LMFDB - Embedded newform 275.3.x.d.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] 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([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,5,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 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			51.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	275.51
Dual form			275.3.x.d.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80902 - 2.48990i) q^{2} +(1.23607 - 3.80423i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-7.23607 - 9.95959i) q^{6} +(-7.66312 + 2.48990i) q^{7} +(-4.30902 - 1.40008i) q^{8} +(-5.66312 - 4.11450i) q^{9} +(-10.8713 + 1.67760i) q^{11} -21.8885 q^{12} +(8.25329 - 11.3597i) q^{13} +(-7.66312 + 23.5847i) q^{14} +(6.42705 - 4.66953i) q^{16} +(-14.2705 - 19.6417i) q^{17} +(-20.4894 + 6.65740i) q^{18} +(8.02786 + 2.60841i) q^{19} +32.2299i q^{21} +(-15.4894 + 30.1033i) q^{22} +25.3820 q^{23} +(-10.6525 + 14.6619i) q^{24} +(-13.3541 - 41.0997i) q^{26} +(6.47214 - 4.70228i) q^{27} +(25.9164 + 35.6709i) q^{28} +(34.7984 - 11.3067i) q^{29} +(8.38197 + 6.08985i) q^{31} -42.5730i q^{32} +(-7.05573 + 43.4306i) q^{33} -74.7214 q^{34} +(-11.8369 + 36.4302i) q^{36} +(6.26393 + 19.2784i) q^{37} +(21.0172 - 15.2699i) q^{38} +(-33.0132 - 45.4387i) q^{39} +(53.1140 + 17.2578i) q^{41} +(80.2492 + 58.3045i) q^{42} -37.2752i q^{43} +(27.1140 + 53.7409i) q^{44} +(45.9164 - 63.1985i) q^{46} +(-26.4230 + 81.3216i) q^{47} +(-9.81966 - 30.2218i) q^{48} +(12.8820 - 9.35930i) q^{49} +(-92.3607 + 30.0098i) q^{51} +(-73.0755 - 23.7437i) q^{52} +(-44.1525 - 32.0787i) q^{53} -24.6215i q^{54} +36.5066 q^{56} +(19.8460 - 27.3156i) q^{57} +(34.7984 - 107.098i) q^{58} +(18.3115 + 56.3571i) q^{59} +(21.5836 + 29.7073i) q^{61} +(30.3262 - 9.85359i) q^{62} +(53.6418 + 17.4293i) q^{63} +(-80.2943 - 58.3372i) q^{64} +(95.3738 + 96.1347i) q^{66} -17.8197 q^{67} +(-78.0902 + 107.482i) q^{68} +(31.3738 - 96.5587i) q^{69} +(-4.70820 + 3.42071i) q^{71} +(18.6418 + 25.6583i) q^{72} +(-48.6656 + 15.8124i) q^{73} +(59.3328 + 19.2784i) q^{74} -46.1903i q^{76} +(79.1312 - 39.9241i) q^{77} -172.859 q^{78} +(20.1722 - 27.7647i) q^{79} +(-29.3566 - 90.3504i) q^{81} +(139.054 - 101.029i) q^{82} +(85.7295 + 117.997i) q^{83} +(167.735 - 54.5002i) q^{84} +(-92.8115 - 67.4315i) q^{86} -146.357i q^{87} +(49.1935 + 7.99197i) q^{88} -127.949 q^{89} +(-34.9615 + 107.600i) q^{91} +(-42.9205 - 132.096i) q^{92} +(33.5279 - 24.3594i) q^{93} +(154.683 + 212.903i) q^{94} +(-161.957 - 52.6232i) q^{96} +(-73.0689 - 53.0877i) q^{97} -49.0059i q^{98} +(68.4681 + 35.2296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 4 q^{3} - 9 q^{4} - 20 q^{6} - 15 q^{7} - 15 q^{8} - 7 q^{9} - q^{11} - 16 q^{12} - 5 q^{13} - 15 q^{14} + 19 q^{16} + 10 q^{17} - 35 q^{18} + 50 q^{19} - 15 q^{22} + 106 q^{23} + 20 q^{24}+ \cdots + 133 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 - 4 * q^3 - 9 * q^4 - 20 * q^6 - 15 * q^7 - 15 * q^8 - 7 * q^9 - q^11 - 16 * q^12 - 5 * q^13 - 15 * q^14 + 19 * q^16 + 10 * q^17 - 35 * q^18 + 50 * q^19 - 15 * q^22 + 106 * q^23 + 20 * q^24 - 40 * q^26 + 8 * q^27 + 50 * q^28 + 90 * q^29 + 38 * q^31 - 64 * q^33 - 120 * q^34 - 63 * q^36 + 34 * q^37 + 55 * q^38 + 20 * q^39 + 85 * q^41 + 160 * q^42 - 19 * q^44 + 130 * q^46 + 24 * q^47 - 84 * q^48 + 56 * q^49 - 280 * q^51 - 100 * q^52 - 114 * q^53 + 70 * q^56 - 180 * q^57 + 90 * q^58 - 128 * q^59 + 140 * q^61 + 90 * q^62 + 105 * q^63 - 149 * q^64 + 140 * q^66 - 116 * q^67 - 290 * q^68 - 116 * q^69 + 8 * q^71 - 35 * q^72 + 20 * q^73 + 130 * q^74 + 160 * q^77 - 280 * q^78 - 210 * q^79 + 95 * q^81 + 270 * q^82 + 410 * q^83 + 340 * q^84 - 170 * q^86 - 78 * q^89 - 75 * q^91 - 241 * q^92 + 152 * q^93 + 375 * q^94 - 460 * q^96 - 176 * q^97 + 133 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	1.80902	−	2.48990i	0.904508	−	1.24495i	−0.0644990	−	0.997918i	$-0.520545\pi$
$2$	1.80902	−	2.48990i	0.904508	−	1.24495i	0.969007	−	0.247031i	$-0.0794551\pi$
$3$	1.23607	−	3.80423i	0.412023	−	1.26808i	−0.502864	−	0.864365i	$-0.667720\pi$
$3$	1.23607	−	3.80423i	0.412023	−	1.26808i	0.914887	−	0.403710i	$-0.132280\pi$
$4$	−1.69098	−	5.20431i	−0.422746	−	1.30108i
$5$		0			0
$5$		0			0
$6$	−7.23607	−	9.95959i	−1.20601	−	1.65993i
$7$	−7.66312	+	2.48990i	−1.09473	+	0.355700i	−0.800073	−	0.599903i	$-0.795206\pi$
$7$	−7.66312	+	2.48990i	−1.09473	+	0.355700i	−0.294658	+	0.955603i	$0.595206\pi$
$8$	−4.30902	−	1.40008i	−0.538627	−	0.175011i
$9$	−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
$12$	−21.8885			−1.82405
$13$	8.25329	−	11.3597i	0.634868	−	0.873821i	−0.363460	−	0.931610i	$-0.618405\pi$
$13$	8.25329	−	11.3597i	0.634868	−	0.873821i	0.998329	+	0.0577883i	$0.0184048\pi$
$14$	−7.66312	+	23.5847i	−0.547366	+	1.68462i
$15$		0			0
$16$	6.42705	−	4.66953i	0.401691	−	0.291845i
$17$	−14.2705	−	19.6417i	−0.839442	−	1.15539i	−0.986091	−	0.166204i	$-0.946849\pi$
$17$	−14.2705	−	19.6417i	−0.839442	−	1.15539i	0.146650	−	0.989188i	$-0.453151\pi$
$18$	−20.4894	+	6.65740i	−1.13830	+	0.369855i
$19$	8.02786	+	2.60841i	0.422519	+	0.137285i	0.512556	−	0.858654i	$-0.328699\pi$
$19$	8.02786	+	2.60841i	0.422519	+	0.137285i	−0.0900372	+	0.995938i	$0.528699\pi$
$20$		0			0
$21$			32.2299i			1.53476i
$22$	−15.4894	+	30.1033i	−0.704062	+	1.36833i
$23$	25.3820			1.10356			0.551782	−	0.833988i	$-0.313948\pi$
$23$	25.3820			1.10356			0.551782	+	0.833988i	$0.313948\pi$
$24$	−10.6525	+	14.6619i	−0.443853	+	0.610911i
$25$		0			0
$26$	−13.3541	−	41.0997i	−0.513619	−	1.58076i
$27$	6.47214	−	4.70228i	0.239709	−	0.174159i
$28$	25.9164	+	35.6709i	0.925586	+	1.27396i
$29$	34.7984	−	11.3067i	1.19994	−	0.389885i	0.360204	−	0.932874i	$-0.382707\pi$
$29$	34.7984	−	11.3067i	1.19994	−	0.389885i	0.839740	+	0.542988i	$0.182707\pi$
$30$		0			0
$31$	8.38197	+	6.08985i	0.270386	+	0.196447i	0.714713	−	0.699418i	$-0.246557\pi$
$31$	8.38197	+	6.08985i	0.270386	+	0.196447i	−0.444327	+	0.895865i	$0.646557\pi$
$32$		−	42.5730i		−	1.33041i
$33$	−7.05573	+	43.4306i	−0.213810	+	1.31608i
$34$	−74.7214			−2.19769
$35$		0			0
$36$	−11.8369	+	36.4302i	−0.328802	+	1.01195i
$37$	6.26393	+	19.2784i	0.169295	+	0.521038i	0.999327	−	0.0366784i	$-0.0116777\pi$
$37$	6.26393	+	19.2784i	0.169295	+	0.521038i	−0.830032	+	0.557716i	$0.811678\pi$
$38$	21.0172	−	15.2699i	0.553085	−	0.401840i
$39$	−33.0132	−	45.4387i	−0.846491	−	1.16510i
$40$		0			0
$41$	53.1140	+	17.2578i	1.29546	+	0.420921i	0.874001	−	0.485925i	$-0.161517\pi$
$41$	53.1140	+	17.2578i	1.29546	+	0.420921i	0.421462	+	0.906846i	$0.361517\pi$
$42$	80.2492	+	58.3045i	1.91070	+	1.38820i
$43$		−	37.2752i		−	0.866866i	−0.901186	−	0.433433i	$-0.857302\pi$
$43$		−	37.2752i		−	0.866866i	0.901186	−	0.433433i	$-0.142698\pi$
$44$	27.1140	+	53.7409i	0.616227	+	1.22139i
$45$		0			0
$46$	45.9164	−	63.1985i	0.998183	−	1.37388i
$47$	−26.4230	+	81.3216i	−0.562191	+	1.73025i	0.113962	+	0.993485i	$0.463646\pi$
$47$	−26.4230	+	81.3216i	−0.562191	+	1.73025i	−0.676153	+	0.736761i	$0.736354\pi$
$48$	−9.81966	−	30.2218i	−0.204576	−	0.629621i
$49$	12.8820	−	9.35930i	0.262897	−	0.191006i
$50$		0			0
$51$	−92.3607	+	30.0098i	−1.81099	+	0.588428i
$52$	−73.0755	−	23.7437i	−1.40530	−	0.456609i
$53$	−44.1525	−	32.0787i	−0.833066	−	0.605258i	0.0873594	−	0.996177i	$-0.472157\pi$
$53$	−44.1525	−	32.0787i	−0.833066	−	0.605258i	−0.920425	+	0.390919i	$0.872157\pi$
$54$		−	24.6215i		−	0.455953i
$55$		0			0
$56$	36.5066			0.651903
$57$	19.8460	−	27.3156i	0.348175	−	0.479222i
$58$	34.7984	−	107.098i	0.599972	−	1.84652i
$59$	18.3115	+	56.3571i	0.310365	+	0.955205i	0.977621	+	0.210376i	$0.0674689\pi$
$59$	18.3115	+	56.3571i	0.310365	+	0.955205i	−0.667256	+	0.744829i	$0.732531\pi$
$60$		0			0
$61$	21.5836	+	29.7073i	0.353829	+	0.487004i	0.948417	−	0.317027i	$-0.102685\pi$
$61$	21.5836	+	29.7073i	0.353829	+	0.487004i	−0.594587	+	0.804031i	$0.702685\pi$
$62$	30.3262	−	9.85359i	0.489133	−	0.158929i
$63$	53.6418	+	17.4293i	0.851458	+	0.276655i
$64$	−80.2943	−	58.3372i	−1.25460	−	0.911519i
$65$		0			0
