254680	−	0.0141469i
$820$		0			0
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	−0.999351	−	0.0360337i	$-0.988528\pi$
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	0.530881	+	0.847446i	$0.321861\pi$
$822$	−14.0197	−	3.75657i	−0.488993	−	0.131025i
$823$	27.0285	+	7.24225i	0.942153	+	0.252449i	0.697029	−	0.717043i	$-0.254505\pi$
$823$	27.0285	+	7.24225i	0.942153	+	0.252449i	0.245124	+	0.969492i	$0.421171\pi$
$824$	−2.14101	+	3.70835i	−0.0745858	+	0.129186i
$825$		0			0
$826$	−2.26288	+	0.0374776i	−0.0787355	+	0.00130401i
$827$	−16.8901	−	16.8901i	−0.587325	−	0.587325i	0.349581	−	0.936906i	$-0.386324\pi$
$827$	−16.8901	−	16.8901i	−0.587325	−	0.587325i	−0.936906	+	0.349581i	$0.886324\pi$
$828$	1.27748	+	4.76761i	0.0443954	+	0.165686i
$829$	7.08412	+	12.2701i	0.246042	+	0.426157i	0.962424	−	0.271551i	$-0.0875367\pi$
$829$	7.08412	+	12.2701i	0.246042	+	0.426157i	−0.716382	+	0.697708i	$0.754203\pi$
$830$		0			0
$831$	8.56228	+	4.94343i	0.297022	+	0.171486i
$832$	−0.204875	+	0.204875i	−0.00710276	+	0.00710276i
$833$	3.23673	−	13.9065i	0.112146	−	0.481831i
$834$			25.1049i			0.869311i
$835$		0			0
$836$	−21.7037	+	12.5306i	−0.750638	+	0.433381i
$837$	−7.31770	+	27.3100i	−0.252937	+	0.943972i
$838$	−26.7588	+	7.17000i	−0.924367	+	0.247683i
$839$	18.1874			0.627900			0.313950	−	0.949439i	$-0.398348\pi$
$839$	18.1874			0.627900			0.313950	+	0.949439i	$0.398348\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$	31.8909	−	8.54515i	1.09903	−	0.294485i
$843$	15.4250	−	57.5667i	0.531264	−	1.98270i
$844$	6.55196	−	3.78278i	0.225528	−	0.130209i
$845$		0			0
$846$		−	0.342738i		−	0.0117836i
$847$	−3.86863	−	13.5371i	−0.132928	−	0.465141i
$848$	5.85669	−	5.85669i	0.201120	−	0.201120i
$849$	19.7567	+	11.4065i	0.678048	+	0.391471i
$850$		0			0
$851$	−10.4962	−	18.1799i	−0.359804	−	0.623198i
$852$	3.72699	+	13.9093i	0.127685	+	0.476525i
$853$	17.4820	+	17.4820i	0.598574	+	0.598574i	0.939933	−	0.341359i	$-0.110887\pi$
$853$	17.4820	+	17.4820i	0.598574	+	0.598574i	−0.341359	+	0.939933i	$0.610887\pi$
$854$	15.7037	−	9.41665i	0.537369	−	0.322231i
$855$		0			0
$856$	−7.43604	+	12.8796i	−0.254159	+	0.440216i
$857$	25.2634	+	6.76932i	0.862982	+	0.231235i	0.663051	−	0.748574i	$-0.269261\pi$
$857$	25.2634	+	6.76932i	0.862982	+	0.231235i	0.199932	+	0.979810i	$0.435928\pi$
$858$	2.28592	+	0.612511i	0.0780401	+	0.0209108i
$859$	24.4126	−	42.2838i	0.832946	−	1.44271i	−0.0627455	−	0.998030i	$-0.519986\pi$
$859$	24.4126	−	42.2838i	0.832946	−	1.44271i	0.895692	−	0.444676i	$-0.146681\pi$
$860$		0			0
$861$	11.8701	−	7.11788i	0.404533	−	0.242577i
$862$	−16.9121	−	16.9121i	−0.576027	−	0.576027i
$863$	−3.97256	−	14.8258i	−0.135228	−	0.504676i	−0.999997	−	0.00250685i	$-0.999202\pi$
$863$	−3.97256	−	14.8258i	−0.135228	−	0.504676i	0.864769	−	0.502169i	$-0.167465\pi$
$864$	1.93321	+	3.34841i	0.0657691	+	0.113915i
$865$		0			0
