LMFDB - Embedded newform 275.3.q.c.74.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,18,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	275.74
Dual form			275.3.q.c.249.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.48990 - 1.80902i) q^{2} +(-3.80423 + 1.23607i) q^{3} +(1.69098 - 5.20431i) q^{4} +(-7.23607 + 9.95959i) q^{6} +(-2.48990 + 7.66312i) q^{7} +(-1.40008 - 4.30902i) q^{8} +(5.66312 - 4.11450i) q^{9} +(-10.8713 - 1.67760i) q^{11} +21.8885i q^{12} +(-11.3597 + 8.25329i) q^{13} +(7.66312 + 23.5847i) q^{14} +(6.42705 + 4.66953i) q^{16} +(19.6417 + 14.2705i) q^{17} +(6.65740 - 20.4894i) q^{18} +(-8.02786 + 2.60841i) q^{19} -32.2299i q^{21} +(-30.1033 + 15.4894i) q^{22} +25.3820i q^{23} +(10.6525 + 14.6619i) q^{24} +(-13.3541 + 41.0997i) q^{26} +(4.70228 - 6.47214i) q^{27} +(35.6709 + 25.9164i) q^{28} +(-34.7984 - 11.3067i) q^{29} +(8.38197 - 6.08985i) q^{31} +42.5730 q^{32} +(43.4306 - 7.05573i) q^{33} +74.7214 q^{34} +(-11.8369 - 36.4302i) q^{36} +(-19.2784 - 6.26393i) q^{37} +(-15.2699 + 21.0172i) q^{38} +(33.0132 - 45.4387i) q^{39} +(53.1140 - 17.2578i) q^{41} +(-58.3045 - 80.2492i) q^{42} -37.2752 q^{43} +(-27.1140 + 53.7409i) q^{44} +(45.9164 + 63.1985i) q^{46} +(-81.3216 + 26.4230i) q^{47} +(-30.2218 - 9.81966i) q^{48} +(-12.8820 - 9.35930i) q^{49} +(-92.3607 - 30.0098i) q^{51} +(23.7437 + 73.0755i) q^{52} +(-32.0787 - 44.1525i) q^{53} -24.6215i q^{54} +36.5066 q^{56} +(27.3156 - 19.8460i) q^{57} +(-107.098 + 34.7984i) q^{58} +(-18.3115 + 56.3571i) q^{59} +(21.5836 - 29.7073i) q^{61} +(9.85359 - 30.3262i) q^{62} +(17.4293 + 53.6418i) q^{63} +(80.2943 - 58.3372i) q^{64} +(95.3738 - 96.1347i) q^{66} +17.8197i q^{67} +(107.482 - 78.0902i) q^{68} +(-31.3738 - 96.5587i) q^{69} +(-4.70820 - 3.42071i) q^{71} +(-25.6583 - 18.6418i) q^{72} +(15.8124 - 48.6656i) q^{73} +(-59.3328 + 19.2784i) q^{74} +46.1903i q^{76} +(39.9241 - 79.1312i) q^{77} -172.859i q^{78} +(-20.1722 - 27.7647i) q^{79} +(-29.3566 + 90.3504i) q^{81} +(101.029 - 139.054i) q^{82} +(117.997 + 85.7295i) q^{83} +(-167.735 - 54.5002i) q^{84} +(-92.8115 + 67.4315i) q^{86} +146.357 q^{87} +(7.99197 + 49.1935i) q^{88} +127.949 q^{89} +(-34.9615 - 107.600i) q^{91} +(132.096 + 42.9205i) q^{92} +(-24.3594 + 33.5279i) q^{93} +(-154.683 + 212.903i) q^{94} +(-161.957 + 52.6232i) q^{96} +(53.0877 + 73.0689i) q^{97} -49.0059 q^{98} +(-68.4681 + 35.2296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{4} - 40 q^{6} + 14 q^{9} - 2 q^{11} + 30 q^{14} + 38 q^{16} - 100 q^{19} - 40 q^{24} - 80 q^{26} - 180 q^{29} + 76 q^{31} + 240 q^{34} - 126 q^{36} - 40 q^{39} + 170 q^{41} + 38 q^{44} + 260 q^{46}+ \cdots - 266 q^{99}+O(q^{100}) $ 8 * q + 18 * q^4 - 40 * q^6 + 14 * q^9 - 2 * q^11 + 30 * q^14 + 38 * q^16 - 100 * q^19 - 40 * q^24 - 80 * q^26 - 180 * q^29 + 76 * q^31 + 240 * q^34 - 126 * q^36 - 40 * q^39 + 170 * q^41 + 38 * q^44 + 260 * q^46 - 112 * q^49 - 560 * q^51 + 140 * q^56 + 256 * q^59 + 280 * q^61 + 298 * q^64 + 280 * q^66 + 232 * q^69 + 16 * q^71 - 260 * q^74 + 420 * q^79 + 190 * q^81 - 680 * q^84 - 340 * q^86 + 156 * q^89 - 150 * q^91 - 750 * q^94 - 920 * q^96 - 266 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	2.48990	−	1.80902i	1.24495	−	0.904508i	0.247031	−	0.969007i	$-0.420545\pi$
$2$	2.48990	−	1.80902i	1.24495	−	0.904508i	0.997918	+	0.0644990i	$0.0205449\pi$
$3$	−3.80423	+	1.23607i	−1.26808	+	0.412023i	−0.864365	−	0.502864i	$-0.832280\pi$
$3$	−3.80423	+	1.23607i	−1.26808	+	0.412023i	−0.403710	+	0.914887i	$0.632280\pi$
$4$	1.69098	−	5.20431i	0.422746	−	1.30108i
$5$		0			0
$5$		0			0
$6$	−7.23607	+	9.95959i	−1.20601	+	1.65993i
$7$	−2.48990	+	7.66312i	−0.355700	+	1.09473i	0.599903	+	0.800073i	$0.295206\pi$
$7$	−2.48990	+	7.66312i	−0.355700	+	1.09473i	−0.955603	+	0.294658i	$0.904794\pi$
$8$	−1.40008	−	4.30902i	−0.175011	−	0.538627i
$9$	5.66312	−	4.11450i	0.629235	−	0.457166i
$10$		0			0
$11$	−10.8713	−	1.67760i	−0.988302	−	0.152509i
$11$	−10.8713	−	1.67760i	−0.988302	−	0.152509i
$12$			21.8885i			1.82405i
$13$	−11.3597	+	8.25329i	−0.873821	+	0.634868i	−0.931610	−	0.363460i	$-0.881595\pi$
$13$	−11.3597	+	8.25329i	−0.873821	+	0.634868i	0.0577883	+	0.998329i	$0.481595\pi$
$14$	7.66312	+	23.5847i	0.547366	+	1.68462i
$15$		0			0
$16$	6.42705	+	4.66953i	0.401691	+	0.291845i
$17$	19.6417	+	14.2705i	1.15539	+	0.839442i	0.989188	−	0.146650i	$-0.0468490\pi$
$17$	19.6417	+	14.2705i	1.15539	+	0.839442i	0.166204	+	0.986091i	$0.446849\pi$
$18$	6.65740	−	20.4894i	0.369855	−	1.13830i
$19$	−8.02786	+	2.60841i	−0.422519	+	0.137285i	−0.512556	−	0.858654i	$-0.671301\pi$
$19$	−8.02786	+	2.60841i	−0.422519	+	0.137285i	0.0900372	+	0.995938i	$0.471301\pi$
$20$		0			0
$21$		−	32.2299i		−	1.53476i
$22$	−30.1033	+	15.4894i	−1.36833	+	0.704062i
$23$			25.3820i			1.10356i	0.833988	+	0.551782i	$0.186052\pi$
$23$			25.3820i			1.10356i	−0.833988	+	0.551782i	$0.813948\pi$
$24$	10.6525	+	14.6619i	0.443853	+	0.610911i
$25$		0			0
$26$	−13.3541	+	41.0997i	−0.513619	+	1.58076i
$27$	4.70228	−	6.47214i	0.174159	−	0.239709i
$28$	35.6709	+	25.9164i	1.27396	+	0.925586i
$29$	−34.7984	−	11.3067i	−1.19994	−	0.389885i	−0.360204	−	0.932874i	$-0.617293\pi$
$29$	−34.7984	−	11.3067i	−1.19994	−	0.389885i	−0.839740	+	0.542988i	$0.817293\pi$
$30$		0			0
$31$	8.38197	−	6.08985i	0.270386	−	0.196447i	−0.444327	−	0.895865i	$-0.646557\pi$
$31$	8.38197	−	6.08985i	0.270386	−	0.196447i	0.714713	+	0.699418i	$0.246557\pi$
$32$	42.5730			1.33041
$33$	43.4306	−	7.05573i	1.31608	−	0.213810i
$34$	74.7214			2.19769
$35$		0			0
$36$	−11.8369	−	36.4302i	−0.328802	−	1.01195i
$37$	−19.2784	−	6.26393i	−0.521038	−	0.169295i	0.0366784	−	0.999327i	$-0.488322\pi$
$37$	−19.2784	−	6.26393i	−0.521038	−	0.169295i	−0.557716	+	0.830032i	$0.688322\pi$
$38$	−15.2699	+	21.0172i	−0.401840	+	0.553085i
$39$	33.0132	−	45.4387i	0.846491	−	1.16510i
$40$		0			0
$41$	53.1140	−	17.2578i	1.29546	−	0.420921i	0.421462	−	0.906846i	$-0.361517\pi$
$41$	53.1140	−	17.2578i	1.29546	−	0.420921i	0.874001	+	0.485925i	$0.161517\pi$
$42$	−58.3045	−	80.2492i	−1.38820	−	1.91070i
$43$	−37.2752			−0.866866			−0.433433	−	0.901186i	$-0.642698\pi$
$43$	−37.2752			−0.866866			−0.433433	+	0.901186i	$0.642698\pi$
$44$	−27.1140	+	53.7409i	−0.616227	+	1.22139i
$45$		0			0
$46$	45.9164	+	63.1985i	0.998183	+	1.37388i
$47$	−81.3216	+	26.4230i	−1.73025	+	0.562191i	−0.993485	−	0.113962i	$-0.963646\pi$
$47$	−81.3216	+	26.4230i	−1.73025	+	0.562191i	−0.736761	+	0.676153i	$0.763646\pi$
$48$	−30.2218	−	9.81966i	−0.629621	−	0.204576i
$49$	−12.8820	−	9.35930i	−0.262897	−	0.191006i
$50$		0			0
$51$	−92.3607	−	30.0098i	−1.81099	−	0.588428i
$52$	23.7437	+	73.0755i	0.456609	+	1.40530i
$53$	−32.0787	−	44.1525i	−0.605258	−	0.833066i	0.390919	−	0.920425i	$-0.372157\pi$
$53$	−32.0787	−	44.1525i	−0.605258	−	0.833066i	−0.996177	+	0.0873594i	$0.972157\pi$
$54$		−	24.6215i		−	0.455953i
$55$		0			0
$56$	36.5066			0.651903
$57$	27.3156	−	19.8460i	0.479222	−	0.348175i
$58$	−107.098	+	34.7984i	−1.84652	+	0.599972i
$59$	−18.3115	+	56.3571i	−0.310365	+	0.955205i	0.667256	+	0.744829i	$0.267469\pi$
$59$	−18.3115	+	56.3571i	−0.310365	+	0.955205i	−0.977621	+	0.210376i	$0.932531\pi$
$60$		0			0
$61$	21.5836	−	29.7073i	0.353829	−	0.487004i	−0.594587	−	0.804031i	$-0.702685\pi$
$61$	21.5836	−	29.7073i	0.353829	−	0.487004i	0.948417	+	0.317027i	$0.102685\pi$
$62$	9.85359	−	30.3262i	0.158929	−	0.489133i
$63$	17.4293	+	53.6418i	0.276655	+	0.851458i
$64$	80.2943	−	58.3372i	1.25460	−	0.911519i
$65$		0			0
$66$	95.3738	−	96.1347i	1.44506	−	1.45659i
$67$			17.8197i			0.265965i	0.991118	+	0.132983i	$0.0424554\pi$
$67$			17.8197i			0.265965i	−0.991118	+	0.132983i	$0.957545\pi$
$68$	107.482	−	78.0902i	1.58062	−	1.14838i
$69$	−31.3738	−	96.5587i	−0.454693	−	1.39940i
$70$		0			0
$71$	−4.70820	−	3.42071i	−0.0663127	−	0.0481790i	0.554135	−	0.832427i	$-0.313049\pi$
$71$	−4.70820	−	3.42071i	−0.0663127	−	0.0481790i	−0.620448	+	0.784248i	$0.713049\pi$
$72$	−25.6583	−	18.6418i	−0.356365	−	0.258914i