$66$	95.3738	+	96.1347i	1.44506	+	1.45659i
$67$	−17.8197			−0.265965			−0.132983	−	0.991118i	$-0.542455\pi$
$67$	−17.8197			−0.265965			−0.132983	+	0.991118i	$0.542455\pi$
$68$	−78.0902	+	107.482i	−1.14838	+	1.58062i
$69$	31.3738	−	96.5587i	0.454693	−	1.39940i
$70$		0			0
$71$	−4.70820	+	3.42071i	−0.0663127	+	0.0481790i	−0.620448	−	0.784248i	$-0.713049\pi$
$71$	−4.70820	+	3.42071i	−0.0663127	+	0.0481790i	0.554135	+	0.832427i	$0.313049\pi$
$72$	18.6418	+	25.6583i	0.258914	+	0.356365i
$73$	−48.6656	+	15.8124i	−0.666652	+	0.216609i	−0.622742	−	0.782427i	$-0.713982\pi$
$73$	−48.6656	+	15.8124i	−0.666652	+	0.216609i	−0.0439101	+	0.999035i	$0.513982\pi$
$74$	59.3328	+	19.2784i	0.801795	+	0.260519i
$75$		0			0
$76$		−	46.1903i		−	0.607767i
$77$	79.1312	−	39.9241i	1.02768	−	0.518495i
$78$	−172.859			−2.21614
$79$	20.1722	−	27.7647i	0.255344	−	0.351451i	−0.662030	−	0.749478i	$-0.730305\pi$
$79$	20.1722	−	27.7647i	0.255344	−	0.351451i	0.917374	+	0.398026i	$0.130305\pi$
$80$		0			0
$81$	−29.3566	−	90.3504i	−0.362427	−	1.11544i
$82$	139.054	−	101.029i	1.69578	−	1.23206i
$83$	85.7295	+	117.997i	1.03289	+	1.42164i	0.902759	+	0.430147i	$0.141538\pi$
$83$	85.7295	+	117.997i	1.03289	+	1.42164i	0.130127	+	0.991497i	$0.458462\pi$
$84$	167.735	−	54.5002i	1.99684	−	0.648812i
$85$		0			0
$86$	−92.8115	−	67.4315i	−1.07920	−	0.784087i
$87$		−	146.357i		−	1.68226i
$88$	49.1935	+	7.99197i	0.559017	+	0.0908178i
$89$	−127.949			−1.43763			−0.718816	−	0.695200i	$-0.755316\pi$
$89$	−127.949			−1.43763			−0.718816	+	0.695200i	$0.755316\pi$
$90$		0			0
$91$	−34.9615	+	107.600i	−0.384192	+	1.18242i
$92$	−42.9205	−	132.096i	−0.466527	−	1.43582i
$93$	33.5279	−	24.3594i	0.360515	−	0.261929i
$94$	154.683	+	212.903i	1.64556	+	2.26492i
$95$		0			0
$96$	−161.957	−	52.6232i	−1.68706	−	0.548158i
$97$	−73.0689	−	53.0877i	−0.753287	−	0.547295i	0.143557	−	0.989642i	$-0.454146\pi$
$97$	−73.0689	−	53.0877i	−0.753287	−	0.547295i	−0.896844	+	0.442347i	$0.854146\pi$
$98$		−	49.0059i		−	0.500060i
$99$	68.4681	+	35.2296i	0.691597	+	0.355854i
$100$		0			0
$101$	63.4164	−	87.2852i	0.627885	−	0.864210i	−0.370012	−	0.929027i	$-0.620646\pi$
$101$	63.4164	−	87.2852i	0.627885	−	0.864210i	0.997897	+	0.0648171i	$0.0206464\pi$
$102$	−92.3607	+	284.257i	−0.905497	+	2.78683i
$103$	5.92454	+	18.2339i	0.0575198	+	0.177028i	0.975689	−	0.219162i	$-0.0703323\pi$
$103$	5.92454	+	18.2339i	0.0575198	+	0.177028i	−0.918169	+	0.396190i	$0.870332\pi$
$104$	−51.4681	+	37.3937i	−0.494885	+	0.359555i
$105$		0			0
$106$	−159.745	+	51.9043i	−1.50703	+	0.489664i
$107$	91.5542	+	29.7478i	0.855646	+	0.278016i	0.703809	−	0.710389i	$-0.251481\pi$
$107$	91.5542	+	29.7478i	0.855646	+	0.278016i	0.151837	+	0.988405i	$0.451481\pi$
$108$	−35.4164	−	25.7315i	−0.327930	−	0.238255i
$109$			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
$112$	−37.6246	+	51.7858i	−0.335934	+	0.462374i
$113$	−22.1327	+	68.1176i	−0.195865	+	0.602810i	0.804100	+	0.594493i	$0.202647\pi$
$113$	−22.1327	+	68.1176i	−0.195865	+	0.602810i	−0.999965	+	0.00831694i	$0.997353\pi$
$114$	−32.1115	−	98.8289i	−0.281679	−	0.866920i
$115$		0			0
$116$	−117.687	−	161.982i	−1.01454	−	1.39640i
$117$	−93.4787	+	30.3731i	−0.798963	+	0.259599i
$118$	173.449	+	56.3571i	1.46991	+	0.477602i
$119$	158.262	+	114.984i	1.32994	+	0.966255i
$120$		0			0
$121$	115.371	−	36.4754i	0.953482	−	0.301450i
$122$	113.013			0.926337
$123$	131.305	−	180.726i	1.06752	−	1.46932i
$124$	17.5197	−	53.9202i	0.141288	−	0.434840i
$125$		0			0
$126$	140.436	−	102.033i	1.11457	−	0.809784i
$127$	15.8450	+	21.8088i	0.124764	+	0.171723i	0.866830	−	0.498604i	$-0.166154\pi$
$127$	15.8450	+	21.8088i	0.124764	+	0.171723i	−0.742066	+	0.670327i	$0.766154\pi$
$128$	−128.550	+	41.7685i	−1.00430	+	0.326316i
$129$	−141.803	−	46.0747i	−1.09925	−	0.357168i
$130$		0			0
$131$		−	88.8193i		−	0.678010i	−0.940785	−	0.339005i	$-0.889910\pi$
$131$		−	88.8193i		−	0.678010i	0.940785	−	0.339005i	$-0.110090\pi$
$132$	237.957	−	36.7202i	1.80271	−	0.278183i
$133$	−68.0132			−0.511377
$134$	−32.2361	+	44.3691i	−0.240568	+	0.331113i
$135$		0			0
$136$	33.9919	+	104.616i	0.249940	+	0.769237i
$137$	−97.1378	+	70.5747i	−0.709035	+	0.515144i	−0.882862	−	0.469632i	$-0.844387\pi$
$137$	−97.1378	+	70.5747i	−0.709035	+	0.515144i	0.173827	+	0.984776i	$0.444387\pi$
$138$	−183.666	−	252.794i	−1.33091	−	1.83184i
$139$	3.34501	−	1.08686i	0.0240648	−	0.00781914i	−0.296960	−	0.954890i	$-0.595973\pi$
$139$	3.34501	−	1.08686i	0.0240648	−	0.00781914i	0.321025	+	0.947071i	$0.395973\pi$
$140$		0			0
$141$	276.705	+	201.038i	1.96245	+	1.42580i
$142$			17.9111i			0.126134i
$143$	−70.6672	+	137.340i	−0.494176	+	0.960423i
$144$	−55.6099			−0.386180
$145$		0			0
$146$	−48.6656	+	149.777i	−0.333326	+	1.02587i
$147$	−19.6819	−	60.5746i	−0.133890	−	0.412072i
$148$	89.7386	−	65.1989i	0.606342	−	0.440533i
$149$	54.8460	+	75.4890i	0.368094	+	0.506638i	0.952381	−	0.304909i	$-0.0986260\pi$
$149$	54.8460	+	75.4890i	0.368094	+	0.506638i	−0.584288	+	0.811547i	$0.698626\pi$
$150$		0			0
$151$	93.2148	+	30.2873i	0.617316	+	0.200578i	0.600948	−	0.799288i	$-0.294790\pi$
$151$	93.2148	+	30.2873i	0.617316	+	0.200578i	0.0163680	+	0.999866i	$0.494790\pi$
$152$	−30.9402	−	22.4794i	−0.203554	−	0.147891i
$153$			169.949i			1.11078i
$154$	43.7426	−	269.252i	0.284043	−	1.74839i
$155$		0			0
$156$	−180.652	+	248.647i	−1.15803	+	1.59389i
$157$	53.2304	−	163.826i	0.339047	−	1.04348i	−0.625646	−	0.780107i	$-0.715165\pi$
$157$	53.2304	−	163.826i	0.339047	−	1.04348i	0.964694	−	0.263374i	$-0.0848353\pi$
$158$	−32.6393	−	100.453i	−0.206578	−	0.635782i
$159$	−176.610	+	128.315i	−1.11075	+	0.807010i
$160$		0			0
$161$	−194.505	+	63.1985i	−1.20811	+	0.392537i
$162$	−278.070	−	90.3504i	−1.71648	−	0.557718i
$163$	204.825	+	148.814i	1.25659	+	0.912968i	0.998585	−	0.0531744i	$-0.0169339\pi$
$163$	204.825	+	148.814i	1.25659	+	0.912968i	0.258008	+	0.966143i	$0.416934\pi$
$164$		−	305.604i		−	1.86344i
$165$		0			0
$166$	448.885			2.70413
$167$	−44.3090	+	60.9861i	−0.265323	+	0.365186i	−0.920804	−	0.390026i	$-0.872466\pi$
$167$	−44.3090	+	60.9861i	−0.265323	+	0.365186i	0.655481	+	0.755212i	$0.272466\pi$
$168$	45.1246	−	138.879i	0.268599	−	0.826662i
$169$	−8.70163	−	26.7809i	−0.0514889	−	0.158467i
$170$		0			0
$171$	−34.7304	−	47.8024i	−0.203102	−	0.279546i
$172$	−193.992	+	63.0318i	−1.12786	+	0.366464i
$173$	−106.578	−	34.6293i	−0.616058	−	0.200169i	−0.0156685	−	0.999877i	$-0.504988\pi$
$173$	−106.578	−	34.6293i	−0.616058	−	0.200169i	−0.600389	+	0.799708i	$0.704988\pi$
$174$	−364.413	−	264.762i	−2.09433	−	1.52162i
$175$		0			0
$176$	−62.0370	+	61.5459i	−0.352483	+	0.349693i
$177$	237.029			1.33915
$178$	−231.462	+	318.581i	−1.30035	+	1.78978i
$179$	−64.4321	+	198.302i	−0.359956	+	1.10783i	0.593124	+	0.805111i	$0.297894\pi$
$179$	−64.4321	+	198.302i	−0.359956	+	1.10783i	−0.953080	+	0.302719i	$0.902106\pi$
$180$		0			0
$181$	−64.7082	+	47.0133i	−0.357504	+	0.259742i	−0.752010	−	0.659151i	$-0.770916\pi$
$181$	−64.7082	+	47.0133i	−0.357504	+	0.259742i	0.394506	+	0.918893i	$0.370916\pi$
$182$	204.668	+	281.702i	1.12455	+	1.54781i
$183$	139.692	−	45.3887i	0.763344	−	0.248025i
$184$	−109.371	−	35.5369i	−0.594409	−	0.193135i
$185$		0			0
$186$		−	127.548i		−	0.685740i
$187$	188.090	+	189.591i	1.00583	+	1.01385i
$188$	467.904			2.48885
$189$	−37.8885	+	52.1491i	−0.200468	+	0.275921i
$190$		0			0
$191$	−26.9443	−	82.9259i	−0.141069	−	0.434167i	0.855415	−	0.517943i	$-0.173302\pi$
$191$	−26.9443	−	82.9259i	−0.141069	−	0.434167i	−0.996485	+	0.0837757i	$0.973302\pi$
$192$	−321.177	+	233.349i	−1.67280	+	1.21536i
$193$	−110.528	−	152.129i	−0.572683	−	0.788231i	0.420186	−	0.907438i	$-0.361965\pi$
$193$	−110.528	−	152.129i	−0.572683	−	0.788231i	−0.992869	+	0.119207i	$0.961965\pi$
$194$	−264.366	+	85.8976i	−1.36271	+	0.442771i
$195$		0			0
$196$	−70.4919	−	51.2153i	−0.359652	−	0.261303i
$197$			10.5087i			0.0533437i	0.999644	+	0.0266719i	$0.00849093\pi$
$197$			10.5087i			0.0533437i	−0.999644	+	0.0266719i	$0.991509\pi$