$866$	16.2298	+	9.37026i	0.551510	+	0.318414i
$867$	18.3555	−	18.3555i	0.623387	−	0.623387i
$868$	5.31621	+	18.6025i	0.180444	+	0.631410i
$869$		−	20.5080i		−	0.695686i
$870$		0			0
$871$	−0.792578	+	0.457595i	−0.0268555	+	0.0155050i
$872$	−3.42451	+	12.7804i	−0.115968	+	0.432800i
$873$	−9.85188	+	2.63980i	−0.333436	+	0.0893438i
$874$	28.1515			0.952240
$875$		0			0
$876$	23.3028			0.787330
$877$	−38.1169	+	10.2134i	−1.28712	+	0.344882i	−0.836565	−	0.547868i	$-0.815440\pi$
$877$	−38.1169	+	10.2134i	−1.28712	+	0.344882i	−0.450552	+	0.892750i	$0.648773\pi$
$878$	−3.65133	+	13.6270i	−0.123227	+	0.459888i
$879$	−17.9128	+	10.3420i	−0.604185	+	0.348826i
$880$		0			0
$881$			52.5926i			1.77189i	0.463791	+	0.885945i	$0.346489\pi$
$881$			52.5926i			1.77189i	−0.463791	+	0.885945i	$0.653511\pi$
$882$	−1.72588	+	7.41518i	−0.0581135	+	0.249682i
$883$	−13.0940	+	13.0940i	−0.440649	+	0.440649i	−0.892230	−	0.451581i	$-0.850860\pi$
$883$	−13.0940	+	13.0940i	−0.440649	+	0.440649i	0.451581	+	0.892230i	$0.350860\pi$
$884$	−0.511811	−	0.295494i	−0.0172141	−	0.00993854i
$885$		0			0
$886$	−10.5317	−	18.2414i	−0.353819	−	0.612833i
$887$	−9.56553	−	35.6990i	−0.321179	−	1.19866i	−0.918098	−	0.396354i	$-0.870275\pi$
$887$	−9.56553	−	35.6990i	−0.321179	−	1.19866i	0.596919	−	0.802302i	$-0.296391\pi$
$888$	6.61308	+	6.61308i	0.221920	+	0.221920i
$889$	−8.22991	+	0.136303i	−0.276022	+	0.00457146i
$890$		0			0
$891$	22.3813	−	38.7656i	0.749803	−	1.29870i
$892$	−12.7755	−	3.42318i	−0.427755	−	0.114617i
$893$	−1.88822	−	0.505946i	−0.0631867	−	0.0169308i
$894$	−24.2092	+	41.9316i	−0.809678	+	1.40240i
$895$		0			0
$896$	2.31288	+	1.28475i	0.0772679	+	0.0429205i
$897$	−1.87976	−	1.87976i	−0.0627633	−	0.0627633i
$898$	8.10744	+	30.2574i	0.270549	+	1.00970i
$899$	−26.1742	−	45.3351i	−0.872959	−	1.51201i
$900$		0			0
$901$	14.6310	+	8.44719i	0.487428	+	0.281417i
$902$	−7.39156	+	7.39156i	−0.246112	+	0.246112i
$903$	−36.5311	−	9.14288i	−1.21568	−	0.304256i
$904$			13.7933i			0.458759i
$905$		0			0
$906$	−6.20410	+	3.58194i	−0.206117	+	0.119002i
$907$	4.28883	−	16.0061i	0.142408	−	0.531474i	−0.857449	−	0.514569i	$-0.827952\pi$
$907$	4.28883	−	16.0061i	0.142408	−	0.531474i	0.999857	−	0.0169054i	$-0.00538141\pi$
$908$	−15.6420	+	4.19127i	−0.519099	+	0.139092i
$909$	10.7549			0.356718
$910$		0			0
$911$	−1.46770			−0.0486270			−0.0243135	−	0.999704i	$-0.507740\pi$
$911$	−1.46770			−0.0486270			−0.0243135	+	0.999704i	$0.507740\pi$
$912$	−12.1145	+	3.24606i	−0.401150	+	0.107488i
$913$	−5.69862	+	21.2676i	−0.188597	+	0.703853i
$914$	−2.47817	+	1.43077i	−0.0819705	+	0.0473257i
$915$		0			0
$916$		−	11.7764i		−	0.389103i
$917$	18.5674	−	5.30617i	0.613149	−	0.175225i
$918$	−5.57658	+	5.57658i	−0.184055	+	0.184055i
$919$	24.1523	+	13.9443i	0.796710	+	0.459981i	0.842319	−	0.538979i	$-0.181190\pi$
$919$	24.1523	+	13.9443i	0.796710	+	0.459981i	−0.0456096	+	0.998959i	$0.514523\pi$