$73$	15.8124	−	48.6656i	0.216609	−	0.666652i	−0.782427	−	0.622742i	$-0.786018\pi$
$73$	15.8124	−	48.6656i	0.216609	−	0.666652i	0.999035	−	0.0439101i	$-0.0139815\pi$
$74$	−59.3328	+	19.2784i	−0.801795	+	0.260519i
$75$		0			0
$76$			46.1903i			0.607767i
$77$	39.9241	−	79.1312i	0.518495	−	1.02768i
$78$		−	172.859i		−	2.21614i
$79$	−20.1722	−	27.7647i	−0.255344	−	0.351451i	0.662030	−	0.749478i	$-0.269695\pi$
$79$	−20.1722	−	27.7647i	−0.255344	−	0.351451i	−0.917374	+	0.398026i	$0.869695\pi$
$80$		0			0
$81$	−29.3566	+	90.3504i	−0.362427	+	1.11544i
$82$	101.029	−	139.054i	1.23206	−	1.69578i
$83$	117.997	+	85.7295i	1.42164	+	1.03289i	0.991497	+	0.130127i	$0.0415384\pi$
$83$	117.997	+	85.7295i	1.42164	+	1.03289i	0.430147	+	0.902759i	$0.358462\pi$
$84$	−167.735	−	54.5002i	−1.99684	−	0.648812i
$85$		0			0
$86$	−92.8115	+	67.4315i	−1.07920	+	0.784087i
$87$	146.357			1.68226
$88$	7.99197	+	49.1935i	0.0908178	+	0.559017i
$89$	127.949			1.43763			0.718816	−	0.695200i	$-0.244684\pi$
$89$	127.949			1.43763			0.718816	+	0.695200i	$0.244684\pi$
$90$		0			0
$91$	−34.9615	−	107.600i	−0.384192	−	1.18242i
$92$	132.096	+	42.9205i	1.43582	+	0.466527i
$93$	−24.3594	+	33.5279i	−0.261929	+	0.360515i
$94$	−154.683	+	212.903i	−1.64556	+	2.26492i
$95$		0			0
$96$	−161.957	+	52.6232i	−1.68706	+	0.548158i
$97$	53.0877	+	73.0689i	0.547295	+	0.753287i	0.989642	−	0.143557i	$-0.0458539\pi$
$97$	53.0877	+	73.0689i	0.547295	+	0.753287i	−0.442347	+	0.896844i	$0.645854\pi$
$98$	−49.0059			−0.500060
$99$	−68.4681	+	35.2296i	−0.691597	+	0.355854i
$100$		0			0
$101$	63.4164	+	87.2852i	0.627885	+	0.864210i	0.997897	−	0.0648171i	$-0.0206464\pi$
$101$	63.4164	+	87.2852i	0.627885	+	0.864210i	−0.370012	+	0.929027i	$0.620646\pi$
$102$	−284.257	+	92.3607i	−2.78683	+	0.905497i
$103$	18.2339	+	5.92454i	0.177028	+	0.0575198i	0.396190	−	0.918169i	$-0.370332\pi$
$103$	18.2339	+	5.92454i	0.177028	+	0.0575198i	−0.219162	+	0.975689i	$0.570332\pi$
$104$	51.4681	+	37.3937i	0.494885	+	0.359555i
$105$		0			0
$106$	−159.745	−	51.9043i	−1.50703	−	0.489664i
$107$	−29.7478	−	91.5542i	−0.278016	−	0.855646i	−0.988405	−	0.151837i	$-0.951481\pi$
$107$	−29.7478	−	91.5542i	−0.278016	−	0.855646i	0.710389	−	0.703809i	$-0.248519\pi$
$108$	−25.7315	−	35.4164i	−0.238255	−	0.327930i
$109$			21.0793i			0.193388i	0.995314	+	0.0966940i	$0.0308268\pi$
$109$			21.0793i			0.193388i	−0.995314	+	0.0966940i	$0.969173\pi$
$110$		0			0
$111$	81.0820			0.730469
$112$	−51.7858	+	37.6246i	−0.462374	+	0.335934i
$113$	68.1176	−	22.1327i	0.602810	−	0.195865i	0.00831694	−	0.999965i	$-0.497353\pi$
$113$	68.1176	−	22.1327i	0.602810	−	0.195865i	0.594493	+	0.804100i	$0.297353\pi$
$114$	32.1115	−	98.8289i	0.281679	−	0.866920i
$115$		0			0
$116$	−117.687	+	161.982i	−1.01454	+	1.39640i
$117$	−30.3731	+	93.4787i	−0.259599	+	0.798963i
$118$	56.3571	+	173.449i	0.477602	+	1.46991i
$119$	−158.262	+	114.984i	−1.32994	+	0.966255i
$120$		0			0
$121$	115.371	+	36.4754i	0.953482	+	0.301450i
$122$		−	113.013i		−	0.926337i
$123$	−180.726	+	131.305i	−1.46932	+	1.06752i
$124$	−17.5197	−	53.9202i	−0.141288	−	0.434840i
$125$		0			0
$126$	140.436	+	102.033i	1.11457	+	0.809784i
$127$	−21.8088	−	15.8450i	−0.171723	−	0.124764i	0.498604	−	0.866830i	$-0.333846\pi$
$127$	−21.8088	−	15.8450i	−0.171723	−	0.124764i	−0.670327	+	0.742066i	$0.733846\pi$
$128$	41.7685	−	128.550i	0.326316	−	1.00430i
$129$	141.803	−	46.0747i	1.09925	−	0.357168i
$130$		0			0
$131$			88.8193i			0.678010i	0.940785	+	0.339005i	$0.110090\pi$
$131$			88.8193i			0.678010i	−0.940785	+	0.339005i	$0.889910\pi$
$132$	36.7202	−	237.957i	0.278183	−	1.80271i
$133$		−	68.0132i		−	0.511377i
$134$	32.2361	+	44.3691i	0.240568	+	0.331113i
$135$		0			0
$136$	33.9919	−	104.616i	0.249940	−	0.769237i
$137$	−70.5747	+	97.1378i	−0.515144	+	0.709035i	−0.984776	−	0.173827i	$-0.944387\pi$
$137$	−70.5747	+	97.1378i	−0.515144	+	0.709035i	0.469632	+	0.882862i	$0.344387\pi$
$138$	−252.794	−	183.666i	−1.83184	−	1.33091i
$139$	−3.34501	−	1.08686i	−0.0240648	−	0.00781914i	0.296960	−	0.954890i	$-0.404027\pi$
$139$	−3.34501	−	1.08686i	−0.0240648	−	0.00781914i	−0.321025	+	0.947071i	$0.604027\pi$
$140$		0			0
$141$	276.705	−	201.038i	1.96245	−	1.42580i
$142$	−17.9111			−0.126134
$143$	137.340	−	70.6672i	0.960423	−	0.494176i
$144$	55.6099			0.386180
$145$		0			0
$146$	−48.6656	−	149.777i	−0.333326	−	1.02587i
$147$	60.5746	+	19.6819i	0.412072	+	0.133890i
$148$	−65.1989	+	89.7386i	−0.440533	+	0.606342i
$149$	−54.8460	+	75.4890i	−0.368094	+	0.506638i	−0.952381	−	0.304909i	$-0.901374\pi$
$149$	−54.8460	+	75.4890i	−0.368094	+	0.506638i	0.584288	+	0.811547i	$0.301374\pi$
$150$		0			0
$151$	93.2148	−	30.2873i	0.617316	−	0.200578i	0.0163680	−	0.999866i	$-0.494790\pi$
$151$	93.2148	−	30.2873i	0.617316	−	0.200578i	0.600948	+	0.799288i	$0.294790\pi$
$152$	22.4794	+	30.9402i	0.147891	+	0.203554i
$153$	169.949			1.11078
$154$	−43.7426	−	269.252i	−0.284043	−	1.74839i
$155$		0			0
$156$	−180.652	−	248.647i	−1.15803	−	1.59389i
$157$	163.826	−	53.2304i	1.04348	−	0.339047i	0.263374	−	0.964694i	$-0.415165\pi$
$157$	163.826	−	53.2304i	1.04348	−	0.339047i	0.780107	+	0.625646i	$0.215165\pi$
$158$	−100.453	−	32.6393i	−0.635782	−	0.206578i
$159$	176.610	+	128.315i	1.11075	+	0.807010i
$160$		0			0
$161$	−194.505	−	63.1985i	−1.20811	−	0.392537i
$162$	90.3504	+	278.070i	0.557718	+	1.71648i
$163$	148.814	+	204.825i	0.912968	+	1.25659i	0.966143	+	0.258008i	$0.0830661\pi$
$163$	148.814	+	204.825i	0.912968	+	1.25659i	−0.0531744	+	0.998585i	$0.516934\pi$
$164$		−	305.604i		−	1.86344i
$165$		0			0
$166$	448.885			2.70413
$167$	−60.9861	+	44.3090i	−0.365186	+	0.265323i	−0.755212	−	0.655481i	$-0.772466\pi$
$167$	−60.9861	+	44.3090i	−0.365186	+	0.265323i	0.390026	+	0.920804i	$0.372466\pi$
$168$	−138.879	+	45.1246i	−0.826662	+	0.268599i
$169$	8.70163	−	26.7809i	0.0514889	−	0.158467i
$170$		0			0
$171$	−34.7304	+	47.8024i	−0.203102	+	0.279546i
$172$	−63.0318	+	193.992i	−0.366464	+	1.12786i
$173$	−34.6293	−	106.578i	−0.200169	−	0.616058i	−0.999877	−	0.0156685i	$-0.995012\pi$
$173$	−34.6293	−	106.578i	−0.200169	−	0.616058i	0.799708	−	0.600389i	$-0.204988\pi$
$174$	364.413	−	264.762i	2.09433	−	1.52162i
$175$		0			0
$176$	−62.0370	−	61.5459i	−0.352483	−	0.349693i
$177$		−	237.029i		−	1.33915i
$178$	318.581	−	231.462i	1.78978	−	1.30035i
$179$	64.4321	+	198.302i	0.359956	+	1.10783i	0.953080	+	0.302719i	$0.0978943\pi$
$179$	64.4321	+	198.302i	0.359956	+	1.10783i	−0.593124	+	0.805111i	$0.702106\pi$
$180$		0			0
$181$	−64.7082	−	47.0133i	−0.357504	−	0.259742i	0.394506	−	0.918893i	$-0.370916\pi$
$181$	−64.7082	−	47.0133i	−0.357504	−	0.259742i	−0.752010	+	0.659151i	$0.770916\pi$
$182$	−281.702	−	204.668i	−1.54781	−	1.12455i
$183$	−45.3887	+	139.692i	−0.248025	+	0.763344i
$184$	109.371	−	35.5369i	0.594409	−	0.193135i
$185$		0			0
$186$			127.548i			0.685740i
$187$	−189.591	−	188.090i	−1.01385	−	1.00583i
$188$			467.904i			2.48885i
$189$	37.8885	+	52.1491i	0.200468	+	0.275921i
$190$		0			0
$191$	−26.9443	+	82.9259i	−0.141069	+	0.434167i	−0.996485	−	0.0837757i	$-0.973302\pi$
$191$	−26.9443	+	82.9259i	−0.141069	+	0.434167i	0.855415	+	0.517943i	$0.173302\pi$
$192$	−233.349	+	321.177i	−1.21536	+	1.67280i
$193$	−152.129	−	110.528i	−0.788231	−	0.572683i	0.119207	−	0.992869i	$-0.461965\pi$
$193$	−152.129	−	110.528i	−0.788231	−	0.572683i	−0.907438	+	0.420186i	$0.861965\pi$
$194$	264.366	+	85.8976i	1.36271	+	0.442771i
$195$		0			0
$196$	−70.4919	+	51.2153i	−0.359652	+	0.261303i
$197$	−10.5087			−0.0533437			−0.0266719	−	0.999644i	$-0.508491\pi$
$197$	−10.5087			−0.0533437			−0.0266719	+	0.999644i	$0.508491\pi$
$198$	−106.748	+	211.578i	−0.539129	+	1.06858i
$199$	−8.30806			−0.0417490			−0.0208745	−	0.999782i	$-0.506645\pi$
$199$	−8.30806			−0.0417490			−0.0208745	+	0.999782i	$0.506645\pi$
$200$		0			0
$201$	−22.0263	−	67.7900i	−0.109584	−	0.337264i
$202$	315.801	+	102.610i	1.56337	+	0.507970i
$203$	173.289	−	238.512i	0.853640	−	1.17493i
$204$	−312.361	+	429.928i	−1.53118	+	2.10749i
$205$		0			0
$206$	56.1180	−	18.2339i	0.272418	−	0.0885139i