$198$	211.578	−	106.748i	1.06858	−	0.539129i
$199$	8.30806			0.0417490			0.0208745	−	0.999782i	$-0.493355\pi$
$199$	8.30806			0.0417490			0.0208745	+	0.999782i	$0.493355\pi$
$200$		0			0
$201$	−22.0263	+	67.7900i	−0.109584	+	0.337264i
$202$	−102.610	−	315.801i	−0.507970	−	1.56337i
$203$	−238.512	+	173.289i	−1.17493	+	0.853640i
$204$	312.361	+	429.928i	1.53118	+	2.10749i
$205$		0			0
$206$	56.1180	+	18.2339i	0.272418	+	0.0885139i
$207$	−143.741	−	104.434i	−0.694401	−	0.504512i
$208$		−	111.548i		−	0.536289i
$209$	−91.6494	−	14.8893i	−0.438514	−	0.0712409i
$210$		0			0
$211$	−45.0294	+	61.9777i	−0.213410	+	0.293733i	−0.902279	−	0.431152i	$-0.858107\pi$
$211$	−45.0294	+	61.9777i	−0.213410	+	0.293733i	0.688870	+	0.724885i	$0.258107\pi$
$212$	−92.2862	+	284.028i	−0.435312	+	1.33975i
$213$	7.19350	+	22.1393i	0.0337723	+	0.103940i
$214$	239.692	−	174.146i	1.12006	−	0.813768i
$215$		0			0
$216$	−34.4721	+	11.2007i	−0.159593	+	0.0518550i
$217$	−79.3951	−	25.7970i	−0.365876	−	0.118880i
$218$	52.4853	+	38.1328i	0.240758	+	0.174921i
$219$			204.680i			0.934613i
$220$		0			0
$221$	−340.902			−1.54254
$222$	146.679	−	201.886i	0.660715	−	0.909397i
$223$	−36.1190	+	111.163i	−0.161969	+	0.498488i	−0.998800	−	0.0489724i	$-0.984405\pi$
$223$	−36.1190	+	111.163i	−0.161969	+	0.498488i	0.836832	+	0.547460i	$0.184405\pi$
$224$	106.003	+	326.242i	0.473226	+	1.45644i
$225$		0			0
$226$	129.567	+	178.334i	0.573307	+	0.789089i
$227$	−368.761	+	119.818i	−1.62450	+	0.527831i	−0.972997	−	0.230818i	$-0.925860\pi$
$227$	−368.761	+	119.818i	−1.62450	+	0.527831i	−0.651500	+	0.758649i	$0.725860\pi$
$228$	−175.718	−	57.0943i	−0.770694	−	0.250414i
$229$	−112.172	−	81.4979i	−0.489835	−	0.355886i	0.315286	−	0.948997i	$-0.397900\pi$
$229$	−112.172	−	81.4979i	−0.489835	−	0.355886i	−0.805121	+	0.593111i	$0.797900\pi$
$230$		0			0
$231$	−54.0689	−	350.382i	−0.234064	−	1.51680i
$232$	−165.777			−0.714556
$233$	109.674	−	150.953i	0.470703	−	0.647867i	−0.505982	−	0.862544i	$-0.668870\pi$
$233$	109.674	−	150.953i	0.470703	−	0.647867i	0.976685	+	0.214677i	$0.0688699\pi$
$234$	−93.4787	+	287.698i	−0.399482	+	1.22948i
$235$		0			0
$236$	262.335	−	190.598i	1.11159	−	0.807618i
$237$	−80.6888	−	111.059i	−0.340459	−	0.468602i
$238$	572.599	−	186.049i	2.40588	−	0.781717i
$239$	−165.902	−	53.9047i	−0.694149	−	0.225543i	−0.0593698	−	0.998236i	$-0.518909\pi$
$239$	−165.902	−	53.9047i	−0.694149	−	0.225543i	−0.634780	+	0.772693i	$0.718909\pi$
$240$		0			0
$241$		−	229.308i		−	0.951484i	−0.879585	−	0.475742i	$-0.842180\pi$
$241$		−	229.308i		−	0.951484i	0.879585	−	0.475742i	$-0.157820\pi$
$242$	117.889	−	353.248i	0.487143	−	1.45970i
$243$	−308.000			−1.26749
$244$	118.108	−	162.562i	0.484051	−	0.666239i
$245$		0			0
$246$	−212.456	−	653.872i	−0.863642	−	2.65802i
$247$	95.8870	−	69.6660i	0.388206	−	0.282048i
$248$	−27.5917	−	37.9767i	−0.111257	−	0.153132i
$249$	554.853	−	180.283i	2.22832	−	0.724027i
$250$		0			0
$251$	85.7279	+	62.2850i	0.341546	+	0.248147i	0.745314	−	0.666714i	$-0.232300\pi$
$251$	85.7279	+	62.2850i	0.341546	+	0.248147i	−0.403768	+	0.914861i	$0.632300\pi$
$252$		−	308.641i		−	1.22477i
$253$	−275.936	+	42.5808i	−1.09065	+	0.168303i
$254$	82.9656			0.326636
$255$		0			0
$256$	−5.87132	+	18.0701i	−0.0229349	+	0.0705862i
$257$	79.6362	+	245.095i	0.309869	+	0.953677i	0.977815	+	0.209468i	$0.0671733\pi$
$257$	79.6362	+	245.095i	0.309869	+	0.953677i	−0.667947	+	0.744209i	$0.732827\pi$
$258$	−371.246	+	269.726i	−1.43894	+	1.04545i
$259$	−96.0025	−	132.136i	−0.370666	−	0.510178i
$260$		0			0
$261$	−243.589	−	79.1467i	−0.933290	−	0.303244i
$262$	−221.151	−	160.676i	−0.844087	−	0.613265i
$263$		−	290.347i		−	1.10398i	−0.833851	−	0.551990i	$-0.813869\pi$
$263$		−	290.347i		−	1.10398i	0.833851	−	0.551990i	$-0.186131\pi$
$264$	91.2098	−	177.265i	0.345492	−	0.671457i
$265$		0			0
$266$	−123.037	+	169.346i	−0.462545	+	0.636638i
$267$	−158.154	+	486.748i	−0.592337	+	1.82303i
$268$	30.1327	+	92.7390i	0.112436	+	0.346041i
$269$	267.615	−	194.434i	0.994851	−	0.722802i	0.0338730	−	0.999426i	$-0.489216\pi$
$269$	267.615	−	194.434i	0.994851	−	0.722802i	0.960978	+	0.276625i	$0.0892158\pi$
$270$		0			0
$271$	206.661	−	67.1481i	0.762585	−	0.247779i	0.0981974	−	0.995167i	$-0.468692\pi$
$271$	206.661	−	67.1481i	0.762585	−	0.247779i	0.664388	+	0.747388i	$0.268692\pi$
$272$	−183.435	−	59.6015i	−0.674392	−	0.219123i
$273$	366.122	+	266.003i	1.34110	+	0.974369i
$274$			369.534i			1.34866i
$275$		0			0
$276$	−555.574			−2.01295
$277$	263.699	−	362.950i	0.951980	−	1.31029i	0.00133803	−	0.999999i	$-0.499574\pi$
$277$	263.699	−	362.950i	0.951980	−	1.31029i	0.950642	−	0.310289i	$-0.100426\pi$
$278$	3.34501	−	10.2949i	0.0120324	−	0.0370320i
$279$	−22.4114	−	68.9751i	−0.0803275	−	0.247223i
$280$		0			0
$281$	55.0658	+	75.7915i	0.195964	+	0.269721i	0.895679	−	0.444701i	$-0.146690\pi$
$281$	55.0658	+	75.7915i	0.195964	+	0.269721i	−0.699716	+	0.714421i	$0.746690\pi$
$282$	1001.13	−	325.286i	3.55010	−	1.15350i
$283$	278.002	+	90.3283i	0.982339	+	0.319181i	0.755787	−	0.654818i	$-0.227255\pi$
$283$	278.002	+	90.3283i	0.982339	+	0.319181i	0.226552	+	0.973999i	$0.427255\pi$
$284$	25.7639	+	18.7186i	0.0907181	+	0.0659105i
$285$		0			0
$286$	214.126	+	424.405i	0.748691	+	1.48393i
$287$	−449.989			−1.56791
$288$	−175.167	+	241.096i	−0.608217	+	0.837139i
$289$	−92.8419	+	285.738i	−0.321252	+	0.988713i
$290$		0			0
$291$	−292.276	+	212.351i	−1.00438	+	0.729727i
$292$	164.586	+	226.533i	0.563649	+	0.775796i
$293$	−329.140	+	106.944i	−1.12335	+	0.364997i	−0.811044	−	0.584986i	$-0.801100\pi$
$293$	−329.140	+	106.944i	−1.12335	+	0.364997i	−0.312302	+	0.949983i	$0.601100\pi$
$294$	−186.430	−	60.5746i	−0.634114	−	0.206036i
$295$		0			0
$296$		−	91.8410i		−	0.310274i
$297$	−62.4721	+	61.9777i	−0.210344	+	0.208679i
$298$	287.177			0.963682
$299$	209.485	−	288.331i	0.700618	−	0.964318i
$300$		0			0
$301$	92.8115	+	285.645i	0.308344	+	0.948985i
$302$	244.039	−	177.305i	0.808078	−	0.587103i
$303$	−253.666	−	349.141i	−0.837180	−	1.15228i
$304$	63.7755	−	20.7219i	0.209788	−	0.0681642i
$305$		0			0
$306$	423.156	+	307.441i	1.38286	+	1.00471i
$307$			180.826i			0.589009i	0.955650	+	0.294505i	$0.0951546\pi$
$307$			180.826i			0.589009i	−0.955650	+	0.294505i	$0.904845\pi$
$308$	−341.587	−	344.312i	−1.10905	−	1.11790i
$309$	76.6888			0.248184
$310$		0			0
$311$	−115.313	+	354.897i	−0.370782	+	1.14115i	0.575499	+	0.817802i	$0.304808\pi$
$311$	−115.313	+	354.897i	−0.370782	+	1.14115i	−0.946281	+	0.323346i	$0.895192\pi$
$312$	78.6362	+	242.017i	0.252039	+	0.775697i
$313$	256.753	−	186.542i	0.820296	−	0.595980i	−0.0965012	−	0.995333i	$-0.530765\pi$
$313$	256.753	−	186.542i	0.820296	−	0.595980i	0.916797	+	0.399353i	$0.130765\pi$
$314$	−311.616	−	428.903i	−0.992409	−	1.36593i
$315$		0			0
$316$	−178.607	−	58.0329i	−0.565211	−	0.183648i
$317$	222.314	+	161.521i	0.701306	+	0.509529i	0.880357	−	0.474311i	$-0.157303\pi$
$317$	222.314	+	161.521i	0.701306	+	0.509529i	−0.179051	+	0.983840i	$0.557303\pi$
$318$			671.864i			2.11278i
$319$	−359.336	+	181.296i	−1.12645	+	0.568327i
$320$		0			0
$321$	226.334	−	311.523i	0.705091	−	0.970475i
$322$	−194.505	+	598.625i	−0.604053	+	1.85908i
$323$	−63.3282	−	194.904i	−0.196062	−	0.603418i
$324$	−420.570	+	305.562i	−1.29806	+	0.943092i
$325$		0			0
$326$	741.063	−	240.786i	2.27320	−	0.738607i
$327$	80.1904	+	26.0554i	0.245231	+	0.0796802i
$328$	−204.707	−	148.728i	−0.624106	−	0.453439i
$329$		−	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	$0.286372\pi$
$332$	469.123	−	645.693i	1.41302	−	1.94486i
$333$	43.8475	−	134.949i	0.131674	−	0.405252i
$334$	71.6935	+	220.650i	0.214651	+	0.660628i
$335$		0			0
$336$	150.498	+	207.143i	0.447912	+	0.616498i
$337$	440.410	−	143.098i	1.30686	−	0.424623i	0.428894	−	0.903355i	$-0.358903\pi$
$337$	440.410	−	143.098i	1.30686	−	0.424623i	0.877961	+	0.478732i	$0.158903\pi$
$338$	−82.4230	−	26.7809i	−0.243855	−	0.0792333i
$339$	231.777	+	168.396i	0.683708	+	0.496743i
$340$		0			0
$341$	−101.339	−	52.1432i	−0.297183	−	0.152913i