$920$		0			0
$921$	1.54197	+	2.67078i	0.0508098	+	0.0880051i
$922$	−0.783378	−	2.92361i	−0.0257992	−	0.0962838i
$923$	−1.45920	−	1.45920i	−0.0480302	−	0.0480302i
$924$	−0.357861	−	21.6075i	−0.0117728	−	0.710833i
$925$		0			0
$926$	−13.6393	+	23.6240i	−0.448215	+	0.776332i
$927$	4.49855	+	1.20538i	0.147752	+	0.0395900i
$928$	−6.91477	−	1.85281i	−0.226988	−	0.0608213i
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	0.452368	+	0.891831i	$0.350579\pi$
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	−0.998533	+	0.0541530i	$0.982754\pi$
$930$		0			0
$931$	38.3040	+	20.4544i	1.25536	+	0.670367i
$932$	4.04765	+	4.04765i	0.132585	+	0.132585i
$933$	−5.03824	−	18.8030i	−0.164944	−	0.615581i
$934$	12.5645	+	21.7623i	0.411122	+	0.712084i
$935$		0			0
$936$	0.272906	+	0.157563i	0.00892023	+	0.00515009i
$937$	−25.6651	+	25.6651i	−0.838442	+	0.838442i	−0.988654	−	0.150212i	$-0.952004\pi$
$937$	−25.6651	+	25.6651i	−0.838442	+	0.838442i	0.150212	+	0.988654i	$0.452004\pi$
$938$	6.00642	+	5.81071i	0.196117	+	0.189726i
$939$		−	6.11942i		−	0.199700i
$940$		0			0
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	−0.802475	−	0.596686i	$-0.796484\pi$
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	0.115508	+	0.993307i	$0.463151\pi$
$942$	−3.20377	+	11.9566i	−0.104384	+	0.389568i
$943$	11.3421	−	3.03911i	0.369350	−	0.0989670i
$944$	0.855404			0.0278410
$945$		0			0
$946$	28.4413			0.924707
$947$	−2.07680	+	0.556477i	−0.0674869	+	0.0180831i	−0.292405	−	0.956295i	$-0.594455\pi$
$947$	−2.07680	+	0.556477i	−0.0674869	+	0.0180831i	0.224918	+	0.974378i	$0.427789\pi$
$948$	2.65630	−	9.91343i	0.0862725	−	0.321973i
$949$	−2.89206	+	1.66973i	−0.0938804	+	0.0542019i
$950$		0			0
$951$			3.93980i			0.127757i
$952$	−1.31024	+	5.23517i	−0.0424652	+	0.169673i
$953$	13.1863	−	13.1863i	0.427146	−	0.427146i	−0.460509	−	0.887655i	$-0.652333\pi$
$953$	13.1863	−	13.1863i	0.427146	−	0.427146i	0.887655	+	0.460509i	$0.152333\pi$
$954$	−7.80149	−	4.50419i	−0.252582	−	0.145829i
$955$		0			0
$956$	4.16897	+	7.22087i	0.134834	+	0.233540i
$957$	15.1337	+	56.4796i	0.489202	+	1.82573i
$958$	−5.85973	−	5.85973i	−0.189319	−	0.189319i
$959$	−9.76792	−	16.2895i	−0.315423	−	0.526015i
$960$		0			0
$961$	11.2368	−	19.4627i	0.362477	−	0.627829i
$962$	−1.29459	−	0.346883i	−0.0417391	−	0.0111840i
$963$	15.6241	+	4.18646i	0.503479	+	0.134907i
$964$	1.48219	−	2.56723i	0.0477381	−	0.0826849i
$965$		0			0
$966$	−11.7878	+	21.2210i	−0.379266	+	0.682775i
$967$	27.7931	+	27.7931i	0.893766	+	0.893766i	0.994875	−	0.101109i	$-0.0322392\pi$
$967$	27.7931	+	27.7931i	0.893766	+	0.893766i	−0.101109	+	0.994875i	$0.532239\pi$
$968$	1.37728	+	5.14006i	0.0442673	+	0.165208i
$969$	−12.7910	−	22.1547i	−0.410907	−	0.711711i
$970$		0			0
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	0.681467	−	0.731849i	$-0.261342\pi$