$207$	104.434	+	143.741i	0.504512	+	0.694401i
$208$	−111.548			−0.536289
$209$	91.6494	−	14.8893i	0.438514	−	0.0712409i
$210$		0			0
$211$	−45.0294	−	61.9777i	−0.213410	−	0.293733i	0.688870	−	0.724885i	$-0.258107\pi$
$211$	−45.0294	−	61.9777i	−0.213410	−	0.293733i	−0.902279	+	0.431152i	$0.858107\pi$
$212$	−284.028	+	92.2862i	−1.33975	+	0.435312i
$213$	22.1393	+	7.19350i	0.103940	+	0.0337723i
$214$	−239.692	−	174.146i	−1.12006	−	0.813768i
$215$		0			0
$216$	−34.4721	−	11.2007i	−0.159593	−	0.0518550i
$217$	25.7970	+	79.3951i	0.118880	+	0.365876i
$218$	38.1328	+	52.4853i	0.174921	+	0.240758i
$219$			204.680i			0.934613i
$220$		0			0
$221$	−340.902			−1.54254
$222$	201.886	−	146.679i	0.909397	−	0.660715i
$223$	111.163	−	36.1190i	0.498488	−	0.161969i	−0.0489724	−	0.998800i	$-0.515595\pi$
$223$	111.163	−	36.1190i	0.498488	−	0.161969i	0.547460	+	0.836832i	$0.315595\pi$
$224$	−106.003	+	326.242i	−0.473226	+	1.45644i
$225$		0			0
$226$	129.567	−	178.334i	0.573307	−	0.789089i
$227$	−119.818	+	368.761i	−0.527831	+	1.62450i	0.230818	+	0.972997i	$0.425860\pi$
$227$	−119.818	+	368.761i	−0.527831	+	1.62450i	−0.758649	+	0.651500i	$0.774140\pi$
$228$	−57.0943	−	175.718i	−0.250414	−	0.770694i
$229$	112.172	−	81.4979i	0.489835	−	0.355886i	−0.315286	−	0.948997i	$-0.602100\pi$
$229$	112.172	−	81.4979i	0.489835	−	0.355886i	0.805121	+	0.593111i	$0.202100\pi$
$230$		0			0
$231$	−54.0689	+	350.382i	−0.234064	+	1.51680i
$232$			165.777i			0.714556i
$233$	−150.953	+	109.674i	−0.647867	+	0.470703i	−0.862544	−	0.505982i	$-0.831130\pi$
$233$	−150.953	+	109.674i	−0.647867	+	0.470703i	0.214677	+	0.976685i	$0.431130\pi$
$234$	93.4787	+	287.698i	0.399482	+	1.22948i
$235$		0			0
$236$	262.335	+	190.598i	1.11159	+	0.807618i
$237$	111.059	+	80.6888i	0.468602	+	0.340459i
$238$	−186.049	+	572.599i	−0.781717	+	2.40588i
$239$	165.902	−	53.9047i	0.694149	−	0.225543i	0.0593698	−	0.998236i	$-0.481091\pi$
$239$	165.902	−	53.9047i	0.694149	−	0.225543i	0.634780	+	0.772693i	$0.281091\pi$
$240$		0			0
$241$			229.308i			0.951484i	0.879585	+	0.475742i	$0.157820\pi$
$241$			229.308i			0.951484i	−0.879585	+	0.475742i	$0.842180\pi$
$242$	353.248	−	117.889i	1.45970	−	0.487143i
$243$		−	308.000i		−	1.26749i
$244$	−118.108	−	162.562i	−0.484051	−	0.666239i
$245$		0			0
$246$	−212.456	+	653.872i	−0.863642	+	2.65802i
$247$	69.6660	−	95.8870i	0.282048	−	0.388206i
$248$	−37.9767	−	27.5917i	−0.153132	−	0.111257i
$249$	−554.853	−	180.283i	−2.22832	−	0.724027i
$250$		0			0
$251$	85.7279	−	62.2850i	0.341546	−	0.248147i	−0.403768	−	0.914861i	$-0.632300\pi$
$251$	85.7279	−	62.2850i	0.341546	−	0.248147i	0.745314	+	0.666714i	$0.232300\pi$
$252$	308.641			1.22477
$253$	42.5808	−	275.936i	0.168303	−	1.09065i
$254$	−82.9656			−0.326636
$255$		0			0
$256$	−5.87132	−	18.0701i	−0.0229349	−	0.0705862i
$257$	−245.095	−	79.6362i	−0.953677	−	0.309869i	−0.209468	−	0.977815i	$-0.567173\pi$
$257$	−245.095	−	79.6362i	−0.953677	−	0.309869i	−0.744209	+	0.667947i	$0.767173\pi$
$258$	269.726	−	371.246i	1.04545	−	1.43894i
$259$	96.0025	−	132.136i	0.370666	−	0.510178i
$260$		0			0
$261$	−243.589	+	79.1467i	−0.933290	+	0.303244i
$262$	160.676	+	221.151i	0.613265	+	0.844087i
$263$	−290.347			−1.10398			−0.551990	−	0.833851i	$-0.686131\pi$
$263$	−290.347			−1.10398			−0.551990	+	0.833851i	$0.686131\pi$
$264$	−91.2098	−	177.265i	−0.345492	−	0.671457i
$265$		0			0
$266$	−123.037	−	169.346i	−0.462545	−	0.636638i
$267$	−486.748	+	158.154i	−1.82303	+	0.592337i
$268$	92.7390	+	30.1327i	0.346041	+	0.112436i
$269$	−267.615	−	194.434i	−0.994851	−	0.722802i	−0.0338730	−	0.999426i	$-0.510784\pi$
$269$	−267.615	−	194.434i	−0.994851	−	0.722802i	−0.960978	+	0.276625i	$0.910784\pi$
$270$		0			0
$271$	206.661	+	67.1481i	0.762585	+	0.247779i	0.664388	−	0.747388i	$-0.268692\pi$
$271$	206.661	+	67.1481i	0.762585	+	0.247779i	0.0981974	+	0.995167i	$0.468692\pi$
$272$	59.6015	+	183.435i	0.219123	+	0.674392i
$273$	266.003	+	366.122i	0.974369	+	1.34110i
$274$			369.534i			1.34866i
$275$		0			0
$276$	−555.574			−2.01295
$277$	362.950	−	263.699i	1.31029	−	0.951980i	0.310289	−	0.950642i	$-0.399574\pi$
$277$	362.950	−	263.699i	1.31029	−	0.951980i	0.999999	−	0.00133803i	$-0.000425907\pi$
$278$	−10.2949	+	3.34501i	−0.0370320	+	0.0120324i
$279$	22.4114	−	68.9751i	0.0803275	−	0.247223i
$280$		0			0
$281$	55.0658	−	75.7915i	0.195964	−	0.269721i	−0.699716	−	0.714421i	$-0.746690\pi$
$281$	55.0658	−	75.7915i	0.195964	−	0.269721i	0.895679	+	0.444701i	$0.146690\pi$
$282$	325.286	−	1001.13i	1.15350	−	3.55010i
$283$	90.3283	+	278.002i	0.319181	+	0.982339i	0.973999	+	0.226552i	$0.0727454\pi$
$283$	90.3283	+	278.002i	0.319181	+	0.982339i	−0.654818	+	0.755787i	$0.727255\pi$
$284$	−25.7639	+	18.7186i	−0.0907181	+	0.0659105i
$285$		0			0
$286$	214.126	−	424.405i	0.748691	−	1.48393i
$287$			449.989i			1.56791i
$288$	241.096	−	175.167i	0.837139	−	0.608217i
$289$	92.8419	+	285.738i	0.321252	+	0.988713i
$290$		0			0
$291$	−292.276	−	212.351i	−1.00438	−	0.729727i
$292$	−226.533	−	164.586i	−0.775796	−	0.563649i
$293$	106.944	−	329.140i	0.364997	−	1.12335i	−0.584986	−	0.811044i	$-0.698900\pi$
$293$	106.944	−	329.140i	0.364997	−	1.12335i	0.949983	−	0.312302i	$-0.101100\pi$
$294$	186.430	−	60.5746i	0.634114	−	0.206036i
$295$		0			0
$296$			91.8410i			0.310274i
$297$	−61.9777	+	62.4721i	−0.208679	+	0.210344i
$298$			287.177i			0.963682i
$299$	−209.485	−	288.331i	−0.700618	−	0.964318i
$300$		0			0
$301$	92.8115	−	285.645i	0.308344	−	0.948985i
$302$	177.305	−	244.039i	0.587103	−	0.808078i
$303$	−349.141	−	253.666i	−1.15228	−	0.837180i
$304$	−63.7755	−	20.7219i	−0.209788	−	0.0681642i
$305$		0			0
$306$	423.156	−	307.441i	1.38286	−	1.00471i
$307$	−180.826			−0.589009			−0.294505	−	0.955650i	$-0.595155\pi$
$307$	−180.826			−0.589009			−0.294505	+	0.955650i	$0.595155\pi$
$308$	−344.312	−	341.587i	−1.11790	−	1.10905i
$309$	−76.6888			−0.248184
$310$		0			0
$311$	−115.313	−	354.897i	−0.370782	−	1.14115i	−0.946281	−	0.323346i	$-0.895192\pi$
$311$	−115.313	−	354.897i	−0.370782	−	1.14115i	0.575499	−	0.817802i	$-0.304808\pi$
$312$	−242.017	−	78.6362i	−0.775697	−	0.252039i
$313$	−186.542	+	256.753i	−0.595980	+	0.820296i	−0.995333	−	0.0965012i	$-0.969235\pi$
$313$	−186.542	+	256.753i	−0.595980	+	0.820296i	0.399353	+	0.916797i	$0.369235\pi$
$314$	311.616	−	428.903i	0.992409	−	1.36593i
$315$		0			0
$316$	−178.607	+	58.0329i	−0.565211	+	0.183648i
$317$	−161.521	−	222.314i	−0.509529	−	0.701306i	0.474311	−	0.880357i	$-0.342697\pi$
$317$	−161.521	−	222.314i	−0.509529	−	0.701306i	−0.983840	+	0.179051i	$0.942697\pi$
$318$	671.864			2.11278
$319$	359.336	+	181.296i	1.12645	+	0.568327i
$320$		0			0
$321$	226.334	+	311.523i	0.705091	+	0.970475i
$322$	−598.625	+	194.505i	−1.85908	+	0.604053i
$323$	−194.904	−	63.3282i	−0.603418	−	0.196062i
$324$	420.570	+	305.562i	1.29806	+	0.943092i
$325$		0			0
$326$	741.063	+	240.786i	2.27320	+	0.738607i
$327$	−26.0554	−	80.1904i	−0.0796802	−	0.245231i
$328$	−148.728	−	204.707i	−0.453439	−	0.624106i
$329$		−	688.968i		−	2.09413i
$330$		0			0
$331$	411.681			1.24375			0.621874	−	0.783117i	$-0.286372\pi$
$331$	411.681			1.24375			0.621874	+	0.783117i	$0.286372\pi$
$332$	645.693	−	469.123i	1.94486	−	1.41302i
$333$	−134.949	+	43.8475i	−0.405252	+	0.131674i
$334$	−71.6935	+	220.650i	−0.214651	+	0.660628i
$335$		0			0
$336$	150.498	−	207.143i	0.447912	−	0.616498i
$337$	143.098	−	440.410i	0.424623	−	1.30686i	−0.478732	−	0.877961i	$-0.658903\pi$
$337$	143.098	−	440.410i	0.424623	−	1.30686i	0.903355	−	0.428894i	$-0.141097\pi$
$338$	−26.7809	−	82.4230i	−0.0792333	−	0.243855i
$339$	−231.777	+	168.396i	−0.683708	+	0.496743i
$340$		0			0
$341$	−101.339	+	52.1432i	−0.297183	+	0.152913i
$342$			181.851i			0.531728i
$343$	−215.617	+	156.655i	−0.628621	+	0.456720i
$344$	52.1885	+	160.620i	0.151711	+	0.466917i
$345$		0			0
$346$	−279.025	−	202.723i	−0.806430	−	0.585906i
$347$	−138.324	−	100.498i	−0.398629	−	0.289621i	0.370353	−	0.928891i	$-0.379237\pi$