$342$	−181.851			−0.531728
$343$	156.655	−	215.617i	0.456720	−	0.628621i
$344$	−52.1885	+	160.620i	−0.151711	+	0.466917i
$345$		0			0
$346$	−279.025	+	202.723i	−0.806430	+	0.585906i
$347$	100.498	+	138.324i	0.289621	+	0.398629i	0.928891	−	0.370353i	$-0.120763\pi$
$347$	100.498	+	138.324i	0.289621	+	0.398629i	−0.639270	+	0.768982i	$0.720763\pi$
$348$	−761.686	+	247.487i	−2.18875	+	0.711169i
$349$	−164.289	−	53.3806i	−0.470741	−	0.152953i	0.0640335	−	0.997948i	$-0.479604\pi$
$349$	−164.289	−	53.3806i	−0.470741	−	0.152953i	−0.534775	+	0.844995i	$0.679604\pi$
$350$		0			0
$351$		−	112.331i		−	0.320030i
$352$	71.4205	+	462.825i	0.202899	+	1.31484i
$353$	494.535			1.40095			0.700474	−	0.713678i	$-0.252972\pi$
$353$	494.535			1.40095			0.700474	+	0.713678i	$0.252972\pi$
$354$	428.790	−	590.179i	1.21127	−	1.66717i
$355$		0			0
$356$	216.360	+	665.888i	0.607753	+	1.87047i
$357$	633.050	−	459.937i	1.77325	−	1.28834i
$358$	377.192	+	519.160i	1.05361	+	1.45017i
$359$	146.418	−	47.5742i	0.407850	−	0.132519i	−0.0979045	−	0.995196i	$-0.531214\pi$
$359$	146.418	−	47.5742i	0.407850	−	0.132519i	0.505755	+	0.862677i	$0.331214\pi$
$360$		0			0
$361$	−234.412	−	170.311i	−0.649342	−	0.471774i
$362$			246.165i			0.680013i
$363$	3.84597	−	483.985i	0.0105950	−	1.33329i
$364$	619.105			1.70084
$365$		0			0
$366$	139.692	−	429.928i	0.381672	−	1.17467i
$367$	57.3820	+	176.604i	0.156354	+	0.481209i	0.998296	−	0.0583604i	$-0.0185872\pi$
$367$	57.3820	+	176.604i	0.156354	+	0.481209i	−0.841941	+	0.539569i	$0.818587\pi$
$368$	163.131	−	118.522i	0.443291	−	0.322070i
$369$	−229.784	−	316.270i	−0.622720	−	0.857100i
$370$		0			0
$371$	418.218	+	135.887i	1.12727	+	0.366273i
$372$	−183.469	−	133.298i	−0.493196	−	0.358328i
$373$			268.844i			0.720760i	0.932806	+	0.360380i	$0.117353\pi$
$373$			268.844i			0.720760i	−0.932806	+	0.360380i	$0.882647\pi$
$374$	812.320	−	125.352i	2.17198	−	0.335167i
$375$		0			0
$376$	227.714	−	313.422i	0.605623	−	0.833568i
$377$	158.761	−	488.616i	0.421116	−	1.29606i
$378$	61.3050	+	188.677i	0.162182	+	0.499146i
$379$	243.935	−	177.229i	0.643627	−	0.467622i	−0.217467	−	0.976068i	$-0.569780\pi$
$379$	243.935	−	177.229i	0.643627	−	0.467622i	0.861094	+	0.508445i	$0.169780\pi$
$380$		0			0
$381$	102.551	−	33.3209i	0.269163	−	0.0874563i
$382$	−255.220	−	82.9259i	−0.668115	−	0.217084i
$383$	−393.892	−	286.179i	−1.02844	−	0.747204i	−0.0604431	−	0.998172i	$-0.519251\pi$
$383$	−393.892	−	286.179i	−1.02844	−	0.747204i	−0.967996	+	0.250967i	$0.919251\pi$
$384$			540.662i			1.40797i
$385$		0			0
$386$	−578.731			−1.49930
$387$	−153.369	+	211.094i	−0.396302	+	0.545463i
$388$	−152.726	+	470.043i	−0.393625	+	1.21145i
$389$	118.077	+	363.404i	0.303540	+	0.934200i	0.980218	+	0.197921i	$0.0634189\pi$
$389$	118.077	+	363.404i	0.303540	+	0.934200i	−0.676678	+	0.736279i	$0.736581\pi$
$390$		0			0
$391$	−362.214	−	498.544i	−0.926377	−	1.27505i
$392$	−68.6124	+	22.2935i	−0.175032	+	0.0568712i
$393$	−337.889	−	109.787i	−0.859767	−	0.279355i
$394$	26.1656	+	19.0104i	0.0664102	+	0.0482499i
$395$		0			0
$396$	67.5673	−	415.902i	0.170625	−	1.05026i
$397$	−668.123			−1.68293			−0.841465	−	0.540311i	$-0.818307\pi$
$397$	−668.123			−1.68293			−0.841465	+	0.540311i	$0.818307\pi$
$398$	15.0294	−	20.6862i	0.0377624	−	0.0519754i
$399$	−84.0689	+	258.737i	−0.210699	+	0.648465i
$400$		0			0
$401$	−291.301	+	211.642i	−0.726436	+	0.527787i	−0.888434	−	0.459004i	$-0.848206\pi$
$401$	−291.301	+	211.642i	−0.726436	+	0.527787i	0.161998	+	0.986791i	$0.448206\pi$
$402$	128.944	+	177.477i	0.320757	+	0.441484i
$403$	138.358	−	44.9551i	0.343319	−	0.111551i
$404$	−561.495	−	182.441i	−1.38984	−	0.451586i
$405$		0			0
$406$			907.352i			2.23486i
$407$	−100.439	−	199.073i	−0.246778	−	0.489124i
$408$	440.000			1.07843
$409$	−21.2846	+	29.2958i	−0.0520406	+	0.0716278i	−0.834244	−	0.551395i	$-0.814096\pi$
$409$	−21.2846	+	29.2958i	−0.0520406	+	0.0716278i	0.782204	+	0.623023i	$0.214096\pi$
$410$		0			0
$411$	148.413	+	456.769i	0.361103	+	1.11136i
$412$	84.8763	−	61.6663i	0.206011	−	0.149675i
$413$	−280.647	−	386.277i	−0.679532	−	0.935296i
$414$	−520.060	+	168.978i	−1.25618	+	0.408159i
$415$		0			0
$416$	−483.616	−	351.368i	−1.16254	−	0.844633i
$417$		−	14.0686i		−	0.0337377i
$418$	−202.868	+	201.263i	−0.485331	+	0.481489i
$419$	−423.543			−1.01084			−0.505421	−	0.862873i	$-0.668663\pi$
$419$	−423.543			−1.01084			−0.505421	+	0.862873i	$0.668663\pi$
$420$		0			0
$421$	211.289	−	650.280i	0.501873	−	1.54461i	−0.304091	−	0.952643i	$-0.598353\pi$
$421$	211.289	−	650.280i	0.501873	−	1.54461i	0.805964	−	0.591964i	$-0.201647\pi$
$422$	72.8591	+	224.237i	0.172652	+	0.531368i
$423$	484.234	−	351.817i	1.14476	−	0.831718i
$424$	145.341	+	200.045i	0.342785	+	0.471803i
$425$		0			0
$426$	68.1378	+	22.1393i	0.159948	+	0.0519702i
$427$	−239.366	−	173.909i	−0.560575	−	0.407282i
$428$		−	526.779i		−	1.23079i
$429$	435.125	+	438.596i	1.01428	+	1.02237i
$430$		0			0
$431$	75.8653	−	104.420i	0.176022	−	0.242273i	−0.711886	−	0.702295i	$-0.752159\pi$
$431$	75.8653	−	104.420i	0.176022	−	0.242273i	0.887907	+	0.460022i	$0.152159\pi$
$432$	19.6393	−	60.4436i	0.0454614	−	0.139916i
$433$	170.382	+	524.382i	0.393492	+	1.21104i	0.930130	+	0.367231i	$0.119694\pi$
$433$	170.382	+	524.382i	0.393492	+	1.21104i	−0.536638	+	0.843813i	$0.680306\pi$
$434$	−207.859	+	151.018i	−0.478938	+	0.347969i
$435$		0			0
$436$	109.703	−	35.6447i	0.251613	−	0.0817540i
$437$	203.763	+	66.2066i	0.466277	+	0.151503i
$438$	509.633	+	370.270i	1.16355	+	0.845366i
$439$			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
$442$	−616.697	+	848.811i	−1.39524	+	1.92039i
$443$	−30.6738	+	94.4041i	−0.0692410	+	0.213102i	−0.979689	−	0.200521i	$-0.935737\pi$
$443$	−30.6738	+	94.4041i	−0.0692410	+	0.213102i	0.910448	+	0.413622i	$0.135737\pi$
$444$	−137.108	−	421.976i	−0.308803	−	0.950397i
$445$		0			0
$446$	211.444	+	291.028i	0.474090	+	0.652529i
$447$	354.971	−	115.337i	0.794118	−	0.258024i
$448$	760.559	+	247.120i	1.69768	+	0.551608i
$449$	−110.271	−	80.1169i	−0.245593	−	0.178434i	0.458178	−	0.888860i	$-0.348502\pi$
$449$	−110.271	−	80.1169i	−0.245593	−	0.178434i	−0.703772	+	0.710426i	$0.748502\pi$
$450$		0			0
$451$	−606.371	−	98.5109i	−1.34450	−	0.218428i
$452$	391.931			0.867104
$453$	230.440	−	317.173i	0.508697	−	0.700161i
$454$	−368.761	+	1134.93i	−0.812249	+	2.49984i
$455$		0			0
$456$	−123.761	+	89.9175i	−0.271405	+	0.197188i
$457$	18.1014	+	24.9144i	0.0396092	+	0.0545174i	0.828362	−	0.560193i	$-0.189273\pi$
$457$	18.1014	+	24.9144i	0.0396092	+	0.0545174i	−0.788753	+	0.614710i	$0.789273\pi$
$458$	−405.843	+	131.866i	−0.886120	+	0.287918i
$459$	−184.721	−	60.0196i	−0.402443	−	0.130762i
$460$		0			0
$461$			142.653i			0.309442i	0.987958	+	0.154721i	$0.0494478\pi$
$461$			142.653i			0.309442i	−0.987958	+	0.154721i	$0.950552\pi$
$462$	−970.227	−	499.221i	−2.10006	−	1.08056i
$463$	−490.864			−1.06018			−0.530091	−	0.847941i	$-0.677842\pi$
$463$	−490.864			−1.06018			−0.530091	+	0.847941i	$0.677842\pi$
$464$	170.854	−	235.160i	0.368220	−	0.506811i
$465$		0			0
$466$	−177.456	−	546.153i	−0.380807	−	1.17200i
$467$	−613.182	+	445.503i	−1.31302	+	0.953968i	−0.313033	+	0.949742i	$0.601345\pi$
$467$	−613.182	+	445.503i	−1.31302	+	0.953968i	−0.999991	+	0.00422562i	$0.998655\pi$
$468$	316.142	+	435.132i	0.675517	+	0.929769i
$469$	136.554	−	44.3691i	0.291160	−	0.0946037i
$470$		0			0
$471$	−557.437	−	405.001i	−1.18352	−	0.859875i
$472$		−	268.481i		−	0.568816i
$473$	62.5329	+	405.231i	0.132205	+	0.856725i
$474$	−422.492			−0.891334
$475$		0			0
$476$	330.795	−	1018.08i	0.694948	−	2.13883i
$477$	118.053	+	363.330i	0.247491	+	0.761699i
$478$	−434.336	+	315.564i	−0.908653	+	0.660175i
$479$	−364.989	−	502.364i	−0.761981	−	1.04878i	−0.997047	−	0.0767971i	$-0.975531\pi$
$479$	−364.989	−	502.364i	−0.761981	−	1.04878i	0.235066	−	0.971979i	$-0.424469\pi$
$480$		0			0
$481$	270.694	+	87.9540i	0.562774	+	0.182856i
$482$	−570.953	−	414.821i	−1.18455	−	0.860625i
$483$			818.059i			1.69370i
$484$	−384.920	−	538.749i	−0.795290	−	1.11312i