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	−0.293067	+	0.956092i	$0.594676\pi$
$972$	7.63821	−	7.63821i	0.244996	−	0.244996i
$973$	−22.8425	+	23.6119i	−0.732298	+	0.756963i
$974$			10.6783i			0.342155i
$975$		0			0
$976$	−5.99356	+	3.46038i	−0.191849	+	0.110764i
$977$	−2.16089	+	8.06456i	−0.0691331	+	0.258008i	−0.991839	−	0.127496i	$-0.959306\pi$
$977$	−2.16089	+	8.06456i	−0.0691331	+	0.258008i	0.922706	+	0.385505i	$0.125973\pi$
$978$	−32.3358	+	8.66436i	−1.03399	+	0.277056i
$979$	−12.4120			−0.396690
$980$		0			0
$981$	14.3907			0.459459
$982$	24.8494	−	6.65836i	0.792975	−	0.212477i
$983$	6.30383	−	23.5262i	0.201061	−	0.750370i	−0.789553	−	0.613682i	$-0.789688\pi$
$983$	6.30383	−	23.5262i	0.201061	−	0.750370i	0.990614	−	0.136688i	$-0.0436457\pi$
$984$	−4.53043	+	2.61564i	−0.144425	+	0.0833836i
$985$		0			0
$986$		−	14.6019i		−	0.465018i
$987$	1.17203	−	1.21151i	0.0373062	−	0.0385628i
$988$	1.27091	−	1.27091i	0.0404329	−	0.0404329i
$989$	−27.6681	−	15.9742i	−0.879794	−	0.507949i
$990$		0			0
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	0.693637	−	0.720324i	$-0.256007\pi$
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	−0.970638	+	0.240545i	$0.922674\pi$
$992$	−1.89263	−	7.06340i	−0.0600911	−	0.224263i
$993$	41.3067	+	41.3067i	1.31083	+	1.31083i
$994$	−9.15051	+	16.4733i	−0.290237	+	0.522500i
$995$		0			0
$996$	−5.50936	+	9.54248i	−0.174571	+	0.302365i
$997$	−25.2781	−	6.77324i	−0.800565	−	0.214511i	−0.164733	−	0.986338i	$-0.552676\pi$
$997$	−25.2781	−	6.77324i	−0.800565	−	0.214511i	−0.635832	+	0.771827i	$0.719343\pi$
$998$	−14.1014	−	3.77845i	−0.446371	−	0.119605i
$999$	−8.94255	+	15.4890i	−0.282930	+	0.490049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.c.257.3		16
5.2	odd	4		70.2.k.a.33.4	yes	16
5.3	odd	4	inner	350.2.o.c.243.1		16
5.4	even	2		70.2.k.a.47.2	yes	16
7.3	odd	6	inner	350.2.o.c.157.1		16
15.2	even	4		630.2.bv.c.523.2		16
15.14	odd	2		630.2.bv.c.397.4		16
20.7	even	4		560.2.ci.c.33.1		16
20.19	odd	2		560.2.ci.c.257.1		16
35.2	odd	12		490.2.g.c.293.5		16
35.3	even	12	inner	350.2.o.c.143.3		16
35.4	even	6		490.2.l.c.227.3		16
35.9	even	6		490.2.g.c.97.8		16
35.12	even	12		490.2.g.c.293.8		16
35.17	even	12		70.2.k.a.3.2	✓	16
35.19	odd	6		490.2.g.c.97.5		16
35.24	odd	6		70.2.k.a.17.4	yes	16
35.27	even	4		490.2.l.c.313.3		16
35.32	odd	12		490.2.l.c.423.1		16
35.34	odd	2		490.2.l.c.117.1		16
105.17	odd	12		630.2.bv.c.73.4		16
105.59	even	6		630.2.bv.c.577.2		16
140.59	even	6		560.2.ci.c.17.1		16
140.87	odd	12		560.2.ci.c.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	35.17	even	12
70.2.k.a.17.4	yes	16	35.24	odd	6
70.2.k.a.33.4	yes	16	5.2	odd	4
70.2.k.a.47.2	yes	16	5.4	even	2
350.2.o.c.143.3		16	35.3	even	12	inner
350.2.o.c.157.1		16	7.3	odd	6	inner
350.2.o.c.243.1		16	5.3	odd	4	inner
350.2.o.c.257.3		16	1.1	even	1	trivial
490.2.g.c.97.5		16	35.19	odd	6