$347$	−138.324	−	100.498i	−0.398629	−	0.289621i	−0.768982	+	0.639270i	$0.779237\pi$
$348$	247.487	−	761.686i	0.711169	−	2.18875i
$349$	164.289	−	53.3806i	0.470741	−	0.152953i	−0.0640335	−	0.997948i	$-0.520396\pi$
$349$	164.289	−	53.3806i	0.470741	−	0.152953i	0.534775	+	0.844995i	$0.320396\pi$
$350$		0			0
$351$			112.331i			0.320030i
$352$	−462.825	−	71.4205i	−1.31484	−	0.202899i
$353$			494.535i			1.40095i	0.713678	+	0.700474i	$0.247028\pi$
$353$			494.535i			1.40095i	−0.713678	+	0.700474i	$0.752972\pi$
$354$	−428.790	−	590.179i	−1.21127	−	1.66717i
$355$		0			0
$356$	216.360	−	665.888i	0.607753	−	1.87047i
$357$	459.937	−	633.050i	1.28834	−	1.77325i
$358$	519.160	+	377.192i	1.45017	+	1.05361i
$359$	−146.418	−	47.5742i	−0.407850	−	0.132519i	0.0979045	−	0.995196i	$-0.468786\pi$
$359$	−146.418	−	47.5742i	−0.407850	−	0.132519i	−0.505755	+	0.862677i	$0.668786\pi$
$360$		0			0
$361$	−234.412	+	170.311i	−0.649342	+	0.471774i
$362$	−246.165			−0.680013
$363$	−483.985	+	3.84597i	−1.33329	+	0.0105950i
$364$	−619.105			−1.70084
$365$		0			0
$366$	139.692	+	429.928i	0.381672	+	1.17467i
$367$	−176.604	−	57.3820i	−0.481209	−	0.156354i	0.0583604	−	0.998296i	$-0.481413\pi$
$367$	−176.604	−	57.3820i	−0.481209	−	0.156354i	−0.539569	+	0.841941i	$0.681413\pi$
$368$	−118.522	+	163.131i	−0.322070	+	0.443291i
$369$	229.784	−	316.270i	0.622720	−	0.857100i
$370$		0			0
$371$	418.218	−	135.887i	1.12727	−	0.366273i
$372$	133.298	+	183.469i	0.358328	+	0.493196i
$373$	268.844			0.720760			0.360380	−	0.932806i	$-0.382647\pi$
$373$	268.844			0.720760			0.360380	+	0.932806i	$0.382647\pi$
$374$	−812.320	−	125.352i	−2.17198	−	0.335167i
$375$		0			0
$376$	227.714	+	313.422i	0.605623	+	0.833568i
$377$	488.616	−	158.761i	1.29606	−	0.421116i
$378$	188.677	+	61.3050i	0.499146	+	0.162182i
$379$	−243.935	−	177.229i	−0.643627	−	0.467622i	0.217467	−	0.976068i	$-0.430220\pi$
$379$	−243.935	−	177.229i	−0.643627	−	0.467622i	−0.861094	+	0.508445i	$0.830220\pi$
$380$		0			0
$381$	102.551	+	33.3209i	0.269163	+	0.0874563i
$382$	82.9259	+	255.220i	0.217084	+	0.668115i
$383$	−286.179	−	393.892i	−0.747204	−	1.02844i	−0.998172	−	0.0604431i	$-0.980749\pi$
$383$	−286.179	−	393.892i	−0.747204	−	1.02844i	0.250967	−	0.967996i	$-0.419251\pi$
$384$			540.662i			1.40797i
$385$		0			0
$386$	−578.731			−1.49930
$387$	−211.094	+	153.369i	−0.545463	+	0.396302i
$388$	470.043	−	152.726i	1.21145	−	0.393625i
$389$	−118.077	+	363.404i	−0.303540	+	0.934200i	0.676678	+	0.736279i	$0.263419\pi$
$389$	−118.077	+	363.404i	−0.303540	+	0.934200i	−0.980218	+	0.197921i	$0.936581\pi$
$390$		0			0
$391$	−362.214	+	498.544i	−0.926377	+	1.27505i
$392$	−22.2935	+	68.6124i	−0.0568712	+	0.175032i
$393$	−109.787	−	337.889i	−0.279355	−	0.859767i
$394$	−26.1656	+	19.0104i	−0.0664102	+	0.0482499i
$395$		0			0
$396$	67.5673	+	415.902i	0.170625	+	1.05026i
$397$			668.123i			1.68293i	0.540311	+	0.841465i	$0.318307\pi$
$397$			668.123i			1.68293i	−0.540311	+	0.841465i	$0.681693\pi$
$398$	−20.6862	+	15.0294i	−0.0519754	+	0.0377624i
$399$	84.0689	+	258.737i	0.210699	+	0.648465i
$400$		0			0
$401$	−291.301	−	211.642i	−0.726436	−	0.527787i	0.161998	−	0.986791i	$-0.448206\pi$
$401$	−291.301	−	211.642i	−0.726436	−	0.527787i	−0.888434	+	0.459004i	$0.848206\pi$
$402$	−177.477	−	128.944i	−0.441484	−	0.320757i
$403$	−44.9551	+	138.358i	−0.111551	+	0.343319i
$404$	561.495	−	182.441i	1.38984	−	0.451586i
$405$		0			0
$406$		−	907.352i		−	2.23486i
$407$	199.073	+	100.439i	0.489124	+	0.246778i
$408$			440.000i			1.07843i
$409$	21.2846	+	29.2958i	0.0520406	+	0.0716278i	0.834244	−	0.551395i	$-0.185904\pi$
$409$	21.2846	+	29.2958i	0.0520406	+	0.0716278i	−0.782204	+	0.623023i	$0.785904\pi$
$410$		0			0
$411$	148.413	−	456.769i	0.361103	−	1.11136i
$412$	61.6663	−	84.8763i	0.149675	−	0.206011i
$413$	−386.277	−	280.647i	−0.935296	−	0.679532i
$414$	520.060	+	168.978i	1.25618	+	0.408159i
$415$		0			0
$416$	−483.616	+	351.368i	−1.16254	+	0.844633i
$417$	14.0686			0.0337377
$418$	201.263	−	202.868i	0.481489	−	0.485331i
$419$	423.543			1.01084			0.505421	−	0.862873i	$-0.331337\pi$
$419$	423.543			1.01084			0.505421	+	0.862873i	$0.331337\pi$
$420$		0			0
$421$	211.289	+	650.280i	0.501873	+	1.54461i	0.805964	+	0.591964i	$0.201647\pi$
$421$	211.289	+	650.280i	0.501873	+	1.54461i	−0.304091	+	0.952643i	$0.598353\pi$
$422$	−224.237	−	72.8591i	−0.531368	−	0.172652i
$423$	−351.817	+	484.234i	−0.831718	+	1.14476i
$424$	−145.341	+	200.045i	−0.342785	+	0.471803i
$425$		0			0
$426$	68.1378	−	22.1393i	0.159948	−	0.0519702i
$427$	173.909	+	239.366i	0.407282	+	0.560575i
$428$	−526.779			−1.23079
$429$	−435.125	+	438.596i	−1.01428	+	1.02237i
$430$		0			0
$431$	75.8653	+	104.420i	0.176022	+	0.242273i	0.887907	−	0.460022i	$-0.152159\pi$
$431$	75.8653	+	104.420i	0.176022	+	0.242273i	−0.711886	+	0.702295i	$0.752159\pi$
$432$	60.4436	−	19.6393i	0.139916	−	0.0454614i
$433$	524.382	+	170.382i	1.21104	+	0.393492i	0.843813	−	0.536638i	$-0.180306\pi$
$433$	524.382	+	170.382i	1.21104	+	0.393492i	0.367231	+	0.930130i	$0.380306\pi$
$434$	207.859	+	151.018i	0.478938	+	0.347969i
$435$		0			0
$436$	109.703	+	35.6447i	0.251613	+	0.0817540i
$437$	−66.2066	−	203.763i	−0.151503	−	0.466277i
$438$	370.270	+	509.633i	0.845366	+	1.16355i
$439$			470.583i			1.07194i	0.844236	+	0.535972i	$0.180055\pi$
$439$			470.583i			1.07194i	−0.844236	+	0.535972i	$0.819945\pi$
$440$		0			0
$441$	−111.461			−0.252746
$442$	−848.811	+	616.697i	−1.92039	+	1.39524i
$443$	94.4041	−	30.6738i	0.213102	−	0.0692410i	−0.200521	−	0.979689i	$-0.564263\pi$
$443$	94.4041	−	30.6738i	0.213102	−	0.0692410i	0.413622	+	0.910448i	$0.364263\pi$
$444$	137.108	−	421.976i	0.308803	−	0.950397i
$445$		0			0
$446$	211.444	−	291.028i	0.474090	−	0.652529i
$447$	115.337	−	354.971i	0.258024	−	0.794118i
$448$	247.120	+	760.559i	0.551608	+	1.69768i
$449$	110.271	−	80.1169i	0.245593	−	0.178434i	−0.458178	−	0.888860i	$-0.651498\pi$
$449$	110.271	−	80.1169i	0.245593	−	0.178434i	0.703772	+	0.710426i	$0.251498\pi$
$450$		0			0
$451$	−606.371	+	98.5109i	−1.34450	+	0.218428i
$452$		−	391.931i		−	0.867104i
$453$	−317.173	+	230.440i	−0.700161	+	0.508697i
$454$	368.761	+	1134.93i	0.812249	+	2.49984i
$455$		0			0
$456$	−123.761	−	89.9175i	−0.271405	−	0.197188i
$457$	−24.9144	−	18.1014i	−0.0545174	−	0.0396092i	0.560193	−	0.828362i	$-0.310727\pi$
$457$	−24.9144	−	18.1014i	−0.0545174	−	0.0396092i	−0.614710	+	0.788753i	$0.710727\pi$
$458$	131.866	−	405.843i	0.287918	−	0.886120i
$459$	184.721	−	60.0196i	0.402443	−	0.130762i
$460$		0			0
$461$		−	142.653i		−	0.309442i	−0.987958	−	0.154721i	$-0.950552\pi$
$461$		−	142.653i		−	0.309442i	0.987958	−	0.154721i	$-0.0494478\pi$
$462$	499.221	+	970.227i	1.08056	+	2.10006i
$463$		−	490.864i		−	1.06018i	−0.847941	−	0.530091i	$-0.822158\pi$
$463$		−	490.864i		−	1.06018i	0.847941	−	0.530091i	$-0.177842\pi$
$464$	−170.854	−	235.160i	−0.368220	−	0.506811i
$465$		0			0
$466$	−177.456	+	546.153i	−0.380807	+	1.17200i
$467$	−445.503	+	613.182i	−0.953968	+	1.31302i	−0.00422562	+	0.999991i	$0.501345\pi$
$467$	−445.503	+	613.182i	−0.953968	+	1.31302i	−0.949742	+	0.313033i	$0.898655\pi$
$468$	435.132	+	316.142i	0.929769	+	0.675517i
$469$	−136.554	−	44.3691i	−0.291160	−	0.0946037i
$470$		0			0
$471$	−557.437	+	405.001i	−1.18352	+	0.859875i
$472$	268.481			0.568816
$473$	405.231	+	62.5329i	0.856725	+	0.132205i
$474$	422.492			0.891334
$475$		0			0
$476$	330.795	+	1018.08i	0.694948	+	2.13883i
$477$	−363.330	−	118.053i	−0.761699	−	0.247491i
$478$	315.564	−	434.336i	0.660175	−	0.908653i
$479$	364.989	−	502.364i	0.761981	−	1.04878i	−0.235066	−	0.971979i	$-0.575531\pi$
$479$	364.989	−	502.364i	0.761981	−	1.04878i	0.997047	−	0.0767971i	$-0.0244694\pi$
$480$		0			0
$481$	270.694	−	87.9540i	0.562774	−	0.182856i
$482$	414.821	+	570.953i	0.860625	+	1.18455i
$483$	818.059			1.69370
$484$	384.920	−	538.749i	0.795290	−	1.11312i
$485$		0			0
$486$	−557.177	−	766.889i	−1.14646	−	1.57796i
$487$	374.442	−	121.664i	0.768876	−	0.249823i	0.101792	−	0.994806i	$-0.467542\pi$