$485$		0			0
$486$	−557.177	+	766.889i	−1.14646	+	1.57796i
$487$	121.664	−	374.442i	0.249823	−	0.768876i	−0.744983	−	0.667084i	$-0.767542\pi$
$487$	121.664	−	374.442i	0.249823	−	0.768876i	0.994806	−	0.101792i	$-0.0324576\pi$
$488$	−51.4114	−	158.228i	−0.105351	−	0.324238i
$489$	819.299	−	595.255i	1.67546	−	1.21729i
$490$		0			0
$491$	−616.943	+	200.457i	−1.25650	+	0.408262i	−0.860247	−	0.509878i	$-0.829691\pi$
$491$	−616.943	+	200.457i	−1.25650	+	0.408262i	−0.396256	+	0.918140i	$0.629691\pi$
$492$	−1162.59	−	377.748i	−2.36298	−	0.767780i
$493$	−718.673	−	522.146i	−1.45775	−	1.05912i
$494$		−	364.776i		−	0.738413i
$495$		0			0
$496$	82.3081			0.165944
$497$	27.5623	−	37.9363i	0.0554574	−	0.0763305i
$498$	554.853	−	1707.66i	1.11416	−	3.42904i
$499$	−221.573	−	681.931i	−0.444034	−	1.36660i	−0.883540	−	0.468356i	$-0.844846\pi$
$499$	−221.573	−	681.931i	−0.444034	−	1.36660i	0.439506	−	0.898240i	$-0.355154\pi$
$500$		0			0
$501$	177.236	+	243.945i	0.353765	+	0.486915i
$502$	310.167	−	100.779i	0.617862	−	0.200755i
$503$	−596.635	−	193.858i	−1.18615	−	0.385404i	−0.351503	−	0.936187i	$-0.614329\pi$
$503$	−596.635	−	193.858i	−1.18615	−	0.385404i	−0.834649	+	0.550782i	$0.814329\pi$
$504$	−206.741	−	150.206i	−0.410201	−	0.298028i
$505$		0			0
$506$	−393.150	+	764.081i	−0.776977	+	1.51004i
$507$	−112.636			−0.222162
$508$	86.7061	−	119.341i	0.170681	−	0.234923i
$509$	−79.8228	+	245.669i	−0.156823	+	0.482651i	−0.998341	−	0.0575779i	$-0.981662\pi$
$509$	−79.8228	+	245.669i	−0.156823	+	0.482651i	0.841518	+	0.540229i	$0.181662\pi$
$510$		0			0
$511$	333.559	−	242.345i	0.652758	−	0.474256i
$512$	−283.422	−	390.097i	−0.553559	−	0.761908i
$513$	64.2229	−	20.8673i	0.125191	−	0.0406770i
$514$	754.325	+	245.095i	1.46756	+	0.476839i
$515$		0			0
$516$			815.900i			1.58120i
$517$	150.828	−	928.400i	0.291737	−	1.79575i
$518$	−502.676			−0.970416
$519$	−263.475	+	362.643i	−0.507659	+	0.698733i
$520$		0			0
$521$	92.8597	+	285.793i	0.178234	+	0.548547i	0.999766	−	0.0216146i	$-0.00688069\pi$
$521$	92.8597	+	285.793i	0.178234	+	0.548547i	−0.821533	+	0.570161i	$0.806881\pi$
$522$	−637.723	+	463.333i	−1.22169	+	0.887611i
$523$	−247.497	−	340.650i	−0.473225	−	0.651338i	0.503961	−	0.863727i	$-0.331876\pi$
$523$	−247.497	−	340.650i	−0.473225	−	0.651338i	−0.977185	+	0.212389i	$0.931876\pi$
$524$	−462.243	+	150.192i	−0.882143	+	0.286626i
$525$		0			0
$526$	−722.934	−	525.242i	−1.37440	−	0.998559i
$527$		−	251.541i		−	0.477308i
$528$	157.453	+	312.078i	0.298206	+	0.591056i
$529$	115.244			0.217853
$530$		0			0
$531$	128.181	−	394.500i	0.241395	−	0.742937i
$532$	115.009	+	353.962i	0.216183	+	0.665341i
$533$	634.408	−	460.924i	1.19026	−	0.864773i
$534$	925.850	+	1274.32i	1.73380	+	2.38637i
$535$		0			0
$536$	76.7852	+	24.9490i	0.143256	+	0.0465467i
$537$	674.741	+	490.228i	1.25650	+	0.912902i
$538$		−	1018.07i		−	1.89232i
$539$	−124.343	+	123.359i	−0.230692	+	0.228866i
$540$		0			0
$541$	112.764	−	155.206i	0.208436	−	0.286888i	−0.691981	−	0.721916i	$-0.743262\pi$
$541$	112.764	−	155.206i	0.208436	−	0.286888i	0.900417	+	0.435028i	$0.143262\pi$
$542$	206.661	−	636.036i	0.381293	−	1.17350i
$543$	98.8653	+	304.276i	0.182072	+	0.560361i
$544$	−836.205	+	607.539i	−1.53714	+	1.11680i
$545$		0			0
$546$	1324.64	−	430.402i	2.42608	−	0.788281i
$547$	−189.538	−	61.5846i	−0.346504	−	0.112586i	0.130594	−	0.991436i	$-0.458312\pi$
$547$	−189.538	−	61.5846i	−0.346504	−	0.112586i	−0.477099	+	0.878850i	$0.658312\pi$
$548$	531.551	+	386.194i	0.969984	+	0.704734i
$549$		−	257.041i		−	0.468199i
$550$		0			0
$551$	308.849			0.560525
$552$	−270.381	+	372.147i	−0.489820	+	0.674180i
$553$	−85.4508	+	262.991i	−0.154522	+	0.475571i
$554$	−426.673	−	1313.16i	−0.770168	−	2.37033i
$555$		0			0
$556$	−11.3127	−	15.5706i	−0.0203466	−	0.0280047i
$557$	−720.414	+	234.077i	−1.29338	+	0.420245i	−0.873274	−	0.487229i	$-0.838008\pi$
$557$	−720.414	+	234.077i	−1.29338	+	0.420245i	−0.420108	+	0.907474i	$0.638008\pi$
$558$	−212.284	−	68.9751i	−0.380437	−	0.123611i
$559$	−423.435	−	307.643i	−0.757486	−	0.550346i
$560$		0			0
$561$	953.738	−	481.190i	1.70007	−	0.857737i
$562$	288.328			0.513039
$563$	−89.0871	+	122.618i	−0.158236	+	0.217794i	−0.880773	−	0.473539i	$-0.842976\pi$
$563$	−89.0871	+	122.618i	−0.158236	+	0.217794i	0.722536	+	0.691333i	$0.242976\pi$
$564$	578.361	−	1780.01i	1.02546	−	3.15605i
$565$		0			0
$566$	727.818	−	528.791i	1.28590	−	0.934260i
$567$	449.926	+	619.271i	0.793521	+	1.09219i
$568$	25.0770	−	8.14802i	0.0441497	−	0.0143451i
$569$	836.163	+	271.686i	1.46953	+	0.477480i	0.930967	−	0.365104i	$-0.118967\pi$
$569$	836.163	+	271.686i	1.46953	+	0.477480i	0.538565	+	0.842584i	$0.318967\pi$
$570$		0			0
$571$			324.644i			0.568554i	0.958742	+	0.284277i	$0.0917536\pi$
$571$			324.644i			0.568554i	−0.958742	+	0.284277i	$0.908246\pi$
$572$	834.259	+	135.534i	1.45850	+	0.236947i
$573$	−348.774			−0.608681
$574$	−814.037	+	1120.43i	−1.41818	+	1.95196i
$575$		0			0
$576$	214.688	+	660.741i	0.372722	+	1.14712i
$577$	−421.177	+	306.003i	−0.729943	+	0.530335i	−0.889545	−	0.456847i	$-0.848979\pi$
$577$	−421.177	+	306.003i	−0.729943	+	0.530335i	0.159602	+	0.987181i	$0.448979\pi$
$578$	543.506	+	748.072i	0.940322	+	1.29424i
$579$	−715.351	+	232.432i	−1.23549	+	0.401437i
$580$		0			0
$581$	−950.755	−	690.764i	−1.63641	−	1.18892i
$582$			1111.88i			1.91045i
$583$	533.811	+	274.667i	0.915628	+	0.471127i
$584$	231.840			0.396986
$585$		0			0
$586$	−329.140	+	1012.99i	−0.561673	+	1.72865i
$587$	305.959	+	941.646i	0.521225	+	1.60417i	0.771661	+	0.636034i	$0.219426\pi$
$587$	305.959	+	941.646i	0.521225	+	1.60417i	−0.250436	+	0.968133i	$0.580574\pi$
$588$	−281.967	+	204.861i	−0.479537	+	0.348404i
$589$	51.4044	+	70.7521i	0.0872741	+	0.120122i
$590$		0			0
$591$	39.9775	+	12.9895i	0.0676439	+	0.0219788i
$592$	130.280	+	94.6537i	0.220067	+	0.159888i
$593$			289.152i			0.487609i	0.969824	+	0.243804i	$0.0783955\pi$
$593$			289.152i			0.487609i	−0.969824	+	0.243804i	$0.921604\pi$
$594$	41.3050	+	267.668i	0.0695370	+	0.450619i
$595$		0			0
$596$	300.125	−	413.086i	0.503565	−	0.693097i
$597$	10.2693	−	31.6057i	0.0172015	−	0.0529409i
$598$	−338.953	−	1043.19i	−0.566812	−	1.74447i
$599$	−674.089	+	489.754i	−1.12536	+	0.817620i	−0.985013	−	0.172483i	$-0.944821\pi$
$599$	−674.089	+	489.754i	−1.12536	+	0.817620i	−0.140345	+	0.990103i	$0.544821\pi$
$600$		0			0
$601$	−89.9741	+	29.2343i	−0.149707	+	0.0486428i	−0.382912	−	0.923785i	$-0.625079\pi$
$601$	−89.9741	+	29.2343i	−0.149707	+	0.0486428i	0.233205	+	0.972428i	$0.425079\pi$
$602$	879.123	+	285.645i	1.46034	+	0.474493i
$603$	100.915	+	73.3189i	0.167355	+	0.121590i
$604$		−	536.334i		−	0.887970i
$605$		0			0
$606$	−1328.21			−2.19177
$607$	124.839	−	171.826i	0.205666	−	0.283074i	−0.693707	−	0.720257i	$-0.744024\pi$
$607$	124.839	−	171.826i	0.205666	−	0.283074i	0.899373	+	0.437183i	$0.144024\pi$
$608$	111.048	−	341.770i	0.182645	−	0.562123i
$609$	364.413	+	1121.55i	0.598380	+	1.84162i
$610$		0			0
$611$	705.710	+	971.327i	1.15501	+	1.58973i
$612$	884.468	−	287.381i	1.44521	−	0.469577i
$613$	750.498	+	243.852i	1.22430	+	0.397801i	0.848648	−	0.528958i	$-0.177417\pi$
$613$	750.498	+	243.852i	1.22430	+	0.397801i	0.375656	+	0.926759i	$0.377417\pi$
$614$	450.238	+	327.117i	0.733287	+	0.532764i
$615$		0			0
$616$	−396.875	+	61.2434i	−0.644277	+	0.0994211i
$617$	−181.544			−0.294237			−0.147118	−	0.989119i	$-0.547000\pi$
$617$	−181.544			−0.294237			−0.147118	+	0.989119i	$0.547000\pi$
$618$	138.731	−	190.947i	0.224484	−	0.308976i
$619$	−11.1606	+	34.3488i	−0.0180301	+	0.0554908i	−0.959667	−	0.281140i	$-0.909287\pi$
$619$	−11.1606	+	34.3488i	−0.0180301	+	0.0554908i	0.941637	+	0.336631i	$0.109287\pi$
$620$		0			0
$621$	164.276	−	119.353i	0.264534	−	0.192195i
$622$	675.055	+	929.133i	1.08530	+	1.49378i
$623$	980.491	−	318.581i	1.57382	−	0.511366i
$624$	−424.354	−	137.881i	−0.680055	−	0.220963i
$625$		0			0
$626$		−	976.745i		−	1.56030i
$627$	−169.927	+	330.251i	−0.271016	+	0.526716i
$628$	−942.616			−1.50098