490.2.g.c.97.8		16	35.9	even	6
490.2.g.c.293.5		16	35.2	odd	12
490.2.g.c.293.8		16	35.12	even	12
490.2.l.c.117.1		16	35.34	odd	2
490.2.l.c.227.3		16	35.4	even	6
490.2.l.c.313.3		16	35.27	even	4
490.2.l.c.423.1		16	35.32	odd	12
560.2.ci.c.17.1		16	140.59	even	6
560.2.ci.c.33.1		16	20.7	even	4
560.2.ci.c.257.1		16	20.19	odd	2
560.2.ci.c.353.1		16	140.87	odd	12
630.2.bv.c.73.4		16	105.17	odd	12
630.2.bv.c.397.4		16	15.14	odd	2
630.2.bv.c.523.2		16	15.2	even	4
630.2.bv.c.577.2		16	105.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.523277 + 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +2.02179i q^{6} +(-1.83959 + 1.90155i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +(2.01999 + 3.49872i) q^{11} +(0.523277 + 1.95290i) q^{12} +(-0.204875 - 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.97024 + 0.527924i) q^{17} +(-1.05057 - 0.281498i) q^{18} +(-3.10166 + 5.37224i) q^{19} +(-2.75092 - 4.58757i) q^{21} +(2.85669 + 2.85669i) q^{22} +(-1.17456 - 4.38350i) q^{23} +(1.01089 + 1.75092i) q^{24} +(-0.250919 - 0.144868i) q^{26} +(-2.73397 + 2.73397i) q^{27} +(-0.642357 + 2.56659i) q^{28} -7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-7.88965 + 2.11403i) q^{33} +2.03974 q^{34} -1.08763 q^{36} +(4.46814 - 1.19723i) q^{37} +(-1.60554 + 5.99195i) q^{38} +(0.507306 - 0.292893i) q^{39} +2.58745i q^{41} +(-3.84454 - 3.71926i) q^{42} +(4.97801 - 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.0815604 + 0.304388i) q^{47} +(1.42962 + 1.42962i) q^{48} +(-0.231803 - 6.99616i) q^{49} +(-2.06196 + 3.57142i) q^{51} +(-0.279864 - 0.0749894i) q^{52} +(8.00039 + 2.14370i) q^{53} +(-1.93321 + 3.34841i) q^{54} +(0.0438127 + 2.64539i) q^{56} +(-8.86840 - 8.86840i) q^{57} +(-1.85281 - 6.91477i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(5.17076 - 5.17076i) q^{62} +(2.76682 - 0.790700i) q^{63} -1.00000i q^{64} +(-7.07367 + 4.08398i) q^{66} +(0.817530 - 3.05106i) q^{67} +(1.97024 - 0.527924i) q^{68} +9.17514 q^{69} +7.12240 q^{71} +(-1.05057 + 0.281498i) q^{72} +(2.98311 - 11.1331i) q^{73} +(4.00603 - 2.31288i) q^{74} +6.20333i q^{76} +(-10.3690 - 2.59511i) q^{77} +(0.414214 - 0.414214i) q^{78} +(-4.39618 - 2.53813i) q^{79} +(-5.53997 - 9.59552i) q^{81} +(0.669683 + 2.49929i) q^{82} +(3.85372 + 3.85372i) q^{83} +(-4.67615 - 2.59749i) q^{84} +(3.51999 - 6.09680i) q^{86} +(13.9802 + 3.74598i) q^{87} +(3.90231 + 1.04562i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 - 3.20895i) q^{92} +(3.82650 + 14.2807i) q^{93} +(0.157563 + 0.272906i) q^{94} +(1.75092 + 1.01089i) q^{96} +(6.63103 - 6.63103i) q^{97} +(-2.03464 - 6.69778i) q^{98} -4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46}+ \cdots - 40 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

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Database

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