$487$	374.442	−	121.664i	0.768876	−	0.249823i	0.667084	+	0.744983i	$0.267542\pi$
$488$	−158.228	−	51.4114i	−0.324238	−	0.105351i
$489$	−819.299	−	595.255i	−1.67546	−	1.21729i
$490$		0			0
$491$	−616.943	−	200.457i	−1.25650	−	0.408262i	−0.396256	−	0.918140i	$-0.629691\pi$
$491$	−616.943	−	200.457i	−1.25650	−	0.408262i	−0.860247	+	0.509878i	$0.829691\pi$
$492$	377.748	+	1162.59i	0.767780	+	2.36298i
$493$	−522.146	−	718.673i	−1.05912	−	1.45775i
$494$		−	364.776i		−	0.738413i
$495$		0			0
$496$	82.3081			0.165944
$497$	37.9363	−	27.5623i	0.0763305	−	0.0554574i
$498$	−1707.66	+	554.853i	−3.42904	+	1.11416i
$499$	221.573	−	681.931i	0.444034	−	1.36660i	−0.439506	−	0.898240i	$-0.644846\pi$
$499$	221.573	−	681.931i	0.444034	−	1.36660i	0.883540	−	0.468356i	$-0.155154\pi$
$500$		0			0
$501$	177.236	−	243.945i	0.353765	−	0.486915i
$502$	100.779	−	310.167i	0.200755	−	0.617862i
$503$	−193.858	−	596.635i	−0.385404	−	1.18615i	−0.936187	−	0.351503i	$-0.885671\pi$
$503$	−193.858	−	596.635i	−0.385404	−	1.18615i	0.550782	−	0.834649i	$-0.314329\pi$
$504$	206.741	−	150.206i	0.410201	−	0.298028i
$505$		0			0
$506$	−393.150	−	764.081i	−0.776977	−	1.51004i
$507$			112.636i			0.222162i
$508$	−119.341	+	86.7061i	−0.234923	+	0.170681i
$509$	79.8228	+	245.669i	0.156823	+	0.482651i	0.998341	−	0.0575779i	$-0.0183378\pi$
$509$	79.8228	+	245.669i	0.156823	+	0.482651i	−0.841518	+	0.540229i	$0.818338\pi$
$510$		0			0
$511$	333.559	+	242.345i	0.652758	+	0.474256i
$512$	390.097	+	283.422i	0.761908	+	0.553559i
$513$	−20.8673	+	64.2229i	−0.0406770	+	0.125191i
$514$	−754.325	+	245.095i	−1.46756	+	0.476839i
$515$		0			0
$516$		−	815.900i		−	1.58120i
$517$	928.400	−	150.828i	1.79575	−	0.291737i
$518$		−	502.676i		−	0.970416i
$519$	263.475	+	362.643i	0.507659	+	0.698733i
$520$		0			0
$521$	92.8597	−	285.793i	0.178234	−	0.548547i	−0.821533	−	0.570161i	$-0.806881\pi$
$521$	92.8597	−	285.793i	0.178234	−	0.548547i	0.999766	+	0.0216146i	$0.00688069\pi$
$522$	−463.333	+	637.723i	−0.887611	+	1.22169i
$523$	−340.650	−	247.497i	−0.651338	−	0.473225i	0.212389	−	0.977185i	$-0.431876\pi$
$523$	−340.650	−	247.497i	−0.651338	−	0.473225i	−0.863727	+	0.503961i	$0.831876\pi$
$524$	462.243	+	150.192i	0.882143	+	0.286626i
$525$		0			0
$526$	−722.934	+	525.242i	−1.37440	+	0.998559i
$527$	251.541			0.477308
$528$	312.078	+	157.453i	0.591056	+	0.298206i
$529$	−115.244			−0.217853
$530$		0			0
$531$	128.181	+	394.500i	0.241395	+	0.742937i
$532$	−353.962	−	115.009i	−0.665341	−	0.216183i
$533$	−460.924	+	634.408i	−0.864773	+	1.19026i
$534$	−925.850	+	1274.32i	−1.73380	+	2.38637i
$535$		0			0
$536$	76.7852	−	24.9490i	0.143256	−	0.0465467i
$537$	−490.228	−	674.741i	−0.912902	−	1.25650i
$538$	−1018.07			−1.89232
$539$	124.343	+	123.359i	0.230692	+	0.228866i
$540$		0			0
$541$	112.764	+	155.206i	0.208436	+	0.286888i	0.900417	−	0.435028i	$-0.143262\pi$
$541$	112.764	+	155.206i	0.208436	+	0.286888i	−0.691981	+	0.721916i	$0.743262\pi$
$542$	636.036	−	206.661i	1.17350	−	0.381293i
$543$	304.276	+	98.8653i	0.560361	+	0.182072i
$544$	836.205	+	607.539i	1.53714	+	1.11680i
$545$		0			0
$546$	1324.64	+	430.402i	2.42608	+	0.788281i
$547$	61.5846	+	189.538i	0.112586	+	0.346504i	0.991436	−	0.130594i	$-0.0416885\pi$
$547$	61.5846	+	189.538i	0.112586	+	0.346504i	−0.878850	+	0.477099i	$0.841688\pi$
$548$	386.194	+	531.551i	0.704734	+	0.969984i
$549$		−	257.041i		−	0.468199i
$550$		0			0
$551$	308.849			0.560525
$552$	−372.147	+	270.381i	−0.674180	+	0.489820i
$553$	262.991	−	85.4508i	0.475571	−	0.154522i
$554$	426.673	−	1313.16i	0.770168	−	2.37033i
$555$		0			0
$556$	−11.3127	+	15.5706i	−0.0203466	+	0.0280047i
$557$	−234.077	+	720.414i	−0.420245	+	1.29338i	0.487229	+	0.873274i	$0.338008\pi$
$557$	−234.077	+	720.414i	−0.420245	+	1.29338i	−0.907474	+	0.420108i	$0.861992\pi$
$558$	−68.9751	−	212.284i	−0.123611	−	0.380437i
$559$	423.435	−	307.643i	0.757486	−	0.550346i
$560$		0			0
$561$	953.738	+	481.190i	1.70007	+	0.857737i
$562$		−	288.328i		−	0.513039i
$563$	122.618	−	89.0871i	0.217794	−	0.158236i	−0.473539	−	0.880773i	$-0.657024\pi$
$563$	122.618	−	89.0871i	0.217794	−	0.158236i	0.691333	+	0.722536i	$0.257024\pi$
$564$	−578.361	−	1780.01i	−1.02546	−	3.15605i
$565$		0			0
$566$	727.818	+	528.791i	1.28590	+	0.934260i
$567$	−619.271	−	449.926i	−1.09219	−	0.793521i
$568$	−8.14802	+	25.0770i	−0.0143451	+	0.0441497i
$569$	−836.163	+	271.686i	−1.46953	+	0.477480i	−0.930967	−	0.365104i	$-0.881033\pi$
$569$	−836.163	+	271.686i	−1.46953	+	0.477480i	−0.538565	+	0.842584i	$0.681033\pi$
$570$		0			0
$571$		−	324.644i		−	0.568554i	−0.958742	−	0.284277i	$-0.908246\pi$
$571$		−	324.644i		−	0.568554i	0.958742	−	0.284277i	$-0.0917536\pi$
$572$	−135.534	−	834.259i	−0.236947	−	1.45850i
$573$		−	348.774i		−	0.608681i
$574$	814.037	+	1120.43i	1.41818	+	1.95196i
$575$		0			0
$576$	214.688	−	660.741i	0.372722	−	1.14712i
$577$	−306.003	+	421.177i	−0.530335	+	0.729943i	−0.987181	−	0.159602i	$-0.948979\pi$
$577$	−306.003	+	421.177i	−0.530335	+	0.729943i	0.456847	+	0.889545i	$0.348979\pi$
$578$	748.072	+	543.506i	1.29424	+	0.940322i
$579$	715.351	+	232.432i	1.23549	+	0.401437i
$580$		0			0
$581$	−950.755	+	690.764i	−1.63641	+	1.18892i
$582$	−1111.88			−1.91045
$583$	274.667	+	533.811i	0.471127	+	0.915628i
$584$	−231.840			−0.396986
$585$		0			0
$586$	−329.140	−	1012.99i	−0.561673	−	1.72865i
$587$	−941.646	−	305.959i	−1.60417	−	0.521225i	−0.636034	−	0.771661i	$-0.719426\pi$
$587$	−941.646	−	305.959i	−1.60417	−	0.521225i	−0.968133	+	0.250436i	$0.919426\pi$
$588$	204.861	−	281.967i	0.348404	−	0.479537i
$589$	−51.4044	+	70.7521i	−0.0872741	+	0.120122i
$590$		0			0
$591$	39.9775	−	12.9895i	0.0676439	−	0.0219788i
$592$	−94.6537	−	130.280i	−0.159888	−	0.220067i
$593$	289.152			0.487609			0.243804	−	0.969824i	$-0.421604\pi$
$593$	289.152			0.487609			0.243804	+	0.969824i	$0.421604\pi$
$594$	−41.3050	+	267.668i	−0.0695370	+	0.450619i
$595$		0			0
$596$	300.125	+	413.086i	0.503565	+	0.693097i
$597$	31.6057	−	10.2693i	0.0529409	−	0.0172015i
$598$	−1043.19	−	338.953i	−1.74447	−	0.566812i
$599$	674.089	+	489.754i	1.12536	+	0.817620i	0.985013	−	0.172483i	$-0.0551789\pi$
$599$	674.089	+	489.754i	1.12536	+	0.817620i	0.140345	+	0.990103i	$0.455179\pi$
$600$		0			0
$601$	−89.9741	−	29.2343i	−0.149707	−	0.0486428i	0.233205	−	0.972428i	$-0.425079\pi$
$601$	−89.9741	−	29.2343i	−0.149707	−	0.0486428i	−0.382912	+	0.923785i	$0.625079\pi$
$602$	−285.645	−	879.123i	−0.474493	−	1.46034i
$603$	73.3189	+	100.915i	0.121590	+	0.167355i
$604$		−	536.334i		−	0.887970i
$605$		0			0
$606$	−1328.21			−2.19177
$607$	171.826	−	124.839i	0.283074	−	0.205666i	−0.437183	−	0.899373i	$-0.644024\pi$
$607$	171.826	−	124.839i	0.283074	−	0.205666i	0.720257	+	0.693707i	$0.244024\pi$
$608$	−341.770	+	111.048i	−0.562123	+	0.182645i
$609$	−364.413	+	1121.55i	−0.598380	+	1.84162i
$610$		0			0
$611$	705.710	−	971.327i	1.15501	−	1.58973i
$612$	287.381	−	884.468i	0.469577	−	1.44521i
$613$	243.852	+	750.498i	0.397801	+	1.22430i	0.926759	+	0.375656i	$0.122583\pi$
$613$	243.852	+	750.498i	0.397801	+	1.22430i	−0.528958	+	0.848648i	$0.677417\pi$
$614$	−450.238	+	327.117i	−0.733287	+	0.532764i
$615$		0			0
$616$	−396.875	−	61.2434i	−0.644277	−	0.0994211i
$617$			181.544i			0.294237i	0.989119	+	0.147118i	$0.0469998\pi$
$617$			181.544i			0.294237i	−0.989119	+	0.147118i	$0.953000\pi$
$618$	−190.947	+	138.731i	−0.308976	+	0.224484i
$619$	11.1606	+	34.3488i	0.0180301	+	0.0554908i	0.959667	−	0.281140i	$-0.0907125\pi$
$619$	11.1606	+	34.3488i	0.0180301	+	0.0554908i	−0.941637	+	0.336631i	$0.890713\pi$
$620$		0			0
$621$	164.276	+	119.353i	0.264534	+	0.192195i
$622$	−929.133	−	675.055i	−1.49378	−	1.08530i
$623$	−318.581	+	980.491i	−0.511366	+	1.57382i
$624$	424.354	−	137.881i	0.680055	−	0.220963i
$625$		0			0
$626$			976.745i			1.56030i
$627$	−330.251	+	169.927i	−0.526716	+	0.271016i
$628$		−	942.616i		−	1.50098i
$629$	−289.271	−	398.147i	−0.459890	−	0.632984i
$630$		0			0
$631$	311.846	−	959.763i	0.494209	−	1.52102i	−0.323976	−	0.946065i	$-0.605020\pi$