$629$	289.271	−	398.147i	0.459890	−	0.632984i
$630$		0			0
$631$	311.846	+	959.763i	0.494209	+	1.52102i	0.818186	+	0.574954i	$0.194980\pi$
$631$	311.846	+	959.763i	0.494209	+	1.52102i	−0.323976	+	0.946065i	$0.605020\pi$
$632$	−125.795	+	91.3956i	−0.199043	+	0.144613i
$633$	180.118	+	247.911i	0.284546	+	0.391644i
$634$	804.340	−	261.346i	1.26867	−	0.412217i
$635$		0			0
$636$	966.433	+	702.155i	1.51955	+	1.10402i
$637$		−	223.580i		−	0.350989i
$638$	−198.636	+	1222.68i	−0.311342	+	1.91642i
$639$	40.7376			0.0637521
$640$		0			0
$641$	−33.2415	+	102.307i	−0.0518588	+	0.159605i	−0.973632	−	0.228125i	$-0.926741\pi$
$641$	−33.2415	+	102.307i	−0.0518588	+	0.159605i	0.921773	+	0.387730i	$0.126741\pi$
$642$	−366.217	−	1127.10i	−0.570431	−	1.75561i
$643$	−21.8723	+	15.8911i	−0.0340160	+	0.0247141i	−0.604663	−	0.796481i	$-0.706692\pi$
$643$	−21.8723	+	15.8911i	−0.0340160	+	0.0247141i	0.570647	+	0.821195i	$0.306692\pi$
$644$	657.809	+	905.397i	1.02144	+	1.40590i
$645$		0			0
$646$	−599.853	−	194.904i	−0.928565	−	0.301709i
$647$	−903.123	−	656.158i	−1.39586	−	1.01415i	−0.995193	−	0.0979314i	$-0.968777\pi$
$647$	−903.123	−	656.158i	−1.39586	−	1.01415i	−0.400670	−	0.916222i	$-0.631223\pi$
$648$			430.423i			0.664233i
$649$	−293.615	−	581.957i	−0.452412	−	0.896698i
$650$		0			0
$651$	−196.276	+	270.150i	−0.301499	+	0.414977i
$652$	428.118	−	1317.61i	0.656623	−	2.02088i
$653$	338.002	+	1040.26i	0.517615	+	1.59305i	0.778474	+	0.627677i	$0.215994\pi$
$653$	338.002	+	1040.26i	0.517615	+	1.59305i	−0.260859	+	0.965377i	$0.584006\pi$
$654$	209.941	−	152.531i	0.321011	−	0.233228i
$655$		0			0
$656$	421.952	−	137.100i	0.643219	−	0.208995i
$657$	340.659	+	110.687i	0.518507	+	0.168473i
$658$	−1715.46	−	1246.35i	−2.60708	−	1.89416i
$659$			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	$0.404891\pi$
$662$	744.737	−	1025.04i	1.12498	−	1.54840i
$663$	−421.378	+	1296.87i	−0.635562	+	1.95606i
$664$	−204.205	−	628.478i	−0.307537	−	0.946502i
$665$		0			0
$666$	−256.688	−	353.301i	−0.385417	−	0.530481i
$667$	883.251	−	286.986i	1.32421	−	0.430263i
$668$	392.317	+	127.471i	0.587300	+	0.190825i
$669$	378.243	+	274.810i	0.565386	+	0.410777i
$670$		0			0
$671$	−284.479	−	286.749i	−0.423963	−	0.427345i
$672$	1372.13			2.04185
$673$	−602.060	+	828.664i	−0.894591	+	1.23130i	0.0775708	+	0.996987i	$0.475284\pi$
$673$	−602.060	+	828.664i	−0.894591	+	1.23130i	−0.972162	+	0.234312i	$0.924716\pi$
$674$	440.410	−	1355.44i	0.653428	−	2.01104i
$675$		0			0
$676$	−124.662	+	90.5719i	−0.184411	+	0.133982i
$677$	−145.396	−	200.121i	−0.214766	−	0.295599i	0.688019	−	0.725693i	$-0.258481\pi$
$677$	−145.396	−	200.121i	−0.214766	−	0.295599i	−0.902784	+	0.430093i	$0.858481\pi$
$678$	838.577	−	272.470i	1.23684	−	0.401874i
$679$	692.118	+	224.883i	1.01932	+	0.331197i
$680$		0			0
$681$			1550.95i			2.27746i
$682$	−313.156	+	157.997i	−0.459173	+	0.231667i
$683$	979.967			1.43480			0.717399	−	0.696662i	$-0.245332\pi$
$683$	979.967			1.43480			0.717399	+	0.696662i	$0.245332\pi$
$684$	−190.050	+	261.581i	−0.277851	+	0.382428i
$685$		0			0
$686$	−253.473	−	780.110i	−0.369494	−	1.13719i
$687$	−448.689	+	325.992i	−0.653113	+	0.474515i
$688$	−174.058	−	239.570i	−0.252991	−	0.348212i
$689$	−728.806	+	236.804i	−1.05777	+	0.343692i
$690$		0			0
$691$	537.473	+	390.497i	0.777818	+	0.565118i	0.904323	−	0.426848i	$-0.140376\pi$
$691$	537.473	+	390.497i	0.777818	+	0.565118i	−0.126505	+	0.991966i	$0.540376\pi$
$692$			613.222i			0.886160i
$693$	−612.397	−	99.4899i	−0.883690	−	0.143564i
$694$	526.217			0.758237
$695$		0			0
$696$	−204.912	+	630.654i	−0.294413	+	0.906111i
$697$	−418.992	−	1289.52i	−0.601136	−	1.85011i
$698$	−430.113	+	312.496i	−0.616208	+	0.447702i
$699$	−438.695	−	603.812i	−0.627604	−	0.863823i
$700$		0			0
$701$	−984.515	−	319.888i	−1.40444	−	0.456332i	−0.493819	−	0.869565i	$-0.664399\pi$
$701$	−984.515	−	319.888i	−1.40444	−	0.456332i	−0.910625	+	0.413233i	$0.864399\pi$
$702$	−279.692	−	203.208i	−0.398422	−	0.289470i
$703$			171.103i			0.243390i
$704$	970.772	+	499.501i	1.37894	+	0.709519i
$705$		0			0
$706$	894.622	−	1231.34i	1.26717	−	1.74411i
$707$	−268.636	+	826.777i	−0.379966	+	1.16942i
$708$	−400.813	−	1233.57i	−0.566120	−	1.74234i
$709$	996.643	−	724.104i	1.40570	−	1.02130i	0.411773	−	0.911287i	$-0.364910\pi$
$709$	996.643	−	724.104i	1.40570	−	1.02130i	0.993930	−	0.110016i	$-0.0350903\pi$
$710$		0			0
$711$	−228.475	+	74.2361i	−0.321344	+	0.104411i
$712$	551.336	+	179.140i	0.774348	+	0.251601i
$713$	212.751	+	154.572i	0.298388	+	0.216792i
$714$		−	2408.26i		−	3.37292i
$715$		0			0
$716$	1140.98			1.59354
$717$	−410.132	+	564.498i	−0.572011	+	0.787305i
$718$	146.418	−	450.629i	0.203925	−	0.627617i
$719$	229.638	+	706.754i	0.319385	+	0.982967i	0.973912	+	0.226928i	$0.0728682\pi$
$719$	229.638	+	706.754i	0.319385	+	0.982967i	−0.654526	+	0.756039i	$0.727132\pi$
$720$		0			0
$721$	−90.8009	−	124.977i	−0.125937	−	0.173338i
$722$	−848.112	+	275.568i	−1.17467	+	0.381673i
$723$	−872.338	−	283.440i	−1.20655	−	0.392033i
$724$	354.092	+	257.263i	0.489077	+	0.355336i
$725$		0			0
$726$	−1198.12	−	885.113i	−1.65030	−	1.21916i
$727$	10.4678			0.0143987			0.00719934	−	0.999974i	$-0.497708\pi$
$727$	10.4678			0.0143987			0.00719934	+	0.999974i	$0.497708\pi$
$728$	301.299	−	414.703i	0.413873	−	0.569647i
$729$	−116.499	+	358.548i	−0.159807	+	0.491836i
$730$		0			0
$731$	−732.148	+	531.937i	−1.00157	+	0.727683i
$732$	−472.433	−	650.249i	−0.645401	−	0.888318i
$733$	−961.151	+	312.297i	−1.31126	+	0.426053i	−0.879484	−	0.475929i	$-0.842112\pi$
$733$	−961.151	+	312.297i	−1.31126	+	0.426053i	−0.431773	+	0.901982i	$0.642112\pi$
$734$	543.530	+	176.604i	0.740504	+	0.240604i
$735$		0			0
$736$		−	1080.59i		−	1.46819i
$737$	193.723	−	29.8942i	0.262854	−	0.0405621i
$738$	−1203.16			−1.63030
$739$	−339.077	+	466.699i	−0.458832	+	0.631528i	−0.974266	−	0.225401i	$-0.927631\pi$
$739$	−339.077	+	466.699i	−0.458832	+	0.631528i	0.515434	+	0.856929i	$0.327631\pi$
$740$		0			0
$741$	−146.502	−	450.888i	−0.197709	−	0.608485i
$742$	1094.91	−	795.498i	1.47562	−	1.07210i
$743$	−677.947	−	933.113i	−0.912445	−	1.25587i	−0.966325	−	0.257325i	$-0.917159\pi$
$743$	−677.947	−	933.113i	−0.912445	−	1.25587i	0.0538800	−	0.998547i	$-0.482841\pi$
$744$	−178.577	+	58.0233i	−0.240023	+	0.0779883i
$745$		0			0
$746$	669.393	+	486.342i	0.897310	+	0.651934i
$747$		−	1020.96i		−	1.36675i
$748$	668.632	−	1299.47i	0.893893	−	1.73727i
$749$	−775.659			−1.03559
$750$		0			0
$751$	447.403	−	1376.97i	0.595743	−	1.83351i	0.0447527	−	0.998998i	$-0.485750\pi$
$751$	447.403	−	1376.97i	0.595743	−	1.83351i	0.550991	−	0.834511i	$-0.314250\pi$
$752$	209.911	+	646.041i	0.279137	+	0.859097i
$753$	342.912	−	249.140i	0.455394	−	0.330863i
$754$	−929.402	−	1279.21i	−1.23263	−	1.69657i
$755$		0			0
$756$	335.469	+	109.000i	0.443742	+	0.144181i
$757$	427.516	+	310.608i	0.564750	+	0.410315i	0.833194	−	0.552980i	$-0.186510\pi$
$757$	427.516	+	310.608i	0.564750	+	0.410315i	−0.268444	+	0.963295i	$0.586510\pi$
$758$		−	927.982i		−	1.22425i
$759$	−179.088	+	1102.35i	−0.235953	+	1.45238i
$760$		0			0
$761$	128.577	−	176.972i	0.168958	−	0.232551i	−0.716138	−	0.697958i	$-0.754092\pi$
$761$	128.577	−	176.972i	0.168958	−	0.232551i	0.885097	+	0.465407i	$0.154092\pi$
$762$	102.551	−	315.620i	0.134581	−	0.414199i
$763$	−52.4853	−	161.533i	−0.0687881	−	0.211708i
$764$	−386.010	+	280.453i	−0.505249	+	0.367085i
$765$		0			0
$766$	−1425.11	+	463.048i	−1.86046	+	0.604501i
$767$	791.329	+	257.118i	1.03172	+	0.335226i
$768$	61.4853	+	44.6717i	0.0800590	+	0.0581662i
$769$		−	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
$772$	−604.823	+	832.468i	−0.783450	+	1.07833i
$773$	−100.881	+	310.480i	−0.130506	+	0.401656i	−0.994864	−	0.101221i	$-0.967725\pi$
$773$	−100.881	+	310.480i	−0.130506	+	0.401656i	0.864358	+	0.502877i	$0.167725\pi$
$774$	248.156	+	763.745i	0.320615	+	0.986751i
$775$		0			0
$776$	240.528	+	331.058i	0.309959	+	0.426621i
$777$	−621.341	+	201.886i	−0.799667	+	0.259828i
$778$	1118.44	+	363.404i	1.43759	+	0.467100i
$779$	381.376	+	277.086i	0.489572	+	0.355695i
$780$		0			0
$781$	45.4458	−	45.0861i	0.0581893	−	0.0577287i
$782$	−1896.58			−2.42529
$783$	172.053	−	236.810i	0.219735	−	0.302439i
$784$	39.0896	−	120.305i	0.0498592	−	0.153451i
$785$		0			0
$786$	−884.604	+	642.702i	−1.12545	+	0.817687i
$787$	−227.621	−	313.294i	−0.289226	−	0.398086i	0.639536	−	0.768761i	$-0.279126\pi$
$787$	−227.621	−	313.294i	−0.289226	−	0.398086i	−0.928763	+	0.370675i	$0.879126\pi$
$788$	54.6906	−	17.7701i	0.0694043	−	0.0225508i
$789$	−1104.54	−	358.888i	−1.39993	−	0.454865i
$790$		0			0
$791$		−	577.101i		−	0.729585i
$792$	−245.706	−	247.666i	−0.310234	−	0.312710i
$793$	515.601			0.650190
$794$	−1208.65	+	1663.56i	−1.52222	+	2.09516i
$795$		0			0
$796$	−14.0488	−	43.2377i	−0.0176492	−	0.0543187i
$797$	−17.7812	+	12.9188i	−0.0223101	+	0.0162092i	−0.598884	−	0.800835i	$-0.704389\pi$
$797$	−17.7812	+	12.9188i	−0.0223101	+	0.0162092i	0.576574	+	0.817045i	$0.304389\pi$
$798$	492.148	+	677.383i	0.616727	+	0.848851i
$799$	1974.36	−	641.509i	2.47104	−	0.802890i
$800$		0			0
$801$	724.592	+	526.447i	0.904609	+	0.657237i
$802$			1108.17i			1.38176i
$803$	502.533	−	253.543i	0.625819	−	0.315745i
$804$	390.046			0.485132
$805$		0			0
$806$	138.358	−	425.821i	0.171660	−	0.528314i
$807$	−408.879	−	1258.40i	−0.506666	−	1.55936i
$808$	−395.469	+	287.325i	−0.489442	+	0.355600i
$809$	599.477	+	825.109i	0.741010	+	1.01991i	0.998560	+	0.0536476i	$0.0170848\pi$
$809$	599.477	+	825.109i	0.741010	+	1.01991i	−0.257550	+	0.966265i	$0.582915\pi$
$810$		0			0
$811$	−940.701	−	305.652i	−1.15993	−	0.376883i	−0.335053	−	0.942199i	$-0.608754\pi$
$811$	−940.701	−	305.652i	−1.15993	−	0.376883i	−0.824875	+	0.565316i	$0.808754\pi$
$812$	1305.17	+	948.260i	1.60735	+	1.16781i
$813$		−	869.183i		−	1.06911i
$814$	−677.368	−	110.045i	−0.832147	−	0.135190i
$815$		0			0
$816$	−453.475	+	624.155i	−0.555729	+	0.764896i
$817$	97.2291	−	299.240i	0.119007	−	0.366267i
$818$	34.4392	+	105.993i	0.0421018	+	0.129576i
$819$	640.713	−	465.505i	0.782311	−	0.568382i
$820$		0			0
$821$	−729.758	+	237.113i	−0.888864	+	0.288810i	−0.717633	−	0.696421i	$-0.754775\pi$
$821$	−729.758	+	237.113i	−0.888864	+	0.288810i	−0.171231	+	0.985231i	$0.554775\pi$
$822$	1405.79	+	456.769i	1.71021	+	0.555680i
$823$	674.965	+	490.391i	0.820128	+	0.595858i	0.916749	−	0.399463i	$-0.130804\pi$
$823$	674.965	+	490.391i	0.820128	+	0.595858i	−0.0966212	+	0.995321i	$0.530804\pi$
$824$		−	86.8648i		−	0.105418i
$825$		0			0
$826$	−1469.49			−1.77904
$827$	329.248	−	453.171i	0.398123	−	0.547970i	−0.562148	−	0.827036i	$-0.690025\pi$
$827$	329.248	−	453.171i	0.398123	−	0.547970i	0.960272	+	0.279067i	$0.0900250\pi$
$828$	−300.443	+	924.669i	−0.362854	+	1.11675i
$829$	−371.006	−	1141.84i	−0.447534	−	1.37737i	−0.879681	−	0.475565i	$-0.842244\pi$
$829$	−371.006	−	1141.84i	−0.447534	−	1.37737i	0.432147	−	0.901803i	$-0.357756\pi$
$830$		0			0
$831$	−1054.79	−	1451.80i	−1.26931	−	1.74705i
$832$	−1325.38	+	430.643i	−1.59301	+	0.517600i
$833$	−367.664	−	119.461i	−0.441374	−	0.143411i
$834$	−35.0294	−	25.4504i	−0.0420017	−	0.0305160i
$835$		0			0
$836$	77.4888	+	502.149i	0.0926899	+	0.600657i
$837$	82.8854			0.0990268
$838$	−766.196	+	1054.58i	−0.914315	+	1.25845i
$839$	162.370	−	499.723i	0.193528	−	0.595618i	−0.806463	−	0.591285i	$-0.798621\pi$
$839$	162.370	−	499.723i	0.193528	−	0.595618i	0.999991	−	0.00433286i	$-0.00137920\pi$
$840$		0			0
$841$	402.703	−	292.581i	0.478838	−	0.347896i
$842$	−1236.91	−	1702.45i	−1.46901	−	2.02192i
$843$	356.393	−	115.799i	0.422768	−	0.137366i
$844$	398.695	+	129.544i	0.472387	+	0.153488i
$845$		0			0
$846$		−	1842.14i		−	2.17746i
$847$	−793.284	+	566.779i	−0.936581	+	0.669160i
$848$	−433.562			−0.511276
$849$	687.259	−	945.930i	0.809492	−	1.11417i
$850$		0			0
$851$	158.991	+	489.324i	0.186828	+	0.574998i
$852$	103.056	−	74.8744i	0.120957	−	0.0878807i
$853$	−563.318	−	775.340i	−0.660396	−	0.908957i	0.339099	−	0.940751i	$-0.389878\pi$
$853$	−563.318	−	775.340i	−0.660396	−	0.908957i	−0.999494	+	0.0317938i	$0.989878\pi$
$854$	−866.033	+	281.391i	−1.01409	+	0.329498i
$855$		0			0
$856$	−352.859	−	256.367i	−0.412219	−	0.299494i
$857$			56.2536i			0.0656402i	0.999461	+	0.0328201i	$0.0104488\pi$
$857$			56.2536i			0.0656402i	−0.999461	+	0.0328201i	$0.989551\pi$
$858$	1879.21	−	289.988i	2.19022	−	0.337982i
$859$	−1517.29			−1.76634			−0.883171	−	0.469051i	$-0.844596\pi$
$859$	−1517.29			−1.76634			−0.883171	+	0.469051i	$0.844596\pi$
$860$		0			0
$861$	−556.217	+	1711.86i	−0.646012	+	1.98822i
$862$	−122.753	−	377.794i	−0.142405	−	0.438276i
$863$	−887.101	+	644.517i	−1.02793	+	0.746833i	−0.967893	−	0.251363i	$-0.919121\pi$
$863$	−887.101	+	644.517i	−1.02793	+	0.746833i	−0.0600344	+	0.998196i	$0.519121\pi$
$864$	−200.190	−	275.538i	−0.231702	−	0.318910i
$865$		0			0
$866$	1613.88	+	524.382i	1.86360	+	0.605522i
$867$	972.253	+	706.383i	1.12140	+	0.814744i
$868$			456.819i			0.526289i
$869$	−172.721	+	335.680i	−0.198758	+	0.386283i
$870$		0			0
$871$	−147.071	+	202.426i	−0.168853	+	0.232406i
$872$	29.5128	−	90.8310i	0.0338449	−	0.104164i
$873$	195.369	+	601.283i	0.223790	+	0.688755i
$874$	533.458	−	387.580i	0.610364	−	0.443456i
$875$		0			0
$876$	1065.22	−	346.111i	1.21600	−	0.395104i
$877$	1081.62	+	351.441i	1.23332	+	0.400731i	0.851917	−	0.523677i	$-0.175440\pi$
$877$	1081.62	+	351.441i	1.23332	+	0.400731i	0.381405	+	0.924408i	$0.375440\pi$
$878$	1171.70	+	851.293i	1.33451	+	0.969582i
$879$			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	$0.339593\pi$
$882$	−201.635	+	277.526i	−0.228611	+	0.314656i
$883$	−157.572	+	484.958i	−0.178451	+	0.549216i	−0.999774	−	0.0212471i	$-0.993236\pi$
$883$	−157.572	+	484.958i	−0.178451	+	0.549216i	0.821323	+	0.570463i	$0.193236\pi$
$884$	576.459	+	1774.16i	0.652103	+	2.00697i
$885$		0			0
$886$	179.567	+	247.153i	0.202672	+	0.278954i
$887$	554.947	−	180.313i	0.625645	−	0.203284i	0.0209998	−	0.999779i	$-0.493315\pi$
$887$	554.947	−	180.313i	0.625645	−	0.203284i	0.604645	+	0.796495i	$0.293315\pi$
$888$	−349.384	−	113.522i	−0.393450	−	0.127840i
$889$	−175.724	−	127.671i	−0.197665	−	0.143612i
$890$		0			0
$891$	470.717	+	932.979i	0.528302	+	1.04711i
$892$	639.603			0.717043
$893$	−424.240	+	583.917i	−0.475073	+	0.653882i
$894$	354.971	−	1092.49i	0.397059	−	1.22202i
$895$		0			0
$896$	881.096	−	640.153i	0.983366	−	0.714457i
$897$	−837.939	−	1153.32i	−0.934157	−	1.28576i
$898$	−398.966	+	129.632i	−0.444283	+	0.144356i
$899$	360.535	+	117.145i	0.401040	+	0.130306i
$900$		0			0
$901$			1325.01i			1.47060i
$902$	−1342.22	+	1331.59i	−1.48805	+	1.47627i
$903$	1201.38			1.33043
$904$	190.741	−	262.532i	0.210996	−	0.290412i
$905$		0			0
$906$	−372.859	−	1147.54i	−0.411544	−	1.26660i
$907$	518.177	−	376.478i	0.571309	−	0.415080i	−0.264272	−	0.964448i	$-0.585132\pi$
$907$	518.177	−	376.478i	0.571309	−	0.415080i	0.835580	+	0.549368i	$0.185132\pi$
$908$	1247.14	+	1716.54i	1.37350	+	1.89046i
$909$	−718.269	+	233.380i	−0.790175	+	0.256744i
$910$		0			0
$911$	885.922	+	643.660i	0.972472	+	0.706542i	0.956014	−	0.293322i	$-0.0947609\pi$
$911$	885.922	+	643.660i	0.972472	+	0.706542i	0.0164582	+	0.999865i	$0.494761\pi$
$912$		−	268.230i		−	0.294112i
$913$	−1129.94	−	1138.96i	−1.23762	−	1.24749i
$914$	94.7802			0.103698
$915$		0			0
$916$	−234.459	+	721.591i	−0.255960	+	0.787763i
$917$	221.151	+	680.633i	0.241168	+	0.742238i
$918$	−483.607	+	351.361i	−0.526805	+	0.382746i
$919$	−729.402	−	1003.94i	−0.793691	−	1.09242i	−0.993639	−	0.112615i	$-0.964077\pi$
$919$	−729.402	−	1003.94i	−0.793691	−	1.09242i	0.199948	−	0.979807i	$-0.435923\pi$
$920$		0			0
$921$	687.902	+	223.513i	0.746908	+	0.242685i
$922$	355.190	+	258.061i	0.385239	+	0.279893i
$923$			81.7158i			0.0885328i
$924$	−1732.07	+	873.881i	−1.87453	+	0.945759i
$925$		0			0
$926$	−887.982	+	1222.20i	−0.958943	+	1.31987i
$927$	41.4718	−	127.637i	0.0447376	−	0.137688i
$928$	−481.359	−	1481.47i	−0.518706	−	1.59641i
$929$	−834.947	+	606.624i	−0.898758	+	0.652986i	−0.938147	−	0.346238i	$-0.887459\pi$