$631$	311.846	−	959.763i	0.494209	−	1.52102i	0.818186	−	0.574954i	$-0.194980\pi$
$632$	−91.3956	+	125.795i	−0.144613	+	0.199043i
$633$	247.911	+	180.118i	0.391644	+	0.284546i
$634$	−804.340	−	261.346i	−1.26867	−	0.412217i
$635$		0			0
$636$	966.433	−	702.155i	1.51955	−	1.10402i
$637$	223.580			0.350989
$638$	1222.68	−	198.636i	1.91642	−	0.311342i
$639$	−40.7376			−0.0637521
$640$		0			0
$641$	−33.2415	−	102.307i	−0.0518588	−	0.159605i	0.921773	−	0.387730i	$-0.126741\pi$
$641$	−33.2415	−	102.307i	−0.0518588	−	0.159605i	−0.973632	+	0.228125i	$0.926741\pi$
$642$	1127.10	+	366.217i	1.75561	+	0.570431i
$643$	15.8911	−	21.8723i	0.0247141	−	0.0340160i	−0.796481	−	0.604663i	$-0.793308\pi$
$643$	15.8911	−	21.8723i	0.0247141	−	0.0340160i	0.821195	+	0.570647i	$0.193308\pi$
$644$	−657.809	+	905.397i	−1.02144	+	1.40590i
$645$		0			0
$646$	−599.853	+	194.904i	−0.928565	+	0.301709i
$647$	656.158	+	903.123i	1.01415	+	1.39586i	0.916222	+	0.400670i	$0.131223\pi$
$647$	656.158	+	903.123i	1.01415	+	1.39586i	0.0979314	+	0.995193i	$0.468777\pi$
$648$	430.423			0.664233
$649$	293.615	−	581.957i	0.452412	−	0.896698i
$650$		0			0
$651$	−196.276	−	270.150i	−0.301499	−	0.414977i
$652$	1317.61	−	428.118i	2.02088	−	0.656623i
$653$	1040.26	+	338.002i	1.59305	+	0.517615i	0.965377	−	0.260859i	$-0.0840059\pi$
$653$	1040.26	+	338.002i	1.59305	+	0.517615i	0.627677	+	0.778474i	$0.284006\pi$
$654$	−209.941	−	152.531i	−0.321011	−	0.233228i
$655$		0			0
$656$	421.952	+	137.100i	0.643219	+	0.208995i
$657$	−110.687	−	340.659i	−0.168473	−	0.518507i
$658$	−1246.35	−	1715.46i	−1.89416	−	2.60708i
$659$			587.822i			0.891991i	0.895035	+	0.445996i	$0.147150\pi$
$659$			587.822i			0.891991i	−0.895035	+	0.445996i	$0.852850\pi$
$660$		0			0
$661$	389.155			0.588736			0.294368	−	0.955692i	$-0.404891\pi$
$661$	389.155			0.588736			0.294368	+	0.955692i	$0.404891\pi$
$662$	1025.04	−	744.737i	1.54840	−	1.12498i
$663$	1296.87	−	421.378i	1.95606	−	0.635562i
$664$	204.205	−	628.478i	0.307537	−	0.946502i
$665$		0			0
$666$	−256.688	+	353.301i	−0.385417	+	0.530481i
$667$	286.986	−	883.251i	0.430263	−	1.32421i
$668$	127.471	+	392.317i	0.190825	+	0.587300i
$669$	−378.243	+	274.810i	−0.565386	+	0.410777i
$670$		0			0
$671$	−284.479	+	286.749i	−0.423963	+	0.427345i
$672$		−	1372.13i		−	2.04185i
$673$	828.664	−	602.060i	1.23130	−	0.894591i	0.234312	−	0.972162i	$-0.424716\pi$
$673$	828.664	−	602.060i	1.23130	−	0.894591i	0.996987	+	0.0775708i	$0.0247164\pi$
$674$	−440.410	−	1355.44i	−0.653428	−	2.01104i
$675$		0			0
$676$	−124.662	−	90.5719i	−0.184411	−	0.133982i
$677$	200.121	+	145.396i	0.295599	+	0.214766i	0.725693	−	0.688019i	$-0.241519\pi$
$677$	200.121	+	145.396i	0.295599	+	0.214766i	−0.430093	+	0.902784i	$0.641519\pi$
$678$	−272.470	+	838.577i	−0.401874	+	1.23684i
$679$	−692.118	+	224.883i	−1.01932	+	0.331197i
$680$		0			0
$681$		−	1550.95i		−	2.27746i
$682$	−157.997	+	313.156i	−0.231667	+	0.459173i
$683$			979.967i			1.43480i	0.696662	+	0.717399i	$0.254668\pi$
$683$			979.967i			1.43480i	−0.696662	+	0.717399i	$0.745332\pi$
$684$	190.050	+	261.581i	0.277851	+	0.382428i
$685$		0			0
$686$	−253.473	+	780.110i	−0.369494	+	1.13719i
$687$	−325.992	+	448.689i	−0.474515	+	0.653113i
$688$	−239.570	−	174.058i	−0.348212	−	0.252991i
$689$	728.806	+	236.804i	1.05777	+	0.343692i
$690$		0			0
$691$	537.473	−	390.497i	0.777818	−	0.565118i	−0.126505	−	0.991966i	$-0.540376\pi$
$691$	537.473	−	390.497i	0.777818	−	0.565118i	0.904323	+	0.426848i	$0.140376\pi$
$692$	−613.222			−0.886160
$693$	−99.4899	−	612.397i	−0.143564	−	0.883690i
$694$	−526.217			−0.758237
$695$		0			0
$696$	−204.912	−	630.654i	−0.294413	−	0.906111i
$697$	1289.52	+	418.992i	1.85011	+	0.601136i
$698$	312.496	−	430.113i	0.447702	−	0.616208i
$699$	438.695	−	603.812i	0.627604	−	0.863823i
$700$		0			0
$701$	−984.515	+	319.888i	−1.40444	+	0.456332i	−0.910625	−	0.413233i	$-0.864399\pi$
$701$	−984.515	+	319.888i	−1.40444	+	0.456332i	−0.493819	+	0.869565i	$0.664399\pi$
$702$	203.208	+	279.692i	0.289470	+	0.398422i
$703$	171.103			0.243390
$704$	−970.772	+	499.501i	−1.37894	+	0.709519i
$705$		0			0
$706$	894.622	+	1231.34i	1.26717	+	1.74411i
$707$	−826.777	+	268.636i	−1.16942	+	0.379966i
$708$	−1233.57	−	400.813i	−1.74234	−	0.566120i
$709$	−996.643	−	724.104i	−1.40570	−	1.02130i	−0.993930	−	0.110016i	$-0.964910\pi$
$709$	−996.643	−	724.104i	−1.40570	−	1.02130i	−0.411773	−	0.911287i	$-0.635090\pi$
$710$		0			0
$711$	−228.475	−	74.2361i	−0.321344	−	0.104411i
$712$	−179.140	−	551.336i	−0.251601	−	0.774348i
$713$	154.572	+	212.751i	0.216792	+	0.298388i
$714$		−	2408.26i		−	3.37292i
$715$		0			0
$716$	1140.98			1.59354
$717$	−564.498	+	410.132i	−0.787305	+	0.572011i
$718$	−450.629	+	146.418i	−0.627617	+	0.203925i
$719$	−229.638	+	706.754i	−0.319385	+	0.982967i	0.654526	+	0.756039i	$0.272868\pi$
$719$	−229.638	+	706.754i	−0.319385	+	0.982967i	−0.973912	+	0.226928i	$0.927132\pi$
$720$		0			0
$721$	−90.8009	+	124.977i	−0.125937	+	0.173338i
$722$	−275.568	+	848.112i	−0.381673	+	1.17467i
$723$	−283.440	−	872.338i	−0.392033	−	1.20655i
$724$	−354.092	+	257.263i	−0.489077	+	0.355336i
$725$		0			0
$726$	−1198.12	+	885.113i	−1.65030	+	1.21916i
$727$		−	10.4678i		−	0.0143987i	−0.999974	−	0.00719934i	$-0.997708\pi$
$727$		−	10.4678i		−	0.0143987i	0.999974	−	0.00719934i	$-0.00229164\pi$
$728$	−414.703	+	301.299i	−0.569647	+	0.413873i
$729$	116.499	+	358.548i	0.159807	+	0.491836i
$730$		0			0
$731$	−732.148	−	531.937i	−1.00157	−	0.727683i
$732$	650.249	+	472.433i	0.888318	+	0.645401i
$733$	312.297	−	961.151i	0.426053	−	1.31126i	−0.475929	−	0.879484i	$-0.657888\pi$
$733$	312.297	−	961.151i	0.426053	−	1.31126i	0.901982	−	0.431773i	$-0.142112\pi$
$734$	−543.530	+	176.604i	−0.740504	+	0.240604i
$735$		0			0
$736$			1080.59i			1.46819i
$737$	29.8942	−	193.723i	0.0405621	−	0.262854i
$738$		−	1203.16i		−	1.63030i
$739$	339.077	+	466.699i	0.458832	+	0.631528i	0.974266	−	0.225401i	$-0.0723694\pi$
$739$	339.077	+	466.699i	0.458832	+	0.631528i	−0.515434	+	0.856929i	$0.672369\pi$
$740$		0			0
$741$	−146.502	+	450.888i	−0.197709	+	0.608485i
$742$	795.498	−	1094.91i	1.07210	−	1.47562i
$743$	−933.113	−	677.947i	−1.25587	−	0.912445i	−0.257325	−	0.966325i	$-0.582841\pi$
$743$	−933.113	−	677.947i	−1.25587	−	0.912445i	−0.998547	+	0.0538800i	$0.982841\pi$
$744$	178.577	+	58.0233i	0.240023	+	0.0779883i
$745$		0			0
$746$	669.393	−	486.342i	0.897310	−	0.651934i
$747$	1020.96			1.36675
$748$	−1299.47	+	668.632i	−1.73727	+	0.893893i
$749$	775.659			1.03559
$750$		0			0
$751$	447.403	+	1376.97i	0.595743	+	1.83351i	0.550991	+	0.834511i	$0.314250\pi$
$751$	447.403	+	1376.97i	0.595743	+	1.83351i	0.0447527	+	0.998998i	$0.485750\pi$
$752$	−646.041	−	209.911i	−0.859097	−	0.279137i
$753$	−249.140	+	342.912i	−0.330863	+	0.455394i
$754$	929.402	−	1279.21i	1.23263	−	1.69657i
$755$		0			0
$756$	335.469	−	109.000i	0.443742	−	0.144181i
$757$	−310.608	−	427.516i	−0.410315	−	0.564750i	0.552980	−	0.833194i	$-0.313490\pi$
$757$	−310.608	−	427.516i	−0.410315	−	0.564750i	−0.963295	+	0.268444i	$0.913490\pi$
$758$	−927.982			−1.22425
$759$	179.088	+	1102.35i	0.235953	+	1.45238i
$760$		0			0
$761$	128.577	+	176.972i	0.168958	+	0.232551i	0.885097	−	0.465407i	$-0.154092\pi$
$761$	128.577	+	176.972i	0.168958	+	0.232551i	−0.716138	+	0.697958i	$0.754092\pi$
$762$	315.620	−	102.551i	0.414199	−	0.134581i
$763$	−161.533	−	52.4853i	−0.211708	−	0.0687881i
$764$	386.010	+	280.453i	0.505249	+	0.367085i
$765$		0			0
$766$	−1425.11	−	463.048i	−1.86046	−	0.604501i
$767$	−257.118	−	791.329i	−0.335226	−	1.03172i
$768$	44.6717	+	61.4853i	0.0581662	+	0.0800590i
$769$		−	162.687i		−	0.211557i	−0.994390	−	0.105778i	$-0.966267\pi$
$769$		−	162.687i		−	0.211557i	0.994390	−	0.105778i	$-0.0337334\pi$
$770$		0			0
$771$	1030.83			1.33701
$772$	−832.468	+	604.823i	−1.07833	+	0.783450i
$773$	310.480	−	100.881i	0.401656	−	0.130506i	−0.101221	−	0.994864i	$-0.532275\pi$
$773$	310.480	−	100.881i	0.401656	−	0.130506i	0.502877	+	0.864358i	$0.332275\pi$
$774$	−248.156	+	763.745i	−0.320615	+	0.986751i
$775$		0			0
$776$	240.528	−	331.058i	0.309959	−	0.426621i
$777$	−201.886	+	621.341i	−0.259828	+	0.799667i
$778$	363.404	+	1118.44i	0.467100	+	1.43759i
$779$	−381.376	+	277.086i	−0.489572	+	0.355695i
$780$		0			0
$781$	45.4458	+	45.0861i	0.0581893	+	0.0577287i
$782$			1896.58i			2.42529i
$783$	−236.810	+	172.053i	−0.302439	+	0.219735i
$784$	−39.0896	−	120.305i	−0.0498592	−	0.153451i
$785$		0			0
$786$	−884.604	−	642.702i	−1.12545	−	0.817687i
$787$	313.294	+	227.621i	0.398086	+	0.289226i	0.768761	−	0.639536i	$-0.220874\pi$
$787$	313.294	+	227.621i	0.398086	+	0.289226i	−0.370675	+	0.928763i	$0.620874\pi$
$788$	−17.7701	+	54.6906i	−0.0225508	+	0.0694043i
$789$	1104.54	−	358.888i	1.39993	−	0.454865i
$790$		0			0
$791$			577.101i			0.729585i
$792$	247.666	+	245.706i	0.312710	+	0.310234i
$793$			515.601i			0.650190i
$794$	1208.65	+	1663.56i	1.52222	+	2.09516i
$795$		0			0
$796$	−14.0488	+	43.2377i	−0.0176492	+	0.0543187i
$797$	−12.9188	+	17.7812i	−0.0162092	+	0.0223101i	−0.817045	−	0.576574i	$-0.804389\pi$
$797$	−12.9188	+	17.7812i	−0.0162092	+	0.0223101i	0.800835	+	0.598884i	$0.204389\pi$
$798$	677.383	+	492.148i	0.848851	+	0.616727i
$799$	−1974.36	−	641.509i	−2.47104	−	0.802890i
$800$		0			0
$801$	724.592	−	526.447i	0.904609	−	0.657237i
$802$	−1108.17			−1.38176
$803$	−253.543	+	502.533i	−0.315745	+	0.625819i
$804$	−390.046			−0.485132
$805$		0			0
$806$	138.358	+	425.821i	0.171660	+	0.528314i
$807$	1258.40	+	408.879i	1.55936	+	0.506666i
$808$	287.325	−	395.469i	0.355600	−	0.489442i
$809$	−599.477	+	825.109i	−0.741010	+	1.01991i	0.257550	+	0.966265i	$0.417085\pi$
$809$	−599.477	+	825.109i	−0.741010	+	1.01991i	−0.998560	+	0.0536476i	$0.982915\pi$
$810$		0			0
$811$	−940.701	+	305.652i	−1.15993	+	0.376883i	−0.824875	−	0.565316i	$-0.808754\pi$
$811$	−940.701	+	305.652i	−1.15993	+	0.376883i	−0.335053	+	0.942199i	$0.608754\pi$
$812$	−948.260	−	1305.17i	−1.16781	−	1.60735i
$813$	−869.183			−1.06911
$814$	677.368	−	110.045i	0.832147	−	0.135190i
$815$		0			0
$816$	−453.475	−	624.155i	−0.555729	−	0.764896i
$817$	299.240	−	97.2291i	0.366267	−	0.119007i
$818$	105.993	+	34.4392i	0.129576	+	0.0421018i
$819$	−640.713	−	465.505i	−0.782311	−	0.568382i
$820$		0			0
$821$	−729.758	−	237.113i	−0.888864	−	0.288810i	−0.171231	−	0.985231i	$-0.554775\pi$
$821$	−729.758	−	237.113i	−0.888864	−	0.288810i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	−456.769	−	1405.79i	−0.555680	−	1.71021i
$823$	490.391	+	674.965i	0.595858	+	0.820128i	0.995321	−	0.0966212i	$-0.0308035\pi$
$823$	490.391	+	674.965i	0.595858	+	0.820128i	−0.399463	+	0.916749i	$0.630804\pi$
$824$		−	86.8648i		−	0.105418i
$825$		0			0
$826$	−1469.49			−1.77904
$827$	453.171	−	329.248i	0.547970	−	0.398123i	−0.279067	−	0.960272i	$-0.590025\pi$
$827$	453.171	−	329.248i	0.547970	−	0.398123i	0.827036	+	0.562148i	$0.190025\pi$
$828$	924.669	−	300.443i	1.11675	−	0.362854i
$829$	371.006	−	1141.84i	0.447534	−	1.37737i	−0.432147	−	0.901803i	$-0.642244\pi$
$829$	371.006	−	1141.84i	0.447534	−	1.37737i	0.879681	−	0.475565i	$-0.157756\pi$
$830$		0			0
$831$	−1054.79	+	1451.80i	−1.26931	+	1.74705i
$832$	−430.643	+	1325.38i	−0.517600	+	1.59301i
$833$	−119.461	−	367.664i	−0.143411	−	0.441374i
$834$	35.0294	−	25.4504i	0.0420017	−	0.0305160i
$835$		0			0
$836$	77.4888	−	502.149i	0.0926899	−	0.600657i
$837$		−	82.8854i		−	0.0990268i
$838$	1054.58	−	766.196i	1.25845	−	0.914315i
$839$	−162.370	−	499.723i	−0.193528	−	0.595618i	−0.999991	−	0.00433286i	$-0.998621\pi$
$839$	−162.370	−	499.723i	−0.193528	−	0.595618i	0.806463	−	0.591285i	$-0.201379\pi$
$840$		0			0
$841$	402.703	+	292.581i	0.478838	+	0.347896i
$842$	1702.45	+	1236.91i	2.02192	+	1.46901i
$843$	−115.799	+	356.393i	−0.137366	+	0.422768i
$844$	−398.695	+	129.544i	−0.472387	+	0.153488i
$845$		0			0
$846$			1842.14i			2.17746i
$847$	−566.779	+	793.284i	−0.669160	+	0.936581i
$848$		−	433.562i		−	0.511276i
$849$	−687.259	−	945.930i	−0.809492	−	1.11417i
$850$		0			0
$851$	158.991	−	489.324i	0.186828	−	0.574998i
$852$	74.8744	−	103.056i	0.0878807	−	0.120957i
$853$	−775.340	−	563.318i	−0.908957	−	0.660396i	0.0317938	−	0.999494i	$-0.489878\pi$
$853$	−775.340	−	563.318i	−0.908957	−	0.660396i	−0.940751	+	0.339099i	$0.889878\pi$
$854$	866.033	+	281.391i	1.01409	+	0.329498i
$855$		0			0
$856$	−352.859	+	256.367i	−0.412219	+	0.299494i
$857$	−56.2536			−0.0656402			−0.0328201	−	0.999461i	$-0.510449\pi$
$857$	−56.2536			−0.0656402			−0.0328201	+	0.999461i	$0.510449\pi$
$858$	−289.988	+	1879.21i	−0.337982	+	2.19022i
$859$	1517.29			1.76634			0.883171	−	0.469051i	$-0.155404\pi$
$859$	1517.29			1.76634			0.883171	+	0.469051i	$0.155404\pi$
$860$		0			0
$861$	−556.217	−	1711.86i	−0.646012	−	1.98822i
$862$	377.794	+	122.753i	0.438276	+	0.142405i
$863$	644.517	−	887.101i	0.746833	−	1.02793i	−0.251363	−	0.967893i	$-0.580879\pi$
$863$	644.517	−	887.101i	0.746833	−	1.02793i	0.998196	−	0.0600344i	$-0.0191211\pi$
$864$	200.190	−	275.538i	0.231702	−	0.318910i
$865$		0			0
$866$	1613.88	−	524.382i	1.86360	−	0.605522i
$867$	−706.383	−	972.253i	−0.814744	−	1.12140i
$868$	456.819			0.526289
$869$	172.721	+	335.680i	0.198758	+	0.386283i
$870$		0			0
$871$	−147.071	−	202.426i	−0.168853	−	0.232406i
$872$	90.8310	−	29.5128i	0.104164	−	0.0338449i
$873$	601.283	+	195.369i	0.688755	+	0.223790i
$874$	−533.458	−	387.580i	−0.610364	−	0.443456i
$875$		0			0
$876$	1065.22	+	346.111i	1.21600	+	0.395104i
$877$	−351.441	−	1081.62i	−0.400731	−	1.23332i	−0.924408	−	0.381405i	$-0.875440\pi$
$877$	−351.441	−	1081.62i	−0.400731	−	1.23332i	0.523677	−	0.851917i	$-0.324560\pi$
$878$	851.293	+	1171.70i	0.969582	+	1.33451i
$879$			1384.31i			1.57487i
$880$		0			0
$881$	850.822			0.965746			0.482873	−	0.875690i	$-0.339593\pi$
$881$	850.822			0.965746			0.482873	+	0.875690i	$0.339593\pi$
$882$	−277.526	+	201.635i	−0.314656	+	0.228611i
$883$	484.958	−	157.572i	0.549216	−	0.178451i	−0.0212471	−	0.999774i	$-0.506764\pi$
$883$	484.958	−	157.572i	0.549216	−	0.178451i	0.570463	+	0.821323i	$0.306764\pi$
$884$	−576.459	+	1774.16i	−0.652103	+	2.00697i
$885$		0			0
$886$	179.567	−	247.153i	0.202672	−	0.278954i
$887$	180.313	−	554.947i	0.203284	−	0.625645i	−0.796495	−	0.604645i	$-0.793315\pi$
$887$	180.313	−	554.947i	0.203284	−	0.625645i	0.999779	−	0.0209998i	$-0.00668494\pi$
$888$	−113.522	−	349.384i	−0.127840	−	0.393450i
$889$	175.724	−	127.671i	0.197665	−	0.143612i
$890$		0			0
$891$	470.717	−	932.979i	0.528302	−	1.04711i
$892$		−	639.603i		−	0.717043i
$893$	583.917	−	424.240i	0.653882	−	0.475073i
$894$	−354.971	−	1092.49i	−0.397059	−	1.22202i
$895$		0			0
$896$	881.096	+	640.153i	0.983366	+	0.714457i
$897$	1153.32	+	837.939i	1.28576	+	0.934157i
$898$	129.632	−	398.966i	0.144356	−	0.444283i
$899$	−360.535	+	117.145i	−0.401040	+	0.130306i
$900$		0			0
$901$		−	1325.01i		−	1.47060i
$902$	−1331.59	+	1342.22i	−1.47627	+	1.48805i
$903$			1201.38i			1.33043i
$904$	−190.741	−	262.532i	−0.210996	−	0.290412i
$905$		0			0
$906$	−372.859	+	1147.54i	−0.411544	+	1.26660i
$907$	376.478	−	518.177i	0.415080	−	0.571309i	−0.549368	−	0.835580i	$-0.685132\pi$
$907$	376.478	−	518.177i	0.415080	−	0.571309i	0.964448	+	0.264272i	$0.0851315\pi$
$908$	1716.54	+	1247.14i	1.89046	+	1.37350i
$909$	718.269	+	233.380i	0.790175	+	0.256744i
$910$		0			0
$911$	885.922	−	643.660i	0.972472	−	0.706542i	0.0164582	−	0.999865i	$-0.494761\pi$
$911$	885.922	−	643.660i	0.972472	−	0.706542i	0.956014	+	0.293322i	$0.0947609\pi$
$912$	268.230			0.294112
$913$	−1138.96	−	1129.94i	−1.24749	−	1.23762i
$914$	−94.7802			−0.103698
$915$		0			0
$916$	−234.459	−	721.591i	−0.255960	−	0.787763i
$917$	−680.633	−	221.151i	−0.742238	−	0.241168i
$918$	351.361	−	483.607i	0.382746	−	0.526805i
$919$	729.402	−	1003.94i	0.793691	−	1.09242i	−0.199948	−	0.979807i	$-0.564077\pi$
$919$	729.402	−	1003.94i	0.793691	−	1.09242i	0.993639	−	0.112615i	$-0.0359228\pi$
$920$		0			0
$921$	687.902	−	223.513i	0.746908	−	0.242685i
$922$	−258.061	−	355.190i	−0.279893	−	0.385239i