$929$	−834.947	+	606.624i	−0.898758	+	0.652986i	0.0393884	+	0.999224i	$0.487459\pi$
$930$		0			0
$931$	127.828	−	41.5337i	0.137301	−	0.0446119i
$932$	−971.063	−	315.517i	−1.04191	−	0.338538i
$933$	1207.57	+	877.354i	1.29429	+	0.940358i
$934$			2332.68i			2.49752i
$935$		0			0
$936$	445.326			0.475776
$937$	−180.209	+	248.036i	−0.192325	+	0.264713i	−0.894279	−	0.447509i	$-0.852311\pi$
$937$	−180.209	+	248.036i	−0.192325	+	0.264713i	0.701954	+	0.712222i	$0.252311\pi$
$938$	136.554	−	420.271i	0.145580	−	0.448050i
$939$	−392.283	−	1207.32i	−0.417767	−	1.28575i
$940$		0			0
$941$	11.2167	+	15.4385i	0.0119200	+	0.0164064i	0.814935	−	0.579552i	$-0.196772\pi$
$941$	11.2167	+	15.4385i	0.0119200	+	0.0164064i	−0.803015	+	0.595958i	$0.796772\pi$
$942$	−2016.82	+	655.306i	−2.14100	+	0.695654i
$943$	1348.14	+	438.036i	1.42963	+	0.464514i
$944$	380.850	+	276.704i	0.403443	+	0.293118i
$945$		0			0
$946$	1122.11	+	577.369i	1.18616	+	0.610327i
$947$	804.636			0.849669			0.424834	−	0.905271i	$-0.360332\pi$
$947$	804.636			0.849669			0.424834	+	0.905271i	$0.360332\pi$
$948$	−441.540	+	607.728i	−0.465760	+	0.641063i
$949$	−222.027	+	683.330i	−0.233959	+	0.720053i
$950$		0			0
$951$	889.256	−	646.082i	0.935075	−	0.679372i
$952$	−520.967	−	717.050i	−0.547235	−	0.753204i
$953$	1763.40	−	572.962i	1.85036	−	0.601220i	0.853591	−	0.520944i	$-0.174420\pi$
$953$	1763.40	−	572.962i	1.85036	−	0.601220i	0.996773	−	0.0802758i	$-0.0255801\pi$
$954$	1118.22	+	363.330i	1.17213	+	0.380850i
$955$		0			0
$956$			954.556i			0.998489i
$957$	245.528	+	1591.09i	0.256560	+	1.66258i
$958$	−1911.11			−1.99489
$959$	568.654	−	782.686i	0.592966	−	0.816148i
$960$		0			0
$961$	−263.794	−	811.875i	−0.274500	−	0.844824i
$962$	708.687	−	514.891i	0.736681	−	0.535230i
$963$	−396.085	−	545.164i	−0.411303	−	0.566111i
$964$	−1193.39	+	387.755i	−1.23795	+	0.402236i
$965$		0			0
$966$	2036.88	+	1479.88i	2.10857	+	1.53197i
$967$			660.803i			0.683353i	0.939818	+	0.341677i	$0.110995\pi$
$967$			660.803i			0.683353i	−0.939818	+	0.341677i	$0.889005\pi$
$968$	−548.206	−	4.35630i	−0.566328	−	0.00450031i
$969$	−819.737			−0.845962
$970$		0			0
$971$	−166.517	+	512.487i	−0.171490	+	0.527793i	−0.999456	−	0.0329859i	$-0.989498\pi$
$971$	−166.517	+	512.487i	−0.171490	+	0.527793i	0.827965	+	0.560779i	$0.189498\pi$
$972$	520.823	+	1602.93i	0.535826	+	1.64910i
$973$	−22.9271	+	16.6575i	−0.0235633	+	0.0171197i
$974$	−712.232	−	980.303i	−0.731244	−	1.00647i
$975$		0			0
$976$	277.438	+	90.1450i	0.284260	+	0.0923617i
$977$	−243.828	−	177.151i	−0.249568	−	0.181322i	0.455967	−	0.889996i	$-0.349293\pi$
$977$	−243.828	−	177.151i	−0.249568	−	0.181322i	−0.705535	+	0.708675i	$0.749293\pi$
$978$		−	3116.80i		−	3.18691i
$979$	1390.98	−	214.648i	1.42082	−	0.219252i
$980$		0			0
$981$	86.7307	−	119.375i	0.0884105	−	0.121687i
$982$	−616.943	+	1898.75i	−0.628251	+	1.93356i
$983$	238.319	+	733.472i	0.242441	+	0.746156i	0.996047	+	0.0888299i	$0.0283128\pi$
$983$	238.319	+	733.472i	0.242441	+	0.746156i	−0.753606	+	0.657327i	$0.771687\pi$
$984$	−818.827	+	594.912i	−0.832141	+	0.604586i
$985$		0			0
$986$	−2600.18	+	844.850i	−2.63710	+	0.856846i
$987$	−2620.99	−	851.611i	−2.65551	−	0.862827i
$988$	−524.707	−	381.222i	−0.531080	−	0.385852i
$989$		−	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	$0.480988\pi$
$992$	259.264	−	356.846i	0.261354	−	0.359723i
$993$	508.865	−	1566.13i	0.512453	−	1.57717i
$994$	−44.5967	−	137.255i	−0.0448659	−	0.138083i
$995$		0			0
$996$	−1876.49	−	2582.77i	−1.88403	−	2.59314i
$997$	−36.0263	+	11.7057i	−0.0361347	+	0.0117409i	−0.327029	−	0.945014i	$-0.606047\pi$
$997$	−36.0263	+	11.7057i	−0.0361347	+	0.0117409i	0.290894	+	0.956755i	$0.406047\pi$
$998$	−2098.77	−	681.931i	−2.10298	−	0.683298i
$999$	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.x.d.51.1		4
5.2	odd	4		275.3.q.c.249.2		8
5.3	odd	4		275.3.q.c.249.1		8
5.4	even	2		55.3.i.a.51.1	yes	4
11.8	odd	10	inner	275.3.x.d.151.1		4
55.8	even	20		275.3.q.c.74.2		8
55.19	odd	10		55.3.i.a.41.1	✓	4
55.39	odd	10		605.3.c.a.241.4		4
55.49	even	10		605.3.c.a.241.1		4
55.52	even	20		275.3.q.c.74.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.41.1	✓	4	55.19	odd	10
55.3.i.a.51.1	yes	4	5.4	even	2
275.3.q.c.74.1		8	55.52	even	20
275.3.q.c.74.2		8	55.8	even	20
275.3.q.c.249.1		8	5.3	odd	4
275.3.q.c.249.2		8	5.2	odd	4
275.3.x.d.51.1		4	1.1	even	1	trivial
275.3.x.d.151.1		4	11.8	odd	10	inner
605.3.c.a.241.1		4	55.49	even	10
605.3.c.a.241.4		4	55.39	odd	10

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.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 - 2.48990i) q^{2} +(1.23607 - 3.80423i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-7.23607 - 9.95959i) q^{6} +(-7.66312 + 2.48990i) q^{7} +(-4.30902 - 1.40008i) q^{8} +(-5.66312 - 4.11450i) q^{9} +(-10.8713 + 1.67760i) q^{11} -21.8885 q^{12} +(8.25329 - 11.3597i) q^{13} +(-7.66312 + 23.5847i) q^{14} +(6.42705 - 4.66953i) q^{16} +(-14.2705 - 19.6417i) q^{17} +(-20.4894 + 6.65740i) q^{18} +(8.02786 + 2.60841i) q^{19} +32.2299i q^{21} +(-15.4894 + 30.1033i) q^{22} +25.3820 q^{23} +(-10.6525 + 14.6619i) q^{24} +(-13.3541 - 41.0997i) q^{26} +(6.47214 - 4.70228i) q^{27} +(25.9164 + 35.6709i) q^{28} +(34.7984 - 11.3067i) q^{29} +(8.38197 + 6.08985i) q^{31} -42.5730i q^{32} +(-7.05573 + 43.4306i) q^{33} -74.7214 q^{34} +(-11.8369 + 36.4302i) q^{36} +(6.26393 + 19.2784i) q^{37} +(21.0172 - 15.2699i) q^{38} +(-33.0132 - 45.4387i) q^{39} +(53.1140 + 17.2578i) q^{41} +(80.2492 + 58.3045i) q^{42} -37.2752i q^{43} +(27.1140 + 53.7409i) q^{44} +(45.9164 - 63.1985i) q^{46} +(-26.4230 + 81.3216i) q^{47} +(-9.81966 - 30.2218i) q^{48} +(12.8820 - 9.35930i) q^{49} +(-92.3607 + 30.0098i) q^{51} +(-73.0755 - 23.7437i) q^{52} +(-44.1525 - 32.0787i) q^{53} -24.6215i q^{54} +36.5066 q^{56} +(19.8460 - 27.3156i) q^{57} +(34.7984 - 107.098i) q^{58} +(18.3115 + 56.3571i) q^{59} +(21.5836 + 29.7073i) q^{61} +(30.3262 - 9.85359i) q^{62} +(53.6418 + 17.4293i) q^{63} +(-80.2943 - 58.3372i) q^{64} +(95.3738 + 96.1347i) q^{66} -17.8197 q^{67} +(-78.0902 + 107.482i) q^{68} +(31.3738 - 96.5587i) q^{69} +(-4.70820 + 3.42071i) q^{71} +(18.6418 + 25.6583i) q^{72} +(-48.6656 + 15.8124i) q^{73} +(59.3328 + 19.2784i) q^{74} -46.1903i q^{76} +(79.1312 - 39.9241i) q^{77} -172.859 q^{78} +(20.1722 - 27.7647i) q^{79} +(-29.3566 - 90.3504i) q^{81} +(139.054 - 101.029i) q^{82} +(85.7295 + 117.997i) q^{83} +(167.735 - 54.5002i) q^{84} +(-92.8115 - 67.4315i) q^{86} -146.357i q^{87} +(49.1935 + 7.99197i) q^{88} -127.949 q^{89} +(-34.9615 + 107.600i) q^{91} +(-42.9205 - 132.096i) q^{92} +(33.5279 - 24.3594i) q^{93} +(154.683 + 212.903i) q^{94} +(-161.957 - 52.6232i) q^{96} +(-73.0689 - 53.0877i) q^{97} -49.0059i q^{98} +(68.4681 + 35.2296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 4 q^{3} - 9 q^{4} - 20 q^{6} - 15 q^{7} - 15 q^{8} - 7 q^{9} - q^{11} - 16 q^{12} - 5 q^{13} - 15 q^{14} + 19 q^{16} + 10 q^{17} - 35 q^{18} + 50 q^{19} - 15 q^{22} + 106 q^{23} + 20 q^{24}+ \cdots + 133 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - 4 * q^3 - 9 * q^4 - 20 * q^6 - 15 * q^7 - 15 * q^8 - 7 * q^9 - q^11 - 16 * q^12 - 5 * q^13 - 15 * q^14 + 19 * q^16 + 10 * q^17 - 35 * q^18 + 50 * q^19 - 15 * q^22 + 106 * q^23 + 20 * q^24 - 40 * q^26 + 8 * q^27 + 50 * q^28 + 90 * q^29 + 38 * q^31 - 64 * q^33 - 120 * q^34 - 63 * q^36 + 34 * q^37 + 55 * q^38 + 20 * q^39 + 85 * q^41 + 160 * q^42 - 19 * q^44 + 130 * q^46 + 24 * q^47 - 84 * q^48 + 56 * q^49 - 280 * q^51 - 100 * q^52 - 114 * q^53 + 70 * q^56 - 180 * q^57 + 90 * q^58 - 128 * q^59 + 140 * q^61 + 90 * q^62 + 105 * q^63 - 149 * q^64 + 140 * q^66 - 116 * q^67 - 290 * q^68 - 116 * q^69 + 8 * q^71 - 35 * q^72 + 20 * q^73 + 130 * q^74 + 160 * q^77 - 280 * q^78 - 210 * q^79 + 95 * q^81 + 270 * q^82 + 410 * q^83 + 340 * q^84 - 170 * q^86 - 78 * q^89 - 75 * q^91 - 241 * q^92 + 152 * q^93 + 375 * q^94 - 460 * q^96 - 176 * q^97 + 133 * q^99

Introduction

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