$923$	81.7158			0.0885328
$924$	1732.07	+	873.881i	1.87453	+	0.945759i
$925$		0			0
$926$	−887.982	−	1222.20i	−0.958943	−	1.31987i
$927$	127.637	−	41.4718i	0.137688	−	0.0447376i
$928$	−1481.47	−	481.359i	−1.59641	−	0.518706i
$929$	834.947	+	606.624i	0.898758	+	0.652986i	0.938147	−	0.346238i	$-0.112541\pi$
$929$	834.947	+	606.624i	0.898758	+	0.652986i	−0.0393884	+	0.999224i	$0.512541\pi$
$930$		0			0
$931$	127.828	+	41.5337i	0.137301	+	0.0446119i
$932$	315.517	+	971.063i	0.338538	+	1.04191i
$933$	877.354	+	1207.57i	0.940358	+	1.29429i
$934$			2332.68i			2.49752i
$935$		0			0
$936$	445.326			0.475776
$937$	−248.036	+	180.209i	−0.264713	+	0.192325i	−0.712222	−	0.701954i	$-0.752311\pi$
$937$	−248.036	+	180.209i	−0.264713	+	0.192325i	0.447509	+	0.894279i	$0.352311\pi$
$938$	−420.271	+	136.554i	−0.448050	+	0.145580i
$939$	392.283	−	1207.32i	0.417767	−	1.28575i
$940$		0			0
$941$	11.2167	−	15.4385i	0.0119200	−	0.0164064i	−0.803015	−	0.595958i	$-0.796772\pi$
$941$	11.2167	−	15.4385i	0.0119200	−	0.0164064i	0.814935	+	0.579552i	$0.196772\pi$
$942$	−655.306	+	2016.82i	−0.695654	+	2.14100i
$943$	438.036	+	1348.14i	0.464514	+	1.42963i
$944$	−380.850	+	276.704i	−0.403443	+	0.293118i
$945$		0			0
$946$	1122.11	−	577.369i	1.18616	−	0.610327i
$947$		−	804.636i		−	0.849669i	−0.905271	−	0.424834i	$-0.860332\pi$
$947$		−	804.636i		−	0.849669i	0.905271	−	0.424834i	$-0.139668\pi$
$948$	607.728	−	441.540i	0.641063	−	0.465760i
$949$	222.027	+	683.330i	0.233959	+	0.720053i
$950$		0			0
$951$	889.256	+	646.082i	0.935075	+	0.679372i
$952$	717.050	+	520.967i	0.753204	+	0.547235i
$953$	−572.962	+	1763.40i	−0.601220	+	1.85036i	−0.0802758	+	0.996773i	$0.525580\pi$
$953$	−572.962	+	1763.40i	−0.601220	+	1.85036i	−0.520944	+	0.853591i	$0.674420\pi$
$954$	−1118.22	+	363.330i	−1.17213	+	0.380850i
$955$		0			0
$956$		−	954.556i		−	0.998489i
$957$	−1591.09	−	245.528i	−1.66258	−	0.256560i
$958$		−	1911.11i		−	1.99489i
$959$	−568.654	−	782.686i	−0.592966	−	0.816148i
$960$		0			0
$961$	−263.794	+	811.875i	−0.274500	+	0.844824i
$962$	514.891	−	708.687i	0.535230	−	0.736681i
$963$	−545.164	−	396.085i	−0.566111	−	0.411303i
$964$	1193.39	+	387.755i	1.23795	+	0.402236i
$965$		0			0
$966$	2036.88	−	1479.88i	2.10857	−	1.53197i
$967$	−660.803			−0.683353			−0.341677	−	0.939818i	$-0.610995\pi$
$967$	−660.803			−0.683353			−0.341677	+	0.939818i	$0.610995\pi$
$968$	−4.35630	−	548.206i	−0.00450031	−	0.566328i
$969$	819.737			0.845962
$970$		0			0
$971$	−166.517	−	512.487i	−0.171490	−	0.527793i	0.827965	−	0.560779i	$-0.189498\pi$
$971$	−166.517	−	512.487i	−0.171490	−	0.527793i	−0.999456	+	0.0329859i	$0.989498\pi$
$972$	−1602.93	−	520.823i	−1.64910	−	0.535826i
$973$	16.6575	−	22.9271i	0.0171197	−	0.0235633i
$974$	712.232	−	980.303i	0.731244	−	1.00647i
$975$		0			0
$976$	277.438	−	90.1450i	0.284260	−	0.0923617i
$977$	177.151	+	243.828i	0.181322	+	0.249568i	0.889996	−	0.455967i	$-0.150707\pi$
$977$	177.151	+	243.828i	0.181322	+	0.249568i	−0.708675	+	0.705535i	$0.750707\pi$
$978$	−3116.80			−3.18691
$979$	−1390.98	−	214.648i	−1.42082	−	0.219252i
$980$		0			0
$981$	86.7307	+	119.375i	0.0884105	+	0.121687i
$982$	−1898.75	+	616.943i	−1.93356	+	0.628251i
$983$	733.472	+	238.319i	0.746156	+	0.242441i	0.657327	−	0.753606i	$-0.271687\pi$
$983$	733.472	+	238.319i	0.746156	+	0.242441i	0.0888299	+	0.996047i	$0.471687\pi$
$984$	818.827	+	594.912i	0.832141	+	0.604586i
$985$		0			0
$986$	−2600.18	−	844.850i	−2.63710	−	0.856846i
$987$	851.611	+	2620.99i	0.862827	+	2.65551i
$988$	−381.222	−	524.707i	−0.385852	−	0.531080i
$989$		−	946.119i		−	0.956642i
$990$		0			0
$991$	118.312			0.119386			0.0596932	−	0.998217i	$-0.480988\pi$
$991$	118.312			0.119386			0.0596932	+	0.998217i	$0.480988\pi$
$992$	356.846	−	259.264i	0.359723	−	0.261354i
$993$	−1566.13	+	508.865i	−1.57717	+	0.512453i
$994$	44.5967	−	137.255i	0.0448659	−	0.138083i
$995$		0			0
$996$	−1876.49	+	2582.77i	−1.88403	+	2.59314i
$997$	−11.7057	+	36.0263i	−0.0117409	+	0.0361347i	−0.956755	−	0.290894i	$-0.906047\pi$
$997$	−11.7057	+	36.0263i	−0.0117409	+	0.0361347i	0.945014	+	0.327029i	$0.106047\pi$
$998$	−681.931	−	2098.77i	−0.683298	−	2.10298i
$999$	−131.193	+	95.3177i	−0.131325	+	0.0954131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.c.74.2		8
5.2	odd	4		275.3.x.d.151.1		4
5.3	odd	4		55.3.i.a.41.1	✓	4
5.4	even	2	inner	275.3.q.c.74.1		8
11.7	odd	10	inner	275.3.q.c.249.1		8
55.7	even	20		275.3.x.d.51.1		4
55.13	even	20		605.3.c.a.241.1		4
55.18	even	20		55.3.i.a.51.1	yes	4
55.29	odd	10	inner	275.3.q.c.249.2		8
55.53	odd	20		605.3.c.a.241.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.41.1	✓	4	5.3	odd	4
55.3.i.a.51.1	yes	4	55.18	even	20
275.3.q.c.74.1		8	5.4	even	2	inner
275.3.q.c.74.2		8	1.1	even	1	trivial
275.3.q.c.249.1		8	11.7	odd	10	inner
275.3.q.c.249.2		8	55.29	odd	10	inner
275.3.x.d.51.1		4	55.7	even	20
275.3.x.d.151.1		4	5.2	odd	4
605.3.c.a.241.1		4	55.13	even	20
605.3.c.a.241.4		4	55.53	odd	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.48990 - 1.80902i) q^{2} +(-3.80423 + 1.23607i) q^{3} +(1.69098 - 5.20431i) q^{4} +(-7.23607 + 9.95959i) q^{6} +(-2.48990 + 7.66312i) q^{7} +(-1.40008 - 4.30902i) q^{8} +(5.66312 - 4.11450i) q^{9} +(-10.8713 - 1.67760i) q^{11} +21.8885i q^{12} +(-11.3597 + 8.25329i) q^{13} +(7.66312 + 23.5847i) q^{14} +(6.42705 + 4.66953i) q^{16} +(19.6417 + 14.2705i) q^{17} +(6.65740 - 20.4894i) q^{18} +(-8.02786 + 2.60841i) q^{19} -32.2299i q^{21} +(-30.1033 + 15.4894i) q^{22} +25.3820i q^{23} +(10.6525 + 14.6619i) q^{24} +(-13.3541 + 41.0997i) q^{26} +(4.70228 - 6.47214i) q^{27} +(35.6709 + 25.9164i) q^{28} +(-34.7984 - 11.3067i) q^{29} +(8.38197 - 6.08985i) q^{31} +42.5730 q^{32} +(43.4306 - 7.05573i) q^{33} +74.7214 q^{34} +(-11.8369 - 36.4302i) q^{36} +(-19.2784 - 6.26393i) q^{37} +(-15.2699 + 21.0172i) q^{38} +(33.0132 - 45.4387i) q^{39} +(53.1140 - 17.2578i) q^{41} +(-58.3045 - 80.2492i) q^{42} -37.2752 q^{43} +(-27.1140 + 53.7409i) q^{44} +(45.9164 + 63.1985i) q^{46} +(-81.3216 + 26.4230i) q^{47} +(-30.2218 - 9.81966i) q^{48} +(-12.8820 - 9.35930i) q^{49} +(-92.3607 - 30.0098i) q^{51} +(23.7437 + 73.0755i) q^{52} +(-32.0787 - 44.1525i) q^{53} -24.6215i q^{54} +36.5066 q^{56} +(27.3156 - 19.8460i) q^{57} +(-107.098 + 34.7984i) q^{58} +(-18.3115 + 56.3571i) q^{59} +(21.5836 - 29.7073i) q^{61} +(9.85359 - 30.3262i) q^{62} +(17.4293 + 53.6418i) q^{63} +(80.2943 - 58.3372i) q^{64} +(95.3738 - 96.1347i) q^{66} +17.8197i q^{67} +(107.482 - 78.0902i) q^{68} +(-31.3738 - 96.5587i) q^{69} +(-4.70820 - 3.42071i) q^{71} +(-25.6583 - 18.6418i) q^{72} +(15.8124 - 48.6656i) q^{73} +(-59.3328 + 19.2784i) q^{74} +46.1903i q^{76} +(39.9241 - 79.1312i) q^{77} -172.859i q^{78} +(-20.1722 - 27.7647i) q^{79} +(-29.3566 + 90.3504i) q^{81} +(101.029 - 139.054i) q^{82} +(117.997 + 85.7295i) q^{83} +(-167.735 - 54.5002i) q^{84} +(-92.8115 + 67.4315i) q^{86} +146.357 q^{87} +(7.99197 + 49.1935i) q^{88} +127.949 q^{89} +(-34.9615 - 107.600i) q^{91} +(132.096 + 42.9205i) q^{92} +(-24.3594 + 33.5279i) q^{93} +(-154.683 + 212.903i) q^{94} +(-161.957 + 52.6232i) q^{96} +(53.0877 + 73.0689i) q^{97} -49.0059 q^{98} +(-68.4681 + 35.2296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{4} - 40 q^{6} + 14 q^{9} - 2 q^{11} + 30 q^{14} + 38 q^{16} - 100 q^{19} - 40 q^{24} - 80 q^{26} - 180 q^{29} + 76 q^{31} + 240 q^{34} - 126 q^{36} - 40 q^{39} + 170 q^{41} + 38 q^{44} + 260 q^{46}+ \cdots - 266 q^{99}+O(q^{100}) \) 8 * q + 18 * q^4 - 40 * q^6 + 14 * q^9 - 2 * q^11 + 30 * q^14 + 38 * q^16 - 100 * q^19 - 40 * q^24 - 80 * q^26 - 180 * q^29 + 76 * q^31 + 240 * q^34 - 126 * q^36 - 40 * q^39 + 170 * q^41 + 38 * q^44 + 260 * q^46 - 112 * q^49 - 560 * q^51 + 140 * q^56 + 256 * q^59 + 280 * q^61 + 298 * q^64 + 280 * q^66 + 232 * q^69 + 16 * q^71 - 260 * q^74 + 420 * q^79 + 190 * q^81 - 680 * q^84 - 340 * q^86 + 156 * q^89 - 150 * q^91 - 750 * q^94 - 920 * q^96 - 266 * q^99

Introduction

L-functions

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